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Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics. These simple models are used in the optimization of real (irreversible) devices and processes, subject to finite‐size and finite‐time constraints. The review traces the development and adoption of the method in several sectors of mainstream thermal engineering and science: cryogenics, heat transfer, education, storage systems, solar power plants, nuclear and fossil power plants, and refrigerators. Emphasis is placed on the fundamental and technological importance of the optimization method and its results, the pedagogical merits of the method, and the chronological development of the field. © 1996 American Institute of Physics.

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... In the advance thermodynamics texts, like that of Bejan [18][19][20][21], the generation of entropy has been formulated using the equation Eq. 9. ...

... Adrian Bejan [18][19][20][21], presented the idea of minimizing entropy-generation-rate with the perspective of heat transfer and fluid dynamics. In the case of devices involving heat transfer, a trade-off lies between heat transfer irreversibility. ...

... Bejan [18][19][20][21] mentions a curve for entropy generation ratio vs. Reynolds number and specifies a point where minimum entropy is generated. The optimum point is at a location where the irreversibility due to heat and friction becomes equal. ...

In this chapter, the thermal enhancement factor is examined numerically based on D-optimal design and then the entropy analysis is done on the optimized geometry. Optimization is now a frequently used tool in engineering design. Under a certain set of variables and constraints, optimization is usually done by defining a function of an output variable and thereby determining its maximum or minimum or say, the optimized point. Efforts are being made to enhance the inner tube, shell, or plate design in heat exchangers as well, where much study is being done to maximise efficiency. The surface improvement has been actively investigated in this regard in recent decades. This sort of augmentation is usually dominant on the tube side. In this paper, with the optimization in view, the design is based on interdisciplinary fields. That is, first a numerical study is performed on the helically grooved tubes to examine the thermal enhancement factor. By comparing the entropy-generation rates of the smooth and grooved tubes, this analysis was conducted. The optimum Reynolds number for that tube is the one at which the lowest entropy-generation-rate is reached. Numerical results are initially validated with published experimental results. The chosen optimised tube is next subjected to an entropy minimization analysis including the Reynolds number based on the D-optimal design for the thermal enhancement factor. The tube that has the most grooves, the most depth, and the smallest pitch exhibits the best performance. However, the optimum Reynolds number is at the point where the tube has the least entropy generated as compared to the smooth tube.

... Entropy can only occur in one of three circumstances: case I: (Ns = 0) for reversible processes, case II: (Ns < 0) for irreversible processes, and case III: (Ns > 0) no entropy estimation is possible. For an isolated system, the entropy may be taken as Ns ≥ 0. The second law of thermodynamics is applied, as the amount of accessible work is directly proportional to the amount of entropy generated [1]. As a result, a thermal device that produces less entropy due to irreversibility consumes less energy. ...

... A nanoparticle's volumetric rate of local entropy generation is written in terms of thermal transport, viscous dissipation, diffusive irreversibility, and a magnetic field. In vector notation, the entropy rate can be expressed as follows [1,14]: ...

... Bejan [1] established the irreversibility distribution ratio as ∆ = N V + N D + N M /N T to determine whether fluid friction exceeds heat-transfer irreversibility or conversely. When 0 ≤ ∆ < 1, heat transmission uplifts, and when ∆ > 1, fluid friction rises. ...

... This can be achieved by modifying the design or adjusting the operating conditions to reduce entropy production and improve system performance. For these and other reasons, the study of entropy production in thermal systems is essential to improve their efficiency, optimize their design and operation, and promote sustainable development [25][26][27]. ...

... In the context of the dimensionless system [53], the formulation of the local total entropy (N s ) is given by: (22) where N s−th , N s−mag , and N s− f r are the local entropies resulting from temperature gradients, magnetic field effects, and viscous dissipation, respectively. The mathematical expressions for each type of these entropies are well documented in the literature [22,23,25,26,52]. The local entropies N s−th and N s− f r are expressed by [53]: ...

The exploration of interactions between magnetic fields and thermal convection represents an extremely interesting field of research, which has captured the considerable attention of the scientific community, as evidenced by several recent publications. This investigation opens up promising horizons in diverse fields of application, such as heat exchange systems, electronic devices, plasma analysis, magnetic cell separation, power generation, and many others. In this perspective, the present paper proposes a three-dimensional numerical study of the influence of the magnetic field on free convection and entropy generation in the presence of thermal conduction. The numerical methodology adopted incorporates the finite difference technique for temperature determination and the lattice Boltzmann method for characterizing fluid flows and the magnetic field. The aim is to perform a three-dimensional numerical study of the effect of changing magnetic field intensity, Rayleigh number, and thermal conductivity on heat exchange in a differentially heated cavity divided by a conducting solid, acting as a heat exchange device. The obtained results show that the heat exchange rate is inversely proportional to the increase of the magnetic field intensity and directly proportional to the thermal conductivity and Rayleigh number. In addition, the impact of the magnetic field on entropy production in the thermal system is examined in a second step. The results reveal that increasing the Hartmann number intensifies entropy production due to magnetic influence. However, this increase simultaneously leads to a reduction in the rate of entropy production, attributable to temperature gradients, fluid friction as well as total entropy production.

... According to Bejan et al. (1996) an optimal system which a designer can develop having the least irreversibility is based on minimization of entropy generation. The application of second law analysis for studying latent heat storage was studied by Bjurstrom and Carlsson (1985) and Adebiyi and Russell (1987) and later added by Bejan (1996). A study was done by El-Dessouky and Al-Juwayhel (1997) for investigating the effect of different variables on the entropy generation number defined by Bejan et al. (1996). ...

... Exergoeconomic analysis helps in quantifying the exergy losses in terms of monetary losses. According to Bejan et al. (1996) exergoeconomics is defined as the branch of engineering that combines exergy analysis and economic principles to provide the system designer or operator with information not available through conventional energy analysis and economic evaluations, but crucial to the design and operation of a cost effective system. Application of exergoeconomic analysis can be found in the literature for processes involving heat transfer and power generation. ...

The present work discusses utilization of geothermal energy for space heating in combination with phase change energy storage system. Thermodynamics and thermoeconomics of the combined heating and thermal storing system were studied to show the scope of energy storage and cost savings. The analysis was done taking second law efficiency into consideration since the second law represents true flow of energy. The space heating is based on geothermal water that is used in a plate type heat exchanger to give heat to the secondary fluid which is passed through the radiators for room heating. Heat supply to the storage system was provided from the geothermal water at the exit of the heat exchanger. A computational model of the combined space heating and thermal storage system was developed and used to perform thermodynamic studies of the heat storage process and heating system efficiency at different times and ambient temperatures. The basis for these studies is daily variations in heating demand that is higher during the night than during the day. The results show the scope of utilization of phase change material for low ambient temperature conditions. Under proper conditions sufficient amount of exergy is stored during charging period at low ambient temperature to fulfill the day time heat load requirement. Under these conditions the cost flow rate of exergy storage is found to be lower than the radiator heating cost flow rate. Thus, the usage of exergy storage at low ambient temperature for heating at higher ambient temperature makes significant contribution in cost saving. The paper makes references too many studies on exergy analysis and thermal energy storage systems using phase change materials. 1. INTRODUCTION Space heating is one of the well-known applications of geothermal energy utilization for decades. The usage of geothermal energy for space heating provides an economical and a non-polluting way for achieving human comforts. In order to study a thermodynamic systems performance which can either involve heating or power generation, second law of thermodynamics plays an important role. The second law helps in better understanding of energy flow processes in addition to first law of thermodynamics. Exergy is the maximum theoretical useful work obtainable as the systems interact to equilibrium, heat transfer occurring with the environment only. Several studies have been conducted on exergy analysis of buildings. The concept of low exergy systems for heating and cooling have been proposed in IEA ECBCS Annex 37(2000). An exergetic life cycle assessment for resource evaluation in the built environment was conducted by Meester et al (2009). Shukuya and Komuro (1996) applied concepts of entropy and exergy for investigating relation between building, passive solar heating and environment. Various results about patterns of human exergy consumption in relation to various heating and cooling systems were given by Saito and Sukaya (2001). Conclusions about inadequacy of energy conservation concept for understanding important aspects of energy utilization processes were made by Yildiz and Gungӧr (2009). The second law analysis is important in order to have an efficient utilization of the available resource.

... The optimum design parameters were found in these optimisation experiments based on criteria such as power, power density, ecological coefficient of performance, exergy, exergy density, minimal entropy generation, and thermoeconomic goal. These studies were reviewed in detail by Durmayaz et al. (2004), Chen et al. (1999) and Bejan (1996). The Carnot heat engine model was used in a significant part of the performance optimisation study (Gutkowicz-Krusin et al., 1978;Salamon et al., 1980;Salamon and Nitzan, 1981;Rubin and Andresen, 1982;Wu, 1988aWu, , 1988bBejan, 1988;Wu and Walker, 1989;Gordon, 1989;Angulo-Brown, 1991;Goktun et al., 1993;Ait-Ali, 1995;Chen et al., 1996;Goktun, 1996;Moukalled et al., 1996). ...

... It has also been demonstrated that the energy efficiency of the endoreversible heat engine under conditions of peak power (η mp ) is a lower limit for actual heat engines. Highly intense performance optimisation experiments were conducted in order to provide more realistic comparisons for actual heat engines, based on irreversible Carnot engine model and several performance criteria (Bejan, 1996;Chen et al., 1999;Durmayaz et al., 2004). For the optimal energy efficiency (η opt ) and optimal power ( ) opt W range of real engines, as a general result of these studies are given as following η mp ≤ η opt ≤ η cc , max 0. ...

... Entropy is a measure of the molecular configuration probability of a system or the ability of a system to perform valuable work [2,3]. Significant efforts to analyze the reservoir energy lost during production processes have been made in recent years [4][5][6]. This paper focuses on the energy availability that exists in a hydrocarbon reservoir and the irreversible losses that occur during extraction processes. ...

... where k rw is the water relative permeability; k ro introduces the oil relative permeability; and λ characterizes the pore size distribution of the porous medium (ranging from 0. [2][3][4][5]. ...

The efficient use of available energy in hydrocarbon extraction processes is essential to reducing overall emissions in the petroleum industry. The inefficient design of an extraction process leads to higher emissions per unit mass of hydrocarbon recovery. Fluid friction and heat transfer are irreversible processes that are vital in decreasing the overall system’s operational efficiency. To reduce these irreversible energy losses in the petroleum reservoir production’s life, contributing factors such as the characteristic features of a reservoir formation, reservoir fluids, and production rate are investigated in this paper. This study examines irreversible energy loss in porous media and wellbore formations using entropy generation minimization at various stages of production and thermodynamic conditions, eventually achieving higher hydrocarbon recovery factors. Entropy production is used to develop predictive models that calculate reservoir and wellbore energy losses for multiphase flow. The proposed models consider oil and water as the working fluids in a porous medium and a wellbore. This paper also investigates the thermophysical effects around the wellbore by incorporating Hawkin’s model. A sensitivity analysis assessed the impact of rock and fluid properties and thermodynamic conditions such as temperature, wettability, and capillary pressure on the total entropy generation. The findings reveal that the capillary pressure significantly impacts the oil and water recovery factor and total entropy production. Additionally, the capillary pressure strongly influences the reservoir production life. The two-phase models show that as the recovery factor increases, the total entropy production decreases at lower production rates. This article helps to address the impact of irreversible processes on multiphase hydrocarbon reservoir operational efficiency. Furthermore, the results obtained from the numerical-simulation model open up a new research area for scholars to maximize the recovery factor using entropy generation minimization in heterogeneous reservoirs.

... For the dual diffusive ow specied by eqn (16), (17), and (23) under the wall and free stream boundary conditions (20), (21), and (24), the converted nonlinear ODE boundary value problem is a coupled multi-degree system of the seventh order. Because of the signicant nonlinearity, a numerical solution is required. ...

In various thermodynamic procedures and the optimisation of thermal manipulation, nanofluids flowing through porous media represent an emerging perspective. The main objective of this study, from the perspective of thermal applications, was the investigation of the flow of nanofluid over a horizontal stretched surface embedded in a porous medium. The effects of the chemical reactions on the surface, magnetic field, and thermal radiations were invoked in the mathematical formulation. The non-Darcy model examines the fluid flow in the porous media. The principles of thermodynamics were employed to integrate entropy optimisation methods with the established theoretical approach to analyse the thermal behaviour of nanomaterials in the chemical reactive diffusion processes. Using the Tiwari-Das nanofluid model, the volume fraction of the nanomaterials was merged in the mathematical equation for the flow model. Water was taken as a base fluid and nanoparticles composed of aluminium oxide (Al 2 O 3) and silver (Ag) were used. The significance of radiation, heat production, and ohmic heating were included in the energy equation. Furthermore, an innovative mathematical model for the diffusion of the autocatalytic reactive species in the boundary layer flow was developed for a linear horizontally stretched surface embedded in a homogeneous non-Darcy porous medium saturated with the nanofluid. The computer-based built-in bvp5c method was used to compute numerically these equations for varied parameters. It is clear that the magnetic parameter has a reversal influence on the entropy rate and velocity. Temperature and velocity are affected in the opposite direction from a higher volume fraction estimate. Thermal field and entropy were increased when the radiation action intensified. The inclusion of nanoparticle fraction by the volume fraction of nanoparticles and Brinkman number also enhances the system entropy. Entropy production can be minimized with the involvement of the porosity factor within the surface.

... This represents one step in a free energy conversion sequence, starting with an atmospheric heat engine performing the work to lift water and with the minimization of frictional dissipation being synonymous with the maximum power transfer to sediment transport along this conversion sequence. Similarly, power plants are engineered to minimize the internal loss by entropy production, referred to as "entropy generation minimization" as a design objective (Bejan, 1996(Bejan, , 1997. ...

Optimality concepts related to energy and entropy have long been proposed to govern Earth system processes, for instance in the form of propositions that certain processes maximize or minimize entropy production. These concepts, however, remain quite obscure, seem contradictory to each other, and have so far been mostly disregarded. This review aims to clarify the role of thermodynamics and optimality in Earth system science by showing that they play a central role in how, and how much, work can be derived from solar forcing and that this imposes a major constraint on the dynamics of dissipative structures of the Earth system. This is, however, not as simple as it may sound. It requires a consistent formulation of Earth system processes in thermodynamic terms, including their linkages and interactions. Thermodynamics then constrains the ability of the Earth system to derive work and generate free energy from solar radiative forcing, which limits the ability to maintain motion, mass transport, geochemical cycling, and biotic activity. It thus limits directly the generation of atmospheric motion and other processes indirectly through their need for transport. I demonstrate the application of this thermodynamic Earth system view by deriving first-order estimates associated with atmospheric motion, hydrologic cycling, and terrestrial productivity that agree very well with observations. This supports the notion that the emergent simplicity and predictability inherent in observed climatological variations can be attributed to these processes working as hard as they can, reflecting thermodynamic limits directly or indirectly. I discuss how this thermodynamic interpretation is consistent with established theoretical concepts in the respective disciplines, interpret other optimality concepts in light of this thermodynamic Earth system view, and describe its utility for Earth system science.

... Considering the maximum high temperature as the exergetically equivalent temperature, then the cycle efficiency can be written as below, according to Bejan [9]: ...

Power plants constitute the main sources of electricity production, and the calculation of their efficiency is a critical factor that is needed in energy studies. The efficiency improvement of power plants through the optimization of the cycle is a critical means of reducing fuel consumption and leading to more sustainable designs. The goal of the present work is the development of semi-empirical models for estimating the thermodynamic efficiency of power cycles. The developed model uses only the lower and the high operating temperature levels, which makes it flexible and easily applicable. The final expression is found by using the literature data for different power cycles, named as: organic Rankine cycles, water-steam Rankine cycles, gas turbines, combined cycles and Stirling engines. According to the results, the real operation of the different cases was found to be a bit lower compared to the respective endoreversible cycle. Specifically, the present global model indicates that the thermodynamic efficiency is a function of the temperature ratio (low cycle temperature to high cycle temperature). The suggested equation can be exploited as a quick and accurate tool for calculating the thermodynamic efficiency of power plants by using the operating temperature levels. Moreover, separate equations are provided for all of the examined thermodynamic cycles.

... a well-known result, also known as the Gouy-Stodola theorem, in classical thermodynamics for the dissipated work; see for example [33,233,234]. Comparing with Equation (356a) derived in the MNEQT, it becomes clear that the above theorem is valid only when the system and the medium have the same temperature to ensure no macroheat exchange, similar to the conditions imposed by Count Rumford. But his observations leave out the situation of a possible heat exchange, so it is not clear what is meant by macroheat converting into macrowork in his statement. ...

The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (μNEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates mk in an extended state space in which macrostates (obtained by ensemble averaging A^) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals dα=(d,de,di) operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by A^dαq, but the stochastic quantities C^αq like macroheat emerge from the commutator C^α of dα and A^. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities deqk such as exchange microwork and microheat become nonfluctuating over mk as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dqk and diqk are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity diQ≡diW≥0 with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The μNEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest.

... Entropy optimization in thermally convection ow was studied in Bejan. [29][30][31] Iikhar et al. 32 analyzed entropy generation for non-Newtonian biviscosity uid in a square cavity. Hayat et al. 33 addressed the magnetized entropy optimized ow of the Reiner-Rivlin material. ...

Here hydromagnetic entropy optimized flow of hybrid ( ) nanoliquid by a curved stretchable surface is addressed. Darcy- Forchheimer model is utilized for porous space. Lead ( ) and ferric...

... Additionally, exergy analysis can be used to assess the efficiency of ion transport processes, such as ion pumps and channels, by quantifying the inputs and outputs of these processes from an energetic point of view [5]. By quantifying the energy inputs, outputs, and losses in cellular processes, exergy analysis could be utilized for assessing the efficiency of various metabolic pathways [6]. The late mentioned method provides a valuable framework for the optimization of cellular processes, by identifying areas for improvement in energy and matter exchange. ...

... They demonstrated that at this maximum power point (MPP), the efficiency is equal to the so called 'nice radical efficiency ' . De Vos [5] and Bejan [6] extended the Finite-Time Thermodynamics (FTT) to the Finite-Size or Finite-Dimension Thermodynamics (FDT) [7], [8]. The main difference is that the energy and entropy balances are here applied to the power plant itself, operating in a steady state, and not to the working fluid evolving in time over a cycle as done in FTT studies. ...

... In fact the development in research has found the point that even if energy being preserved but the quality of energy will be lost when it is entropy generated. Entropy generation is very important in the process for the conversion of heat transportation, solar and storage thermal power, solar collectors, heat exchanger, chemical vapor deposition devices etc. Bejan [8] made fundamental contribution in this direction. Dissipation and entropy generation in Cross fluid flow are addressed by Khan and Ali [9] Entropy in MHD peristaltic flow of nanomaterial is due to Rashidi et al. [10]. ...

Mixed convection in dissipative entropy optimized stagnation point flow of nanomaterial towards stretching Riga sheet is addressed. Brownian and thermophoresis diffusions for nanomaterial are accounted. Constitutive relations for Jeffrey material are utilized. Non-similar solutions for the governing differential systems are developed. OHAM is employed for the convergent series solutions development. Outcomes of pertinent variables on flow quantities of interest are graphically organized. Finally the concluding remarks are arranged.

... So, to combat these losses, researchers looked at entropy production to gauge the thermal system's effectiveness. The investigation of entropy formation and its mitigation techniques was first done by Bejan [19] and [20]. The theoretical and computational contributions to entropy formation resulting from nanofluid flow and heat transfer in various geometries and flow regimes were given by Mahian et al [21]. ...

Wall stresses play a critical role in fluid dynamics and understanding their impact can lead to significant improvements in system performance and efficiency. This article presents a study on the impact of the Reynolds number and magnetic number on wall stresses, energy transport, and thermodynamic irreversibility analysis in axisymmetric flow near the stagnation region. We consider a hybrid nanofluid flow containing titania and silica nanoparticles, using Yamada-Ota and Xue thermal conductivity models. The flow is driven by a cylinder rotating along the z-direction with solar radiation and a magnetic field. To formulate the problem, we use similarity transformation to obtain dimensionless ordinary differential equations and obtain numerical solutions with graphical illustrations by bvp5c in Matlab. The comparison between hybrid nanofluid models indicates a higher rate of heat transformation, with the Yamada-Ota hybrid nanofluid model demonstrating better and faster heat transport properties than the Xue model. This study underlines the importance of understanding the impact of controlled parameters on wall stresses to optimize fluid dynamics system performance and efficiency. Moreover, it highlights the potential of entropy generation analysis to identify changes in thermal processes and reduce the loss of available mechanical power in thermo-fluid systems and provides a foundation for exploring and developing advanced technologies and systems with improved heat transfer performance and energy efficiency.

... Entropy analysis, which focuses on entropy generation, investigates the thermodynamic irreversibility owing to several thermal systems connected to the phoneme, such as heat and mass transfer, magnetic field, and viscous heating in the flow stream. Bejan [39] completed a significant involvement study on entropy generation, which is crucial in a variety of industrial procedures such as heat exchangers, solar gatherers, chemical vapor confession devices, burning, turbomachinery electric icing devices, and so on. Blood pressure fluctuation is an important mechanism in the human body. ...

Homogeneous and heterogeneous reactions play a decisive role in biological procedures such as burning, polymer creation, ceramic construction, distillation, and catalysis. The magnetic properties of hemoglobin molecules are organic. Magnetic resonance imaging (MRI) and electronic components with an electromagnetic field are now readily available, allowing for the explanation of fundamental biological processes. These ideas form the foundation of an ongoing study that attempts to look into the impact of both homogeneous and heterogeneous reactivity on the peristaltic transport of magnetohydrodynamics Oldroyd-B fluid. When convective and partial sliding conditions are present, the configuration changes to a non-uniform vertical channel. The fundamental partial differential equations are resolved utilizing the Homotopy Analysis Method. Entropy optimization has been carried out. The primary limits entering the problem are investigated, and then a graph is used to show the influences of temperature, velocity, skin fraction, Nusselt number, and pressure increase against mean circulation, trapping phenomena, homogeneous reactions, and heterogeneous way to respond. When magnetic parameter rises, the velocity of Oldroyd-B fluid and Bejan number decrease, while temperature, entropy generation, and pressure gradient increase. The tables show that the skin friction coefficient rises for accumulative values of the Grashof number and magnetic parameter, while the skin friction coefficient drops for rising values of the velocity slip parameter and Reynolds number. The Nusselt number increases for large values of Eckert, Grashof numbers, and magnetic parameters.

... Pr stands for the Prandtl number, which is defined as Pr = µ f ·c p,f /λ f . Bejan [29] used the concept of the volume entropy generation rate to evaluate the irreversible heat loss for the energy quality occurring in the microchannel heat sinks, which consists of two kinds of entropy generation in the fluid flow and heat transfer process, i.e., the friction entropy generation rate and the heat transfer entropy generation rate. The definitions of these two parameters are calculated from: ...

The microchannel heat sink has been recognized as an excellent solution in high-density heat flux devices for its high efficiency in heat removal with limited spaces; however, the most effective structure of microchannels for heat dissipation is still unknown. In this study, the fluid flow and heat transfer in high-temperature wavy microchannels with various shaped fins, including the bare wavy channel, and the wavy channel with circular, square, and diamond-shaped fins, are numerically investigated. The liquid metal-cooled characteristics of the proposed microchannels are compared with that of the smooth straight channel, with respect to the pressure drop, average Nusselt number, and overall performance factor. The results indicate that the wavy structure and fin shape have a significant effect on the heat sink performance. Heat transfer augmentation is observed in the wavy channels, especially coupled with different shaped fins; however, a large penalty of pressure drops is also found in these channels. The diamond-shaped fins yield the best heat transfer augmentation but the worst pumping performance, followed by the square-, and circular-shaped fins. When the Re number increases from 117 to 410, the Nu number increases by 61.7% for the diamond fins, while the ∆p increases as much as 7.5 times.

... Therefore, in order to satisfy the necessity of implementing an increase in the system's size, the level of energy consumed by the sections and components implying direct damage to the environment increases. The exergoenvironmental equations are listed below (Bejan, 1996): ...

... Such an objective function must simultaneously account for the useful fluid heat gain and the undesirable heat losses and pressure losses. In conventional heat exchanger theory, functions minimising the entropy rise are widely used [95], [96]. Entropy is generated in the fluid due to the heat gain and also the pressure drop. ...

Concentrated solar thermal energy systems have an immense potential to renewably and sustainably address the growing global energy demand. The application scope of these technologies is broad and ranges from power generation to industrial process heating which in itself is wide ranging. The ability of concentrated solar thermal technologies to produce heat, via a working fluid, at high temperatures is what allows for this broad range of application. Operating temperatures in excess of 1000 °C can well be attained through concentrated solar thermal.
A critical component of any concentrated solar thermal system is its receiver which is the subsystem that absorbs the concentrated solar radiation incident on it and transfers it to a heat transfer fluid that passes through it. The efficiency and effectiveness with which the solar receiver is able to transfer the incident radiation to the heat transfer fluid largely decides the overall performance of any concentrated solar thermal system.
In this thesis, a novel type of solar receiver, is proposed and explored with the objective of developing receivers with performances rivalling or bettering those of the state of the art. The proposed receivers are based on compact heat exchanger concepts in so far that the flow channels of the receivers imitate those typically used in compact heat exchangers. The motivation behind this are the well understood and demonstrated performance enhancements achieved in compact heat exchangers, especially when the working fluid is a gas or a supercritical fluid. This improved performance owes itself to the compactness of the flow channels which boosts the heat transfer to the fluid though at the expense of an increased pressure drop. Smaller sized receivers, which is an inherent feature and advantage of compact structures, results in savings in material costs.
There are several compact flow channel geometries, commonly used in compact heat exchangers, which may be employed in solar receivers. In order to evaluate the performance of each of these flow channel geometries, a numerical model of solar receivers using a pressurised fluid has been developed. The numerical model has been programmed in such a way as to easily facilitate the inclusion of different flow channel geometries and vary their respective geometrical configurations.
Applying the developed numerical model to a central solar pressurised air receiver power plant coupled to a supercritical carbon dioxide Brayton cycle, a steady state parametric and optimisation analysis was performed on six different receiver flow channel geometries. The six geometries selected were the plain rectangular, plain triangular, wavy, offset strip, perforate and louvred fin flow channels. Four geometrical parameters, common to all flow channel geometries, were identified and varied in the parametric study. These are the channel height, channel breadth, channel wall thickness and number of vertical channels. Performance indicators for receiver evaluation were studied and it was determined that exergy efficiency, which accounts for both heat transfer to the fluid and pressure drop in it besides the incident solar radiation, is a useful tool for optimisation and comparison.
The parametric study revealed that perforated fin receivers, followed by plain rectangular and wavy fin receivers, exhibited the highest exergy efficiencies with taller and narrower channels with thicker walls and fewer vertical channels improving this efficiency. The methodology used in this analysis, besides the receiver operating conditions and system modelling assumptions, greatly affects the results and relative performances of the receiver configurations. A validation of the model and some of its underlying assumptions was conducted by comparing it to a previous study and a more complex three-dimensional computational fluid dynamics model.
To substantiate the findings of the numerical model, an experimental campaign on receivers of differing flow channel geometric configurations was proposed. The high flux solar simulator of the IMDEA Energy institute, namely KIRAN-42, was employed as the radiation heat source for the experiments. A calorimetric testbed was designed, assembled and commissioned for the purpose of experimentation on pressurised gas receivers. Procedures for the operation and control of the pressurised receiver testbed were established after a series of preliminary test runs.
Four variants of the plain rectangular fin receiver were designed and fabricated using additive manufacturing. The geometrical variations in the receivers were increased height, increased breadth, and reduced channel wall thickness respectively. The receivers were manufactured in stainless steel and Inconel 718 though only the stainless-steel receivers were experimented on. An experiment plan was drawn out specifying the experimental characterisation to be performed on each receiver. This was performed varying the mass flow rate of air, receiver inlet pressure and incident radiation peak flux.
The experimental campaign confirmed important findings and predictions of the pressurised receiver numerical model. These include the maximum thermal efficiency and pressure loss occurring at the smallest channel size and also the positive effect of taller and narrower channels. The maximum thermal efficiency observed was 94.7% at an inlet pressure of 12 bar, a mass flow rate of 2 g s-1 and a peak incident flux of 400 kW m-2 with the corresponding pressure drop measured at below 1% of the inlet pressure. This performance, in terms of thermal efficiency and relative pressure drops, is on par and even surpasses the state-of-the-art receivers of its type. Such high thermal efficiencies (above 90%) and low relative pressure drops (below 1%) were observed for other operating conditions and receiver geometries as well.
The numerical model of the receiver was modified to better represent experimental realities such as the flow channel surface roughness, non-uniform incident radiation, uneven receiver surface absorptance and receiver inlet/outlet section pressure losses. While the pressurised receiver numerical model generally corresponded well with the experiments, within the bounds of experimental error, a sensitivity analysis was performed to evaluate the influence of operational parameters that had significant associated uncertainties. These included the mass flow rate, incident radiation flux, inlet pressure, air composition and receiver surface absorptance. The performance indicators evaluated in this sensitivity analysis were the receiver outlet temperature, pressure drop, thermal and energy efficiencies.
In conclusion, the use of compact flow channels in pressurised gas receivers has been numerically and experimentally demonstrated to produce high performance receivers. When optimised for geometry, these receivers can effectively transfer incident solar radiation to the heat transfer fluid at thermal efficiency and pressure drop combinations that rival and excel the state of the art in pressurised gas receivers.

... This approach has several advantages over conventional testing methods, including speed, simplicity, and the ability to learn from examples. Thermodynamic optimisation methods, such as entropy generation minimisation (EGM) [15] and constructal theory (CT) [16], may also offer a new perspective on the optimisation process. By considering these parameters, engineers and researchers can gain a deeper understanding of the thermodynamic performance of a system and identify areas for improvement. ...

This paper presents a new way to hyper-optimise a flat plate solar collector using a combination of regenerated point clouds, constructal theory, and physics-informed machine learning (PIML). The behaviour of the flat plate solar collector is studied as solar radiation and ambient temperature change, using both precise numerical simulation and PIML. The novel hyper-optimisation method integrates these two approaches to improve the performance of the solar collector. In this method, the volume of fluid and solid structure of the flat plate solar collector (FPSC) is transformed into point clouds based on constructal theory. The point clouds are then regenerated into a continuous and uniform 3D geometry using optimised parameters. To put the modified version of the flat plate solar collector (FPSC) into practice, a computational method is used to generate a training data set for machine learning, specifically for neural networks. After thoroughly verifying the computational results, the PIM is trained using the generated training data set. This study marked the first time that a regular computational method is replaced with PIML output to reduce the computational cost of prediction. In the second layer of calculation, a deep neural network is used to make predictions based on the outputs generated by PIML. Seven independent parameters are used to predict heat transfer and efficiency over time, including time, heat flux, mass flow rate, inlet temperature, number of pairs and clusters, and volume fraction of nanofluid, while 16 hidden layers and 63 learnable neurons are engaged in this prediction layer. The geometry matrix is redefined by constructal theory principles in a series of iteration loops to generate the first flat plate solar collector based on constructal theory (CTFPSC). The results indicated that the hyper-optimisation method could reduce calculation costs by 18.31% compared with the regular computational method. In addition, the results reveal that maximum outlet temperatures are possible when N c > 3 and N p > 5.

... That is the reason that scientists draw their attention to the investigation of entropy optimization in fluid problems. Initially, entropy generation was investigated by Bejan [18,19]. Odat et al. [20], used magnetic field and investigated entropy optimization in convective flow. ...

... Further difficulties in the non-equilibrium thermodynamics of homogeneous bodies are illustrated by the later developments, by the finite time, and endoreversible thermodynamics [24][25][26], and also by thermodynamics of discrete systems [27]. Their time-dependent, real processes are treated without evolution equations and a dynamic interpretation of the Second Law [28][29][30]. ...

The backbone of non-equilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and stable ones survive. The physical concepts from the stability structure and the related formalism of constrained entropy inequality are universal by construction. Therefore, the mathematical tools and the physical concepts of thermodynamics help formulate dynamical theories of any systems in social and natural sciences.
This article is part of the theme issue ‘Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)’.

... Chang et al. (2009) concluded that wave channels improved heat performance owing to the generation of vortices. In a thermal system, irreversibility deteriorates the system performance, which can be quantified through the rate of entropy generation (Bejan 1998). Hence, several investigators studied entropy generation to optimize system effectiveness. ...

The present investigation discusses the influence of obstacle configurations on the hydrothermal and irreversibility characteristics of a sinusoidal backward-facing step channel. The study investigates the interplay of obstacle configuration, namely profiles, locations, and orientations. Different obstacle profiles of identical areas, including square, rhomboid, triangular, circular, and elliptical, are studied. Nusselt number, pressure drop, irreversibility, and hydrothermal factor are the output parameters. Our results highlight that the reattachment length decreases because of the obstacle placed near the channel's inlet, independent of the obstacle's geometrical configuration. Further, the recirculation zone length is found to be the smallest for the square obstacle. The local Nusselt number is found to be greatest at the location of the obstacle, and the peak value of the local Nusselt number is greatest for the backward-facing step channel with a rhomboid obstacle. It was observed that the average Nusselt number, pressure drop, and irreversibility characteristics all increase with the increase in Richardson number irrespective of the shape of the obstacle, and are greatest in the case of a triangular obstacle. However, the elliptical obstacle has a higher hydrothermal factor, indicating that it has the optimum obstacle geometry. In addition, elliptical obstacles with step obstruction distance along the x and y axis, namely (Lx = 10 and Ly = 2.2), (Lx = 20 and Ly = 2.2), are considered as optimal obstacle locations. The angular orientation of 0° is found to have the maximum hydrothermal factor. These findings demonstrate the interplay of wall-obstacle architecture on hydrothermal and irreversibility performance and highlight their importance as a design feature.

... The concept of irreversibility in a straight pipe with a circular cross-section firstly was surveyed by Bejan [4]. Ozalp [5] computationally detected the effects of temperature difference, Prandtl number and Eckert number on exergy loss and entropy generation in a micropipe, and he discovered that for Poiseuille flow the local exergy loss greatly differs from the entropy generation due to the presence of pressure drop. ...

We study the similarities and differences between one-qubit Novikov quantum heat engines and classic Novikov heat engines. We find that they have similar power-efficiency curves but very different ecological function-power curves. Our analysis shows that in quantum engines the maximum values of the power and ecological function, and the efficiencies at which they are produced depend on the thermal couplings and the energy of the qubit inducing the heat flux that makes the engine to work. We analyze the high-temperature limit of the quantum engines to understand better the similarities and differences between the classic and quantum Novikov heat engines.

The main objective of this work is to create a set of sufficient criteria for proving the existence and
uniqueness of periodic positive solutions of a class of first-order iterative differential equations arising in popula-
tion dynamics. Our study is carried out using Schauder’s fixed point theorem, Banach contraction principle and
some properties of an obtained Green’s function. The derived results complement some previous studies.

In this part, I recalled the modified discrete fractional operators with Mittag-Leffler kernel which was recently introduced. I presented the solutions of some linear discrete fractional order differential equations. Finally, some examples was given to confirm the importance from modelling point of view of the modified discrete fractional operators possessing Mittag-Leffler kernel.
Keywords: modified fractional operators with Mittag-Leffler kernel, modified discrete fractional operators.

The investigation of the effects associated with the temperature-dependent property (viscosity, density and thermal conductivity) variations on fluid flow, entropy generation, and heat transfer in the various hybrid corrugated channels is performed numerically. Water enters the flow domain with a constant inlet temperature of 300[Formula: see text]K and constant inlet velocity corresponding to the different Re values. An in-depth numerical investigation is performed for the two cases that have the least entropy generation among all the cases and these cases are inward arc-outward triangular and inward trapezoidal-outward triangular corrugated channels. The use of corrugated channels with variable properties substantially affects the Nu. The effect of temperature-dependent property variation corresponding to the Re on frictional and heat transfer entropy generation is also presented in this work. The rise in the Re and consideration of variable fluid properties resulted in a decrement in the total entropy generation. Under the considered conditions, the frictional entropy generation contribution in the total entropy generation is very small as compared to the heat transfer entropy generation with constant and variable fluid properties. Furthermore, the consideration of temperature-dependent property variation results in a lower augmentation entropy generation number as compared to the constant property cases at higher Re.

Since energy sources are limited, any activity aimed at recycling energy waste or facilitating energy conversion systems is invaluable. Against this background, most scientists focus on the integration of energy systems and the coupling of different technologies. In this study, a variety of power systems are investigated for optimal power conversion configurations of geothermal sources. Three configurations, Organic Rankine Cycle Geothermal Cooling (GPR/ORC), Kalina Cycle Geothermal Cooling (GPR/Kalina), and Rankine Cycle and Feed water Heater (GPR/FWH) Geothermal Cooling, are classified according to exergy and Study energy economic analysis. Calculations show that the GPR/FWH system has the highest net output power of 2963 kW. In addition, the GPR/Kalina system has the lowest output power and lowest energy efficiency among the systems launched. Across the three proposed systems, the fuel cell generates 1254 kW of electricity, while the Kalina cycle in the GPR/Kalina system generates 487 kW. Exergy studies show that the GPR/Kalina and GPR/FWH systems have the lowest and highest irreversibility (3795.4 kW and 4365.56 kW, respectively). Furthermore, the fuel cell was found to have the greatest exergy destruction rate among the three configurations. The results of the economic analysis show that the fuel cell has the highest cost ratio among all designs. In addition, the values of the dissipation factor show that the absorption chiller has the highest dissipation factor value among the three configurations. Furthermore, the comparative parametric analysis provides new aspects to introduce into the system.

The paper presents an approach to the optimal design of multi-stream heat exchangers used in low-temperature technologies. The design process consists in creating the computational model of multi-stream heat exchangers with heat transfer fluids described in the paper, analyzing and selecting optimality criteria, investigating the influence of all possible mutual flow directions and directly selecting optimal design and operating parameters according to the specified criteria. The process has been demonstrated on the example of a three-flow plate fin heat exchanger used in a natural gas liquefaction scheme. Elements of multi-criteria optimization have been applied. Two optimal variants have been obtained, the first one being in terms of energy indicators, the second one being in terms of productivity.

The convective heat transport and entropy production in \(\textrm{NiZnFe}_2\textrm{O}_4\) (nickel zinc ferrite) + \(\textrm{C}_8\textrm{H}_{18}\) (engine oil) based nanofluid flow across a melting stretching surface are explored in the current study through similarity analysis. It is believed that the physics of flow across the stretched sheet can be fundamental for the extrusion process and heat exchangers along with several scientific and engineering applications such as geophysical applications, especially in some geothermal regions. The Lie group transformations are employed to produce the similarity representation for the partial differential equation’s system, which is then solved via the spectral local linearization method. The quantitative analysis is shown graphically to explore the effect of applicable parameters on fluid flow characteristics along with streamline visualizations. When the melting parameter is varied from \(M=0\) to \(M=1\), the heat transmission rate is increased by \(38\%\); the variation of first and second-order velocity slips from \(\lambda = 0, \, \gamma = 0\) to \(\lambda = 0.2, \, \gamma = -0.25\) reduced the entropy by \(53.7\%\), whereas \(8.4\%\) decrement is noted in the skin friction by the variation of viscous dissipation from Ec \(=0\) to Ec \(=0.5\). Furthermore, the addition of nanoparticles leads to an enhancement of streamline patterns and decrement in the surface friction as well as the heat transference rate. Comparisons and error estimations are done to show the efficiency of numerical approach. This research is found to be useful in many sectors, such as tumor treatments, electromagnetic interfaces, microwave applications, bone plate surgeries, and aerodynamic extrusion processes.

Owing to enhanced thermal impact of nanomaterials, different applications are suggested in engineering and industrial systems like heat transfer devices, energy generation, extrusion processes, engine cooling, thermal systems, heat exchanger, chemical processes, manufacturing systems, hybrid-powered plants etc. The current communication concerns the optimized flow of Sutterby nanofluid due to stretched surface in view of different thermal sources. The investigation is supported with the applications of external heat source, magnetic force and radiative phenomenon. The irreversibility investigation is deliberated with implementation of thermodynamics second law. The thermophoresis and random movement characteristics are also studied. Additionally, first order binary reaction is also examined. The nonlinear system of the governing problem is obtained which are numerically computed by s method. The physical aspects of prominent flow parameters are attributed graphically. Further, the analysis for entropy generation and Bejan number is focused. It is observed that the velocity profile increases due to Reynolds number and Deborah number. Larger Schmidt number reduces the concentration distribution. Further, the entropy generation is improved against Reynolds number and Brinkman parameter.

The present article provides a three‐dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (103≤Ra≤107 ${10}^{3}\le {Ra}\le {10}^{7}$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from Ra=103 ${Ra}={10}^{3}$ to 107 ${10}^{7}$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient φ=10−4 ${\varphi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number (Ra=103 ${Ra}={10}^{3}$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of Ra=104 ${Ra}={10}^{4}$ and 105 ${10}^{5}$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large (Ra≥106 ${Ra}{\ge 10}^{6}$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.

Analysis of second law of thermodynamics in unsteady two-dimensional Magnetohydrodynamic buoyancy flow through a heated vertical permeable plate of infinite length in the existence of the strong magnetic field and radiative heat flux have been discussed. The velocity, temperature field, and the irreversibility distribution in terms of entropy generation number are obtained and discussed. Also, their profiles are presented through figures with the various flow parameters. In continuation, the shear stress in expressions of skin friction coefficient and the heat transfer rate is also conferred and their numerical values are presented through tables. It is found that the effect of the magnetic field, heat source, and thermal radiation parameter perform a significant role in regulating the entropy generation profile. This result is helpful in thermal industries for cooling or heating various objects.

Because of their thermophysical and rheological properties, graphene oxide (GO) nanofluids show promising advances in heat transfer enhancement. In particular, in magnetohydrodynamic (MHD) studies, where the fluid flow is kept in check, heat transfer tends to diminish due to magnetic field strength. GO nanoparticles, with the highest thermal conductivity, significantly impacts heat transfer devices through conductive heat transfer enhancement. This paper computationally investigates the MHD flow of GO nanofluid over a linearly stretching cylinder. The nanofluid flow is modelled using Buongiorno model under the influence of viscous dissipation effects and the effects of nanoparticle characteristics such as thermophoresis and Brownian motion. The modelled equations are solved using spectral collocation method under isothermal and slip boundary conditions. An examination of the impacts of embedded parameters is presented in detail and it is shown that the conductive heat transfer and diffusive mass transfer are enhanced by dispersing GO nanoparticles in the base fluid. A quantitative analysis is made with the previously published results for special cases. As suggested, this study is significant in heat transfer applications which demand the use of magnetic fields.

Finite differences between reservoirs and isotherms of Carnot engines are usually considered for entropy production. This paper analyzes the available work, not only the power, to open and close systems. The closed Carnot system shows the maximum efficiency in the classical Carnot condition, and the existence of a maximum for available work, which is a function of the conductance ratio of warm and cold heat exchanger.

Optimization of the power output of Carnot and closed Brayton cycles is considered for both finite and infinite thermal capacitance rates of the external fluid streams. The method of Lagrange multipliers is used to solve for working fluid temperatures that yield maximum power. Analytical expressions for the maximum power and the cycle efficiency at maximum power are obtained. A comparison of the maximum power from the two cycles for the same boundary conditions, i.e., the same heat source/sink inlet temperatures, thermal capacitance rates, and heat exchanger conductances, shows that the Brayton cycle can produce more power than the Carnot cycle. This comparison illustrates that cycles exist that can produce more power than the Carnot cycle. The optimum heat power cycle, which will provide the upper limit of power obtained from any thermodynamic cycle for specified boundary conditions and heat exchanger conductances is considered. The optimum heat power cycle is identified by optimizing the sum of the power output from a sequence of Carnot cycles. The shape of the optimum heat power cycle, the power output, and corresponding efficiency are presented. The efficiency at maximum power of all cycles investigated in this study is found to be equal to (or well approximated by) eta = 1 -square-root T(L,in)/phi-T(H,in) where phi is a factor relating the entropy changes during heat rejection and heat addition.

The object of this paper is the beginning of a formulation of a method
to find bounds to process functions, such as work and heat, for
processes occurring in finite time. A general variational statement of
the problem is given. Then model problems are solved, all but one of
which are based on the "step-Carnot" cycle. This is similar to the
reversible Carnot cycle but with the external pressure varying in finite
steps. Such a system only needs to go through a finite number of
equilibrium states during its cycle. The problems are the maximization
of effectiveness of the step-Carnot cycle, the maximization of
efficiency of the same cycle, the determination of optimal period for a
step-Carnot cycle whose contact with the external reservoirs has finite
heat conductance, and the determination of the maximum power and the
rate at which maximum power is obtained, for a continuous Carnot cycle
with finite heat conductance between system and thermostats.

We present a finite-time thermodynamic analysis of the Stirling engine cycle based on mass and energy balances with associated heat-transfer-rate equations. These governing equations are formulated as normalized ordinary differential equations which are solved numerically. The effects of heat-transfer contact time and regeneration on power output and efficiency are studied. The results show that there exists an optimum power output for a given engine design, based on engine speed and heat-transfer contact time.

This chapter outlines the method of entropy generation minimization or thermodynamic optimization. It determines the thermodynamically optimal size or operating regime of an engineering system, where by optimal means the condition in which the system destroys the least energy while still performing its fundamental engineering function. The thermodynamic optimum is the condition of the most advantageous trade-off between two or more competing irreversibilities. The entropy generation rate of the finite-size control volume is the volume integral of the volumetric entropy generation rate. The mission of the storage device is to temporarily store energy, not energy. The combined effect of the competing irreversibilities is a characteristic of all sensible-heat storage systems. The optimization of power plant models with heat transfer irreversibilities can be pursued either as a power maximization (PM) problem or as an entropy generation minimization (EGM) problem. Hierarchy and specialization are characteristics of the constructal architecture that follows from the constructal law.

An advanced, practical approach to the first and second laws of thermodynamics. Advanced Engineering Thermodynamics bridges the gap between engineering applications and the first and second laws of thermodynamics. Going beyond the basic coverage offered by most textbooks, this authoritative treatment delves into the advanced topics of energy and work as they relate to various engineering fields. This practical approach describes real-world applications of thermodynamics concepts, including solar energy, refrigeration, air conditioning, thermofluid design, chemical design, constructal design, and more. This new fourth edition has been updated and expanded to include current developments in energy storage, distributed energy systems, entropy minimization, and industrial applications, linking new technologies in sustainability to fundamental thermodynamics concepts. Worked problems have been added to help students follow the thought processes behind various applications, and additional homework problems give them the opportunity to gauge their knowledge. The growing demand for sustainability and energy efficiency has shined a spotlight on the real-world applications of thermodynamics. This book helps future engineers make the fundamental connections, and develop a clear understanding of this complex subject. Delve deeper into the engineering applications of thermodynamics. Work problems directly applicable to engineering fields. Integrate thermodynamics concepts into sustainability design and policy. Understand the thermodynamics of emerging energy technologies. Condensed introductory chapters allow students to quickly review the fundamentals before diving right into practical applications. Designed expressly for engineering students, this book offers a clear, targeted treatment of thermodynamics topics with detailed discussion and authoritative guidance toward even the most complex concepts. Advanced Engineering Thermodynamics is the definitive modern treatment of energy and work for today's newest engineers.

This paper reviews a project which opened up a multi-million pound market to Hallite Seals for a new and innovative range of thermoplastic seals and at the same time drastically reduced the cost of existing products. The project duration was kept to one year by taking advantage of new technologies wherever possible. The project not only achieved the marketing objectives within the planned time-scales, it also provided a significant payback on capital expenditure in less than 12 months. Severe customer service problems on existing products were eliminated and the value of stocks and work-in-progress was significantly reduced.

The objective of this paper is to establish simple rules for use in the design of gas-cooled conducting supports. The rules should allow design for good thermal performance without unnecessary mechanical complexity. The concept of support of cooling the escaping vapor by a counter flow heat exchanger in which the helium vapor intercepts the current flowing in the mechanical support.

This paper presents a simple method for the optimal economic selection of pipe size and insulation thickness for steam piping systems. The primary operating costs inherent in any such system are consequences of fluid-flow friction and heat transfer losses. Striving to conserve energy, the engineer is motivated to select large pipe diameters and insulation thickness. But how large should the pipe diameter be and how much insulation is necessary? The answer is simply to make that investment in piping and insulation which minimizes the sum of the capital and operating costs (friction and heat transfer). Thus, it is imperative that the operating expenses be precisely evaluated. The key is the recognition that it is available energy which is the commodity of value - that it is necessary to assign an economic value (cost) to the steam based on its available energy content.

This chapter deals with entropy production resulting from temperature differences. This thermal conduction energy is the lost heat that goes into entropy production. All forms of entropy production result from dissipative processes involving mass, species, momentum, heat transfer, and electromagnetic or nuclear transport. It is observed that the dissipation can have a diffusive or hysteretic origin, the diffusion being directional and the hysteresis being cyclic. The majority of dissipative processes, including the dissipation of radiation, are diffusive in nature. The chapter explores the thermodynamic foundations of entropy production and briefly reviews radiative stress and develops the local entropy production in terms of this stress. Further, the chapter illustrates entropy production in a stagnant gas and develops a qualitative understanding of radiative heat transfer. It also discusses the relation between entropy production and heat transfer, and the maximum entropy production at flame quenching. The microscales of turbulence and radiation-affected turbulence are presented.

The subject of this chapter is the relatively recent work on melting and lubrication at the interface between two solid parts, one of which is at its melting point. It is an area of research that began in heat transfer, with studies of contact melting inside capsules and around embedded objects. Melt lubrication is now a distinct topic in tribology. The classical application of melt lubrication is in the area of sliding friction on ice and snow. Among the more modern applications is the coating of a metallic part with another metal whose melting point is considerably lower. The function of the latter is to melt and serve as lubricant in a manufacturing process to which the former may be subjected. The research reviewed in this chapter covers the contract melting of crystalline substances, anomalous crystalline substances such as ice, and the contact softening of glass-like substances. These occur in diverse contact-region geometries. The shapes of the mating solid surfaces may be concave, convex, or plane, while the perimeter of plane contact regions may be either rectangular or circular. The types of relative motion reviewed are sliding contact, rolling contact, the movement of a hot body through a melting solid medium, and the movement of a solid melting inside a heated capsule. The effect, the roughness, or contact melting over the tops of asperities is also analyzed.

The idea of exergy—a notion which nowadays is becoming increasingly widespread—was recently introduced into the field of radiation. In this paper formulas for the computation of exergy of heat radiation are set out. The ratio of exergy to the radiation energy has been considered and a discussion is presented of the dependence of substance exergy and radiation on temperature. In addition, the possible applications of radiation energy are mentioned as well as numerical examples using the relations derived in this paper.

An endoreversible heat engine is an internally reversible and externally irreversible cyclic device which exchanges heat and power with its surroundings. Classical engineering thermodynamics is based on the concept of equilibrium. Time is not considered in the energy interactions between the heat engine and its environment. On the other hand, although rate of energy transfer is taught in heat transfer, the course does not cover heat engines. The finite-time thermodynamics is a newly developing field to fill in the gap between thermodynamics and heat transfer. Two types of engines are modelled in this paper—a reciprocating and a steady flow—with results obtained for maximum power output and efficiency at maximum power. It is shown that the latter is the same for both types of engines but that the maximum value of power production is different.

The second law aspects of heat transfer by forced convection are illustrated in terms of four fundamental flow configurations: pipe flow, boundary layer over flat plate, single cylinder in cross-flow, flow in the entrance region of a flat rectangular duct. The interplay between irreversibility due to heat transfer along finite temperature gradients and, on the other hand, irreversibility, entropy generation profiles or maps, and those flow features acting as strong sources of irreversibility are presented. It is shown how the flow geometric parameters may be selected in order to minimize the irreversibility associated with a specific convective heat transfer process.

Several definitions of energy and exergy efficiency for closed systems for thermal energy storage (TES) are developed and discussed. A simple model is utilized in which heat quantities are transferred at specified temperatures to and from a TES. Efficiency definitions are considered for the overall storage process and for the three component periods which comprise a complete storage process (charging, storing, and discharging). It is found that (1) appropriate forms for both energy and exergy efficiency definitions depend on which quantities are considered to be products and inputs; (2) different efficiency definitions are appropriate in different applications; (3) comparisons of different TES systems can only yield logical results it they are based on a common definition, regardless of whether energy or exergy quantities are considered; and (4) exergy efficiencies are generally more meaningful and illuminating than energy efficiencies for evaluating and comparing TES systems. A realistic, but simplified, illustrative example is presented. The efficiency definitions should prove useful in the development of valid and generally accepted standards for the evaluation and comparison of different TES systems.

We examine the exergy balance of a multi-component fluid subject to viscous dissipation processes, heat transfer by conduction, heat transfer by radiation, matter diffusion and chemical reactions. The differential equations for exergy balance in the fluid formalize the relationship between the exergy input/output approach to second law analysis and the entropy generation procedure using the Gouy-Stodola theorem. The balance relations for mass, momentum, energy and entropy are used to establish the validity conditions for the exergy balance equations. In particular, we define the role and significance of the assumption of local thermodynamic equilibrium. The general functions and restrictions of nonequilibrium thermodynamics within second law analysis are also discussed.

The irreversible generation of entropy for two limiting cases of combined forced-convection heat and mass transfer in a two-dimensional channel are investigated. First, convective heat transfer in a channel with either constant heat flux or constant flow. The entropy generation is minimized to yield expressions for optimum plate spacing and optimum Reynolds numbers for both boundary conditions and flow regimes. Second, isothermal convective mass transfer in a channel is considered, assuming the diffusing substance to be an ideal gas with Lewis number equal to unity.

This is an analytical and numerical study of the exergy that can be
delivered by a solar collector installation with temporary energy
storage capability. In the first part of the study, the method of
variational calculus is used to show that under conditions of
time-dependent inlet and outlet flow rates, the total exergy delivered
by the installation is maximum when the collector temperature is
maintained at an optimum constant level throughout the insolation
period. More realistic models of solar collectors with storage
capability are analyzed in the second and third parts of the study. In
each of the models considered, the analysis shows that the relative
timing of the filling and discharge processes has a significant effect
on the total exergy delivered by the installation. The main conclusion
of the study is that the daily regime of operation of the
collection/storage installation can be selected by design in order to
maximize the harvesting of solar exergy per unit of collector area.

We show that a meson-exchange model of the d(gamma,p) reaction can be
constructed to reproduce the energy-dependence of the existing data for
the differential cross section at 90 deg. The prediction of the model in
the GeV energy region is found to be radically different from the QCD
prediction by Brodsky and Hiller. The results will be compared with the
new data presented in a companion paper.

In accordance with the Thomson effect (Thomson, 1853), when a thermoelastic solid is subjected to a tensile stress, it cools. Similarly, when a homogeneous material is subjected to an inhomogeneous stress field or when an heterogeneous material is subjected to any stress field (homogeneous or inhomogeneous), different parts of the material undergo different temperature changes. As a result irreversible heat conduction occurs and entropy is produced. In this paper we take the second law of thermodynamics as our starting point and develop a general theory for calculating the thermoelastic damping from the entropy produced.

Attention focuses on the annular gap between displacer and cylinder shell as the gas passes between expansion and compression spaces. Equations are formulated for velocity and temperature distributions as a function of time and the distance coordinate directions—radial and axial. Local, instantaneous entropy creation rates due to viscous dissipation and heat transfer are computed without the need to refer to the usual friction factor and coefficient of convective heat transfer. From considerations of exergy an estimate of indicated thermodynamic work per cycle follows. This is expressed in terms of performance maps covering the entire range of possible speeds, charge pressures and sizes for a machine of given geometry.

When local, instantaneous departures from ideal reversible behaviour are evaluated in terms of the entropy generation rate, the differential equations describing the unsteady processes in the Stirling cycle machine give way to steady flow forms. A simple multiplication by T o gives immediately the local, instantaneous rate of loss of available work. The paper exploits this fact to obtain, from an ideal model of the flow processes, the indicated cycle work of the real (irreversible) cycle. The result is of the form:
[Formula: see text] {( geometric parameters), τγ, N RE , N PR , N F , … ( dimensionless groups in order of diminishing influence)}
where τ, N RE , N F etc. are dimensionless groups of the operating parameters, engine speed, p ref , T e , T c etc. and γ is the specific heat ratio of the working fluid, which is shown to be the only fluid property that independently influences Z.
The approach is an alternative to the time consuming solution of the defining differential equations and provides a convenient design tool which has long been lacking in this area. The only assumption additional to those invoked in conventional computer modelling of the Stirling cycle is that actual gas processes do not depart excessively from those predicted by the ideal model of the flow—for example from those provided by the so-called ‘adiabatic’ cycle model.

By employing an endoreversible heat-engine model, the design parameters of a heat engine operating under radiative heat-transfer conditions were examined to find the maximum power output. It was found that the ratio of the cold to the hot reservoir temperature must be less than 0.2 for an optimal design. Increasing the heat-transfer area of the cold side rather than that of the hot side improves the thermal efficiency. When the temperature ratio is greater than 0.6, the efficiency of such a cycle approaches that of Curzon and Ahlborn.

The present study deals with solar collectors on the basis of exergy analysis. A criterion is proposed to rank the performance of different solar collectors. There are two considerations involved, namely, the quantity and the quality of the annually collected energy. Rabl's method was used to predict this quantity. The average temperature of the delivered energy must be determined in order to evaluate its quality. The HWB performance equation is employed to predict the average delivery temperature of hot water, assuming a reference insolation of 550 W/m2. The exergy content of the delivered energy is then evaluated by multiplying the delivered energy by the Carnot efficiency. The annual collectible exergy is used to rank the performance of a collector. According to the concept developed in this study, this criterion can be used for any type of collector, e.g., flat-plate, evacuated tube, CPC, tracking concentrators, or central receivers.

The maximum efficiency of solar converters decreases abruptly when the concentration ratio is decreased. The use of flat-plate collectors for work production is not desirable because of reduced efficiency.

We study the power and efficiency of an irreversible heat engine coupled to heating and cooling fluids with finite heat-capacity rates. We consider a specific model, for which the irreversibilities result from the finite rates of heat conductance and the internal irreversibility of the heat engine. The maximum power obtainable from such a system and the corresponding efficiency are derived analytically to provide more realistic limits on the performance of an irreversible heat engine than those obtained from a reversible heat engine. It is seen that two different optimal conditions must be determined. These are the optimal operating temperatures of the working fluids and the optimal allocation fraction of the heat conductance between the heating and cooling fluids. In the limit in which the heat-capacity rates approach infinity, the efficiency of an endoreversible heat engine at maximum power approaches the Curzon-Ahlborn efficiency. The calculated efficiency at maximum power is close to that actually observed in well-designed power plants.

Three expressions for the maximum efficiency of solar-radiation conversion (first proposed by Petela, Spanner, and Jeter, respectively) are compared with the efficiency of a photo-thermal converter, with and without concentration. All three of the expressions may be applied for concentrated radiation. For diffuse solar radiation, good results are obtained from the expressions proposed by Petela and Jeter.

We develop a fomula here to compute the maximum amount of work which can be extracted from a given combined mass of warm and cold ocean water (a quantity called the exergy of the ocean thermal resource). We then compare the second-law efficiencies of various proposed ocean thermal energy conversion power cycles to determine which best utilizes the exergy of the ocean thermal resource. The second-law efficiencies of the multicomponent working fluid cycle, the Beck cycle, and the open and closed single- and multiple-stage Rankine cycles are compared. These types of OTEC power plants are analyzed in a consistent manner, which assumes that all deviations from a plant making use of all the exergy (one with a second-law efficiency of 100%) occur because of irreversible transfer of heat across a finite temperature difference. Conversion of thermal energy to other forms is assumed to occur reversibly. The comparison of second-law efficiencies of various OTEC power cycles shows that the multistage Rankine open cycle with just three stages has the potential of best using the exergy of the ocean thermal resource.

The irreversibility associated with waste heat disposal across an exchanger represents an inherent trade-off point in the design of power plants. On the one hand, a large degree of irreversibility from a large temperature drop across the heat-transfer surface is detrimental to the thermodynamic efficiency of a cycle that produces waste heat. On the other hand, reduction of irreversibility can be achieved only by employing a larger heat transfer area. Therefore, one expects that there must be an optimum design that maximizes the work output per unit of heat transfer area for a given cycle. The efficiency at this optimum condition should be much closer to efficiencies in comparable cases of “good” design, and it must serve as a much more reasonable yardstick in assesing engineering merit.

A second-law analysis of a two-dimensional, fixed-bed regenerator is presented. We assume that the solid matrix has infinite thermal resistance in the flow direction and finite thermal resistance, characterized by the matrix Biot number, perpendicular to the flow direction. A trade-off between mechanical and thermal exergy losses yields optimal Ntu, and effectiveness. Therefore, by specifying a channel geometry, mass flow-rate, matrix porosity and total frontal area, the optimum channel length and operating period can be determined. Increasing the matrix Biot number causes a reduction in the second-law efficiency at high effectiveness and a reduction in the optimum effectiveness corresponding to the maximum second-law efficiency.

The maximum efficiency for the utilization of diffuse solar radiation ranges between 0.053 and 0.474 for non-selective and strongly-selective converters, respectively. Petela's formula gives an accurate upper bound for both selective and non-selective converters, if an appropriate equivalent blackbody temperature is defined for the sky.

The second law of thermodynamics is used as a basis for evaluating the irreversibility (entropy generation) associated with simple heat transfer processes. In the first part of this paper, the irreversibility production is analyzed from the local level, at one point in a convective heat transfer arrangement. The second part of the paper is devoted to a limited review of second law analysis applied to classic engineering components for heat exchange. In this category, the paper includes such topics as: heat transfer augmentation techniques, heat exchanger design, and thermal insulation systems. Analytical methods for evaluating and minimizing the irreversibility associated with textbook-type components of heat transfer equipment are presented.

It has been proposed to extract energy from the subterranean hot dry rock bed (HDR) by creating one or more narrow fractures in the rock and circulating cold water through the fractures. In time, the temperature of the rock region surrounding the crack drops under the influence of time-dependent conduction. This study presents the most basic thermodynamic aspects (first law and second law) of the HDR energy extraction process. It shows which parameters most influence the amount of useful energy (exergy) extracted from the HDR reservoir over a fixed time interval. For example, the water flow rate can be selected optimally in order to maximize the delivery of energy over the lifetime of the HDR system.

The control volume method is used to establish the rate of entropy generation due to heat and mass transfer in a fluid stream, accompanied by fluid friction. We show that unless the intensive form of the Gibbs equation is used, in recognition of the assumption of local thermodynamic equilibrium, errors arise in this analysis. These involve the incorrect use of the absolute mass flux instead of the diffusion flux and the appearance of a spurious coupling term between heat and mass transfer. The results are applied to examples of simultaneous heat and mass transfer in internal and external flows.

This paper shows that the intermittent operation of a defrosting vapour-compression-cycle refrigerator can be optimized with respect to: (1) the frequency of on/off operation, and (2) the way in which the supply of heat exchanger surface is divided between evaporator and condenser. The method used is that of thermodynamic optimization (or entropy generation minimization, or finite-time thermodynamics), in which heat transfer and thermodynamic aspects are accounted for simultaneously to produce a realistic description of the in-time operation of the installation. The optimal on/off frequency and surface allocation ratio are reported in non-dimensional charts, which show the effect of the heat exchanger size, cycle temperature ratio, defrosting time, compressor efficiency, and refrigerant type. The charts are based on the real properties of refrigerants R12 and R134a. The heat exchanger equipment constraint is that of fixed total heat transfer surface. It is shown that, under certain conditions, the optimization conclusions reached in this study are similar to those that would be obtained based on other constraints proposed in the literature.

In solar air heating systems, the compression energy needed to overcome friction losses can reduce essentially the benefit from solar heat. Thus the design of solar air heaters with high heat transfer rates and low friction losses is of particular interest. The net exergy flow as defined here is a suitable quantity for balancing useful energy and friction losses. By maximizing the net exergy flow the sum of exergy losses, including exergy losses by absorption of radiation at the absorber temperature level, is minimized and reasonably optimized designs of absorbers and flow ducts are found.Different types of solar air heaters have been modeled with regard to thermal performance characteristics and to pressure drop for the calculation of net exergy flow.

The entropy generation due to burning particles in a gaseous stream is considered and the contributions to it compared. A second law analysis is undertaken in order to minimize the entropy generation and, therefore, the lost available work. The optimum flow conditions from this thermodynamically advantageous perspective are determined for a burning droplet at low Reynolds number and an optimum transfer number obtained. The transfer number so obtained depends directly on the square of the relative velocity, and inversely on the net enthalpy rise due to burning and the ratio of ambient to flame temperature. In realistic flows, where the transfer number and net heat release are fixed, these quantities are related to the relative velocity and ambient to flame temperature ratio in order to operate at optimum conditions. The square of the relative velocity in such flows is a small fraction of the net heat release so that, to operate at optimum thermodynamic conditions, it is determined that the droplet Reynolds number must be large suggesting a large droplet size and low gas viscosity. Circumstances pertaining to engineering practice are also considered and it is concluded that within constraints practice is consistent with the implications of the second law analysis.

The use of exergy analysis, rather than energy analysis, for the evaluation of the performance of thermal energy storage systems is discussed. The energy and exergy relationships for a simple closed tank storage with heat transfers by heat exchanger are obtained. A complete storing cycle, as well as the individual charging, storing, and discharging periods, are considered. A numerical example for a simple case is given. The work reported is preliminary to the task of developing simplified conventions for the evaluation and comparison of the performance of thermal storages using exergy analysis methods. The establishment of such simplified conventions appears to be a necessary prerequisite to general acceptance of these methods by the engineering community.

The thermal design of counterflow heat exchangers for gas-to-gas applications is based on the thermodynamic irreversibility rate or useful power no longer available as a result of heat exchanger frictional pressure drops and stream-to-stream temperature differences. The irreversibility (entropy production) concept establishes a direct relationship between the heat exchanger design parameters and the useful power wasted due to heat exchanger nonideality. The paper presents a heat exchanger design method for fixed or for minimum irreversibility (number of entropy generation units N/sub s/). In contrast with traditional design procedures, the amount of heat transferred between streams and the pumping power for each side become outputs of the N/sub s/ design approach. To illustrate the use of this method, the paper develops the design of regenerative heat exchangers with minimum heat transfer surface and with fixed irreversibility N/sub s/.

The discussion of the ideal conversion of enclosed thermal radiation revolves round three different theories. Each of these theories has been accused to be incorrect. The objective of this paper is to provide a bird's-eye-view of the relationship between these three theories. It is shown that the theories are individually correct, and that they complement (rather than contradict) one another. The present ''unification'' consists of answering two important questions: What is the origin of the assumed blackbody radiation system. What is the ultimate fate of the blackbody radiation system. It is shown that the supply of high-temperature isotropic radiation postulated by all three theories is the result of a heat input from a high-temperature heat reservoir.

In a previous article a model of a heat engine was defined and studied with the purpose of emphasizing the role of inertial effects, particularly their importance in relation to optimization problems. Here the performance of models of heat engines harmonically driven around a state of equilibrium is compared. For the first model, with inertia, the model is defined, its nonlinear response with emphasis on the linear approximation is calculated, and the issues related to the coupling of the thermal and mechanical driving forces are discussed. The influence of increasing values of the mechanical friction coefficient is studied, and it is shown that when this coefficient is small, the work output displays subharmonic resonances that disappear when the friction coefficient increases. In the second model, without inertial effects, no such resonances appear as expected, since these are due only to the inertial terms.

Physical implications of the thermodynamic inequality derived in the preceding paper are examined in the context of Carnot-like cyclic processes. In terms of the power P and the degradation D associated with such a process, a geometrical picture is developed which vividly describes a number of important results. Our picture also leads to the concept of time efficiency as a natural complement to the concept of power efficiency. Extensions to Carnot-like refrigerators and heat pumps are carried out. Finally, the influence of a heat leak between the two reservoirs is analyzed.

We have studied the efficiency and power output of a simple model of an irreversible heat engine as a function of cyclic operating frequency. The model adopted is defined by a reversibly cycled working substance coupled to heat source and sink by thermally conducting walls. The maximum operating frequency corresponding to zero external power output is associated with the traversal of a limit cycle in the working substance. Closed form expressions for the maximum operating frequencies are derived for the special cases of isothermal and polytropic limit cycles.