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Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes
Journal of Applied Physics
Abstract
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.
... Thermodynamic and economic objectives are frequently used for the optimal design of GSHP systems. Among the thermodynamic objectives, entropy generation minimization is widely used in modeling and optimizing GHEs to reduce thermodynamic imperfections from heat transfer and fluid flow irreversibilities (Bejan 1996;Cheng and Liang 2014). The annual, life cycle and total costs are often used as economic objectives (Ma et al. 2020). ...
... Considering the importance of multi-objective optimization in the appropriate design of GSHPs and the outstanding portion of the GHE in the total cost of the system, this study attempts to determine the optimum value of the multi-borehole GHE design parameters concerning entropy generation and total cost rate as two objective functions. Entropy generation is non-dimensionalized and quantified by entropy generation number (EGN) (Bejan 1996;Maheshkumar and Muraleedharan 2011). A semitwo-dimensional steady-state analytical model describes the GHE thermal behavior in the optimization process. ...
... Entropy generation leads to exergy destruction and loss of available work. Therefore, entropy generation minimization (EGM) is an effective optimization tool to minimize losses and maximize system performance (Bejan 1996;Cheng and Liang 2017). In a vertical GHE, entropy is generated by fluid friction along the tube and finite temperature difference between the fluid and the borehole, resulting in pressure drop and heat transfer losses, respectively (Bejan 1996). ...
Multi-objective optimization and CFD simulation are conducted to optimize the design of a multi-borehole ground heat exchanger (GHE) system and assess its long-time performance. The multi-objective optimization is performed to minimize the entropy generation number (EGN) and total cost rate by using various evolutionary algorithms, including NSGA-II, GDE-3, MOEA/D, PESA-II, SPEA-II, and SMPSO. NSGA-II and GDE-3 algorithms perform best in obtaining Pareto optimal solutions. Three prominent points on the NSGA-II Pareto frontier, representing the results of single-objective thermodynamic, single-objective economic, and multi-objective optimizations, are simulated in three dimensions over three months. The trends of EGN variations extracted from the transient CFD simulation agree well with those from the steady analytical model. The EGN obtained from multi-objective optimization is 58.8% lower than the EGN obtained using single-objective economic optimization and 1.9 times higher than that calculated from single-objective thermodynamic optimization. Likewise, the total cost rate obtained from multi-objective optimization is 64.4% lower than the value obtained from single-objective thermodynamic optimization and four times higher than that calculated using single-objective economic optimization. The proposed optimization approach can be reliably applied to improve the design of multi-borehole GHE systems.
... Before the use of a complete but complex engine model -such as those presented for example in [10,11] -which requires a lot of information sometimes not already available, a simpler model, based for example on Finite Dimen-sions Thermodynamics [12,13] can help to design such systems. This kind of model can thus be used for sort of preliminary designs, for example to obtain a first draft of the relation between the power produced by the engine and its corresponding efficiency, so the usually called "power vs. efficiency" or (η,Ẇ ) characteristic curve. ...
... Although the search for engine models dealing with maximum rates of useful energy is not really new [16,17], such idea have been actually widely spread only after the publication of the seminal paper from Curzon and Ahlborn [18] in 1975. Since then, the method commonly called Finite Time Thermodynamics or Finite Dimensions Thermodynamics, have been applied to the optimization of numerous different energy systems [12,13], including obviously the Stirling engine. Radcenco et al. [19] studied the basic Stirling cycle composed by definition of four strokes : one isochoric compression, one isochoric expansion and two isothermal heat exchanges. ...
Different economical configurations, due for instance to the relative cost of the fuel it consumes, can push a heat engine into operating whether at maximum efficiency or at maximum power produced. Any relevant design of such system hence needs to be based, at least partly, on the knowledge of its specific "power vs. efficiency" characteristic curve. However, even when a simple model is used to describe the engine, obtained for example thanks to Finite Dimensions Thermodynamics, such characteristic curve is often difficult to obtain and takes an explicit form only for the simplest of these models. When more realistic models are considered, including complex internal subsystems or processes, an explicit expression for this curve is practically impossible to obtain. In this paper, we propose to use the called Graham's scan algorithm in order to directly obtain the power vs. efficiency curve of a realistic Stirling engine model, which includes heat leakage, regenerator effectiveness, as well as internal and external irreversibilities. Coupled with an adapted optimization routine, this approach allows to design and optimize the same way simple or complex heat engine models. Such method can then be useful during the practical design task of any thermal power converter, almost regardless to its own internal complexity.
... In addition, due to its direct inference from the basic principles of thermodynamics, it can be used for any energy system (Sciacovelli et al. 2015). Bejan (Bejan 1980(Bejan , 1982(Bejan , 1996 has investigated minimizing the entropy generation in various engineering topics such as designing heat exchangers and thermal insulation systems. ...
... In addition, due to its direct inference from the basic principles of thermodynamics, it can be used for any energy system (Sciacovelli et al. 2015). Bejan (Bejan 1980(Bejan , 1982(Bejan , 1996 has investigated minimizing the entropy generation in various engineering topics such as designing heat exchangers and thermal insulation systems. ...
This study aims to identify the optimal configuration for the cooling process within a cavity by analyzing entropy generation, cooling efficiency, and average total temperature using the Lattice Boltzmann Method. In this setup, the upper and lower walls of the cavity are insulated, while the left and right walls are maintained at constant temperatures. The flow was modeled as two-dimensional, laminar, and steady-state, with all internal surfaces treated as opaque, diffuse, and gray. The momentum and energy equations were solved through the Lattice Boltzmann method, while radiation effects were addressed using the net radiation method. Reynolds numbers of 100, 200, 300, and 400, along with surface emissivities of 0, 0.5, 0.8, and 1, were tested for each configuration, with a constant Richardson number of 1. The results demonstrate that both flow and temperature fields are significantly influenced by configuration and Reynolds number, whereas surface emissivity predominantly affects only the temperature field. Furthermore, increasing surface emissivity enhances the cooling process within the system. Analyzing entropy generation, cooling efficiency, and average total temperature across all configurations reveals that configurations B and F are optimal for cooling. Additionally, the impact of varying Richardson numbers was investigated for configuration B, revealing that an increase in Richardson number leads to reduced entropy generation and improved cooling efficiency.
... Secondly, the ideal cycle involves no net entropy change in the environment, whereas the operation of real machines, always entails a positive entropy generation. In recent years, research on finite-time models of thermodynamic machines has gained a lot of attention [1][2][3][4]. Irreversibilities can be incorporated by assuming a finite rate for heat transfer, internal friction, and heat leakage. Models based on linear irreversible thermodynamics [5,6], the assumption of endoreversibility [7][8][9][10], and weak or low dissipation [11][12][13][14][15][16][17], are some of the approaches which have been pursued. ...
Low-dissipation model and the endoreversible model of heat engines are two of the most commonly studied models of machines in finite-time thermodynamics. In this paper, we compare the performance characteristics of these two models under optimal power output. We point out a basic equivalence between them, in the linear response regime.
... According to Bejan [18], the Bejan number varies from 0 to 1, where Be = 0 tells us that the irreversibility due to fluid viscous dissipation and porosity dominate, whereas Be = 1 2 indicates that the irreversibility due to fluid viscous dissipation and porosity is equal to the irreversibility due to heat transfer in the entropy production and Be = 1 reveals that the irreversibility due to heat transfer dominates. ...
This paper addresses the mixed convective flow and heat transfer in combustible third-grade fluids through a slant porous channel filled with permeable materials. The fluid layer in contact with the channel wall is exposed to asymmetrical slippage and isothermal conditions. We employ the spectral Chebyshev collocation method (SCCM) to the coupled nonlinear flow governing equations and validate using the Shooting–Runge–Kutta method (RK4). Fluid velocity and temperature profiles, local entropy generation, and irreversibility ratio are computed and analyzed quantitatively and qualitatively. The convergence of the numerical method was demonstrated. The flow and thermal effects results, entropy generation rate, and Bejan number revealed fascinating manifestations that have profound implications in the design of thermo-mechanical systems. In particular, the thermal analysis results are pertinent to optimal system designs that achieve efficient energy utilization.
... Systems with a higher degree of irreversibility (or higher entropy generation rate) waste the profitable power and suffer from low efficiency. Minimizing the entropy generation rate will result in higher energy efficiency and therefore lower rates of the entropy generation are desirable [31]. The dimensionless total entropy generation is plotted in Figure 9 for different Reynolds numbers and configurations. ...
In this study, a flat-plate channel configured with pyramidal protrusions are numerically analysed for the first time. Simulations of laminar single-phase fluid flow and heat transfer characteristics are developed using a finite-volume approach under steady-state condition. Pure water is selected as the coolant and its thermo-physical properties are modelled using a set of temperature-dependent functions. Different configurations of the channel, including a plain channel and a channel with nature-inspired protruded surfaces, are studied here for Reynolds numbers ranging from 135 to 1430. The effects of the protrusion shape, size and arrangement on the hydrothermal performance of a flat-plate channel are studied in details. The temperature of the upper and lower surfaces of the channel is kept constant during the simulations. It is observed that utilizing these configurations can boost the heat transfer up to 277.9% and amplify the pressure loss up to 179.4% with a respect to the plain channel. It is found that the overall efficiency of the channels with pyramidal protrusions is improved by 12.0-169.4% compared to the plain channel for the conditions studied here. Furthermore, the thermodynamic performance of the channel is investigated in terms of entropy generation and it is found that equipping the channels with pyramidal protrusions leads to lower irreversibility in the system.
... Understanding and managing entropy generation is crucial in optimizing processes and systems across a wide range of applications. There have been several investigations on the development of entropy [2,3]. Indeed, the study of heat transfer and fluid flow in various geometries and barrier circumstances is a fundamental topic in engineering, particularly in the field of fluid mechanics and thermal sciences. ...
This study focuses on investigating entropy generation in a micropolar fluid flow over a transversely heated sheet. The governing equations of the specific model proposed in this article are transformed into a set of ordinary differential equations (ODEs) using similarity transformations, leading to a non-spatial arrangement. A BVP4C approach is then employed to solve this system of non-spatial ODEs. The Levenberg–Marquardt procedure, known for its effectiveness in artificial neural networks, is utilized to obtain a numerical solution for the entropy generation in micropolar liquid (EGML). This solution is achieved through regression plots, state transition measures, histogram representations, and mean squared errors. In this research, an EGML-based fluid flow problem is examined using an innovative application of an intelligent computer system that leverages neural structures and the Levenberg–Marquardt algorithm (NN-LMA). Through the BVP4C approach, data collection is conducted to facilitate the implementation of the NN-LMA. The EGML results obtained for various scenarios are evaluated using the exercise, acceptance, and trial processes of NN-LMA. A comparison is then made between these results and a reference dataset to validate the accuracy and efficiency of the prospective algorithm NN-LMA for investigating fluid problems associated with EGML. The study delves into how various non-dimensional factors influence flow patterns, temperature distributions, concentration profiles, and velocity profiles. State transition dynamics, regression analysis, mean square error calculations, and error histogram investigations are employed to verify the validity of the proposed NN-LMA method for solving the EGML. Overall, the results obtained through these analyses successfully demonstrate the efficacy and accuracy of the NN-LMA approach in addressing EGML-related fluid flow issues. The framework’s validity is demonstrated by the strong congruence of recommended results with reference solutions, and accuracy of to is also attained.
... Lucia and Grazzini [9] have demonstrated that second law analysis describes both industrial systems (minimum entropy generation criterion) and biological and living systems (maximum entropy generation). Reducing a physical system's total entropy generation rate offers evident advantages and improves processes' efficiency and performance [12]. Therefore, increasing the total entropy generation rate is necessary for biochemical and biological systems and life. ...
... Only recently, on the scale of two hundred years, has there been a shift in advanced engineering from maximizing energy efficiency to minimizing entropy generation. According to Bejan [26], the idea of entropy production minimization emerged in the 1970s and blossomed in the 1990s. He provide a wide range of examples where entropy generation minimization yields the desired results more easily than energy calculations. ...
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a correct introduction to the physics of heat engines when the term calorique is replaced by entropy and entropy is used as the other fundamental thermal quantity besides temperature. Carnot’s concepts of falling entropy as an analogy to the waterfall, and the separation of real thermal processes into reversible and irreversible processes are adopted. Some details of Carnot’s treatise are ignored, but the principal ideas are quoted and assumed without modification. With only two thermal quantities, temperature and entropy, modern heat engines can be explained in detail. Only after the principal function of heat engines is developed is energy introduced as physical quantity in order to compare thermal engines with mechanical and electrical engines and, specifically, to calculate efficiency.
... To investigate irreversible losses in fluid flow and heat transfer within microchannels, Bejan [56] proposed evaluating the efficiency of thermal energy utilization by analyzing the volumetric entropy generation rate at each point within the channel from the perspective of the second law of thermodynamics. The total volumetric entropy generation rate ( ‴ S gen ) encompasses both the frictional volumetric entropy generation rate ( ‴ S gen, p D ) due to frictional losses within the microchannel and the heat transfer volumetric entropy generation rate ( ‴ S gen, T D ) ...
As the integration of microelectronic devices continues to increase, thermal management issues become increasingly prominent. Microchannel heat sinks are effective for heat dissipation in high heat flux microelectronic devices. This study designs five elliptical finned microchannel heat sinks with different aspect ratios (γ) while maintaining a constant elliptical area to enhance heat transfer performance. The values of γ are 0.74, 0.86, 1, 1.17, and 1.35, respectively. Over the Reynolds number (Re) range of 293 to 740, the hydrothermal characteristics and entropy generation of the microchannels with elliptical fins (MC-EFs) are investigated through numerical simulations. The thermal enhancement mechanism of MC-EFs is analyzed via flow, temperature, and pressure fields. The optimal γ value is determined by maximizing the overall performance factor (OPF) and minimizing the augmentation entropy generation number (Ns,a). Results indicate that introducing elliptical fins in the straight microchannel (SMC) significantly improves heat dissipation. An increase in γ enhances thermal performance but also raises flow resistance. Specifically, when γ increases from 0.74 to 1.35, the Nusselt number (Nu) improves by 10.71%-25.64%, and the friction coefficient (f) increases by 30.92%-57.27%. Overall, at Re = 740, the OPF of the MC-EF with γ = 1.35 reaches a maximum of 1.285, and at Re = 597, the Ns,a for this configuration is minimized to 0.578. These findings provide valuable insights for effective thermal management in microelectronic devices.
... Sendo a minimização um dos objetivos usuais de processos de otimização de equipamentos e componentes na engenharia. (Bejan, 1996). ...
... In simple words, it is a measure of a system's disorder or unpredictability. In this regard, Bejan [1][2][3] pioneered the concept of entropy generation minimization by applying basic thermodynamic laws and heat transfer processes of fluid mechanics. It is essential to analyse the factors that contribute to the production of entropy in order to advance technology, reduce energy waste, and increase efficiency in accordance with the fundamental laws of thermodynamics. ...
The influence of polymers on entropy generation processes is substantial, particularly in the fields of fluid dynamics and rheology. The FENE-P (Finitely Extensible Nonlinear Elastic-Peterlin) model describes the polymer’s dynamics as a result of the interaction between the stretching caused by the velocity gradient and the elastic force that restores the polymer to its equilibrium position. Models such as FENE-P aid in understanding and predicting polymer flow behaviour allowing for the reduction of entropy generation by optimizing system designs. A continuum approach is employed to express the heat flux vector and polymer confirmation tensor of the model. The study investigates the complex relationship between polymer conformation, flow dynamics, and heat transfer taking into account the thermophoresis (Soret effect) and mass diffusion-thermal diffusion coupling (Dufour effect) phenomena to optimize processes by reducing entropy. This study illuminates polymer’s significance in entropy minimization, improving engineering design methodologies and applications in materials science, chemical engineering, and fluid dynamics. As result, the presence of polymers leads to a substantial decrease in the total entropy of the system. This understanding provides opportunities for enhancing heat transfer systems, thereby facilitating the development of more efficient and sustainable technology.
... The recent researches [27][28][29] investigated the process of entropy creation through heat transmission and viscous dissipation. Abolbashari et al. [30] examined the production of entropy in a non-Newtonian (Casson) nanofluid using the Optimal Homotopy Asymptotic Method (OHAM). ...
Nanoparticles enhance the heat transmission by recovering energy that was dissipated due to increased thermal conductivity. Engine oil, commonly known as a lubricant, facilitates the movement of energy between various substances. The purpose of this analysis is to investigate the impact of the Maxwell fluid and entropy generation on the movement of ternary hybrid nanoparticles as they flow past a Riga plate under convective boundary conditions. The ternary nanoparticles AA7072, AA7075, and CoFe 2 O 4 are combined with engine oil (EO) as the primary liquid. The heat transfer analysis involves the examination of heat sink/source and thermal radiation. The use of a similarity transformation is employed to convert partial differential equations (PDEs) into a dimensionless form. The altered equation is subsequently solved with the homo-topy analysis method (HAM), a robust analytical technique. The current analysis is marked by convergence, which denotes the answer. The impact of flow properties, such as the Maxwell parameter, modified Hartmann number, thermal radiation, and Biot number, on the velocity distribution and temperature profile. Higher values of the Maxwell fluid parameter have been shown to result in an increase in the velocity curve. The skin friction and heat transmission variances are elucidated through the utilization of tables and figures. Moreover, the findings suggest that the thermal layer of the tri hybrid nanoliquid is strengthened in reaction to higher thermal radiation and Biot number. At the same time, the thermal layer is also strengthened.
... Therefore, researchers delve into the parametric influence on a system's entropy, which constitutes a central aspect of this study. The pioneering work on entropy generation minimization was originally conducted by Bejan [34]. Subsequently, Famouri and Hooman [35] examined entropy within an enclosed cavity featuring horizontal adiabatic walls and isothermal vertical walls. ...
This study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.
... La generación de entropía de un CCP puede ser evaluada a través de la siguiente ecuación reportada por (Bejan, 1996). ...
En este trabajo de tesis, se llevó a cabo un exhaustivo análisis multi-dimensional de un conjunto de concentradores solares de canal parabólico, integrando métodos pasivos de transferencia de calor, con el propósito de generar calor de proceso para aplicaciones industriales en México. El estudio abarcó cuatro tipos de climas representativos del país: árido, seco, tropical y templado, dividiéndose en tres fases, cada una revelando resultados y hallazgos significativos. La primera fase se centró en un estudio comparativo de cuatro categorías de métodos pasivos: nanofluidos, insertos, recubrimiento selectivo y modificación de la geometría del receptor. Se propusieron diversos tipos en cada categoría, evaluándolos en un concentrador de canal parabólico convencional. La eficiencia térmica fue el indicador clave para discernir los mejores tipos en cada categoría. En la segunda fase, se propusieron ocho escenarios que combinaban los métodos pasivos más eficientes de la fase 1. Se llevaron a cabo análisis energéticos, exergéticos, ambientales y económicos (4E) para evaluar diferentes variables en condiciones climáticas diversas. La tercera fase complementó los resultados mediante la creación de una base de datos con diferentes números de colectores, escenarios y tipos de climas. Se generó un modelo gemelo digital utilizando seis algoritmos de regresión, seguido de un análisis de sensibilidad global y optimización multiobjetivo.
Los resultados obtenidos indicaron que, en la primera fase, se realizaron selecciones críticas de métodos pasivos. El nanofluido CuO/H2O emergió como el más eficiente, mostrando un notable aumento del 0.0567% en la eficiencia en comparación con el caso convencional. De igual manera, las cintas retorcidas como insertos exhibieron la mayor mejora con un destacado 0.1573%. En términos de recubrimiento selectivo, el tipo Solel UVAC sobresalió con un valor de 6.50%, marcando el rendimiento más alto en las cuatro categorías. Asimismo, en la modificación de la geometría del receptor, el tubo con diámetro variable indicó el valor óptimo, alcanzando un 0.2049%. Estos resultados sirvieron como base para la propuesta de ocho escenarios distintos, considerando combinaciones de los métodos pasivos analizados.
Respecto a la segunda fase, el escenario caracterizado por la integración de nanofluidos, geometría variable, recubrimiento selectivo y cintas retorcidas, destacó en el análisis energético, exergético y ambiental. Sin embargo, para el análisis económico el escenario caracterizado por la integración de la geometría variable, recubrimiento selectivo y cintas retorcidas fue el mejor. De los cuatro climas evaluados, el templado fue el óptimo ya que se lograron temperaturas de 88.50 °C, con un calor útil de 81.85 kW y una eficiencia térmica del 24.84%. Además, se demostró que este escenario fue el más adecuado para satisfacer las exigencias del proceso industrial en todas las condiciones climáticas, logrando valores anuales de energía significativos.
La tercera y última fase involucró la implementación de seis algoritmos de regresión y diversas técnicas de optimización multiobjetivo. El algoritmo de procesos gaussianos destacó como el predictor óptimo, exhibiendo una precisión destacada en la predicción de la energía del campo solar térmico. Los análisis de sensibilidad resaltaron la importancia del número de concentradores solares en la generación de energía solar térmica, con una influencia significativa de 76.7%. Asimismo, la cantidad de concentradores solares y el tipo de escenario tuvieron impactos notables en el índice de sustentabilidad, el tiempo de retorno de gases de efecto invernadero y el costo nivelado de calor.
Finalmente, la metodología presentada en este trabajo de tesis proporciona una herramienta versátil para diversas aplicaciones industriales, trascendiendo las fronteras climáticas mexicanas. Los resultados obtenidos abren nuevas perspectivas para futuras investigaciones y pretenden ser no solo una contribución significativa al entendimiento actual de los sistemas solares térmicos, sino también un continuo esfuerzo de investigación, destacando la evolución y optimización constante de soluciones energéticas sostenibles, ampliando así la viabilidad y sostenibilidad de enfoques industriales más ecológicos.
... Heat transfer and fluid friction are primarily responsible for irreversibilities in convection problems. The dimensionless local entropy generation due to friction ( " f S ), heat transfer ( " T S ) and total entropy generation ( " gen S ) are given by [38][39][40]: ...
This article presents a comprehensive approach to enhance heat transfer rates in a 3D channel using Ferrofluids. The study investigates the individual and combined impacts of rectangular winglet vortex generators and magnetic fields on flow characteristics, heat transfer enhancement, and entropy generation. Numerical solutions are derived for the governing partial differential equations using the finite volume technique and the SIMPLE algorithm. The investigation assesses the influence of key parameters, including the type of rectangular winglet vortex generator (simple, concave, and convex), Reynolds number, and magnetic field strength. Optimal operational conditions are identified based on thermodynamics' first and second laws. This study has been conducted in three steps, and the interaction of created vortices and their effect on heat transfer, pressure drop, and entropy production were investigated. In the first step, the effect of the vortex generator in different Reynolds has been investigated. In the next step, the impact of applying a magnetic field at different intensities by a current-carrying wire has been studied in a channel without vortex generators. Finally, the application of vortex generators and magnetic fields has been investigated simultaneously. The results showed that using the concave vortex generator in the absence of a magnetic field increased the heat transfer by 50% and pressure drop by 60%. Applying a magnetic field in the channel without vortex generators has increased heat transfer and pressure drop by 70% and 118%, respectively. Moreover, it is observed that the magnetic field induces a greater pressure drop penalty than the vortex generator for achieving the same heat transfer augmentation. The simultaneous application of magnetic field and vortex generator has also increased the heat transfer and pressure drop by 200% and 269%, respectively, for simple vortex generators.
... Cropper [1]. The research on entropy generation(EG) has been investigated by several researchers [2][3][4]. In a thermodynamical system, energy loss from dispersion, fluid viscosity, and internal friction forces results in entropy formation [5]. ...
Entropy generation in nanofluid flows is a critical parameter that influences the performance, efficiency, and sustainability of thermal systems. Understanding and optimizing entropy creation can lead to noteworthy advancements in numerous engineering applications, from renewable energy systems to industrial processes and biomedical equipments. The purpose of this article is to examine the entropy produced in the bioconvection flow of Eyring-Powell nanomaterial with gyrotactic microorganisms. The mathematical equations representing the flow are modeled considering the flow towards a porous surface of a cylinder. Together with the effects of the governing parameters, the mass and heat transfer components of the problem are discussed. The thermal effects of different natures are used in a new way. Overall, entropy creation is designed with regard to the second law of thermodynamics. Activation energy, chemical reaction, thermal radiation, and internal friction force effects are accounted for the development of the mathematical model. Coupled non-linear dimensional equations have been altered into ordinary differential equations (ODEs) and then treated using the MATLAB Finite Difference Method (FDM). Current numerical results are validated in Table 1. Consequence of diverse sundry parameters on entropy production, thermal field, mass concentration profile, Bejan quantity, and motile density of microorganisms is deliberated via plots. Through tables, engineering quantities are analyzed. According to the findings, the velocity profile rises as the curvature and Eyring-Powell fluid parameters rise, while it falls when the magnetic parameter is enhanced.
... Entropy generation problems have garnered significant attention due to their wide applications in industrial, environmental protection, renewable energy systems, biomedical, and engineering contexts, with a focus on minimizing irreversibility while advancing heat conduction [28]. Bejan [29] introduced the concept of entropy generation (EG). EG represents the ratio of thermal irreversibility to the total heat loss caused by fluid frictional effects. ...
The increasing need for a steady energy supply to enhance efficiency is progressively growing in both residential and manufacturing industries. This demand can be addressed by utilizing advanced technologies like a melting heat generator to produce significant amounts of heat and prevent overheating. Based on the above applications of melting heat, the consequences of melting heat transfer induction on ternary hybrid nanofluid (T-HNF) exposed to solar radiation mechanism in an erratic squeezing flow are considered. The nanoparticles Copper (Cu), Silicon dioxide (), Zirconium dioxide () are immersed in base fluid Engine oil (EO) resulting in T-HNF (Cu + + /EO). The model equation also takes into account the entropy generation minimization and Bejan number. Both the spectral collocation technique (SCT) and finite element scheme (FES) are applied to solve the ordinary differential equations (ODEs) through the Mathematica package. Our results reveal that the impact of three-component nanoparticles increases, while the solar radiation parameter raises the energy profile. Also, an increase in the magnetic field deteriorates the velocity distribution. The research has various potential applications, such as in ice and snow melting, solar thermal energy storage, and the food industry.
... Since the flow field of a centrifugal compressor is rather complex with a variety of interacting phenomena like boundary layer separation and inlet recirculation, secondary flow development due to effects of rotation and blade curvature, tip leakage flow, and possible shock waves, Denton [44] acknowledged that it is difficult to distinguish the different sources of losses in a centrifugal compressor (for example, blade boundary layer loss, endwall loss, tip leakage loss), and thus quantifying the entropy generation is a popular approach that provides a quantitative estimate of the net loss [44]. While analyzing the efficiency of any thermal system, it is also important to account for the second law of thermodynamics as reduced entropy generation implies increased available work or exergy, and hence a possibility for a more efficient system design [45,46]. ...
Understanding the flow instabilities encountered by the turbocharger compressor is an important step toward improving its overall design for performance and efficiency. While an experimental study using Particle Image Velocimetry was previously conducted to examine the flow field at the inlet of the turbocharger compressor, the present work complements that effort by analyzing the flow structures leading to stall instability within the same impeller. Experimentally validated three-dimensional computational fluid dynamics predictions are carried out at three discrete mass flow rates, including 77 g/s (stable, maximum flow condition), 57 g/s (near peak efficiency), and 30 g/s (with strong reverse flow from the impeller) at a fixed rotational speed of 80,000 rpm. Large stationary stall cells were observed deep within the impeller at 30 g/s, occupying a significant portion
of the blade passage near the shroud between the suction surface of the main blades and the pressure surface of the splitter blades. These stall cells are mainly created when a substantial portion of the inlet core flow is unable to follow the impeller’s axial to radial bend against the adverse pressure gradient and becomes entrained by the reverse flow and the tip leakage flow, giving rise to a region
of low-momentum fluid in its wake. This phenomenon was observed to a lesser extent at 57 g/s and was completely absent at 77 g/s. On the other hand, the inducer rotating stall was found to be most dominant at 57 g/s. The entrainment of the tip leakage flow by the core flow moving into the impeller, leading to the generation of an unstable, wavy shear layer at the inducer plane, was
instrumental in the generation of rotating stall. The present analyses provide a detailed characterization of both stationary and rotating stall cells and demonstrate the physics behind their formation, as well as their effect on compressor efficiency. The study also characterizes the entropy generation within the impeller under different operating conditions. While at 77 g/s, the entropy generation is mostly concentrated near the shroud of the impeller with the core flow being almost isentropic, at 30 g/s, there is a significant increase in the area within the blade passage that shows elevated entropy production. The tip leakage flow, its interaction with the blades and the core forward flow, and the reverse flow within the impeller are found to be the major sources of irreversibilities.
An advanced numerical investigation was conducted on a tubular heat exchanger utilizing CuO-water nanofluid between 0.01% and 0.04% volume fraction to elucidate enhancements in heat transfer rate and effectiveness. The study incorporated twisted tape inserts with three distinct sweeps (5, 10, and 15) for fully developed turbulent flow conditions. The analysis explored varying mass flow rates of the hot nanofluid (0.2–0.5 kg s-1), while maintaining a constant cold fluid mass flow rate of 0.2 kg s-1. The k-ε turbulence model was employed to accurately predict heat transfer characteristics in the turbulent regime. Swirl flow analysis revealed a bifurcation of flow patterns: one proximal to the wall and another distal. Results demonstrated a linear correlation between mass flow rate and both heat transfer rate and effectiveness. Peak performance was observed at the highest flow rate, with the maximum effectiveness reaching 0.37 and the heat transfer coefficient attaining 2511 W m-2 K-1. This study provides valuable insights into the thermal performance optimization of tubular heat exchangers using nanofluid and twisted tape inserts, offering potential for significant efficiency improvements in heat transfer applications.
This paper proposes a design methodology for evaporator tubes of a steam generator by applying the entropy generation minimization (EGM) approach. A two-phase flow-based entropy generation model for steam generator evaporator tubes is developed, with coolant volume as a constraint. For a target steam generation rate, the total entropy generation of the evaporator circuit is minimized using system volume and furnace heat flux as two constraints. It is observed that for a fixed steam generation rate, with increasing evaporator diameter, the furnace height decreases while the cross-sectional area increases. The analysis reveals that for a steam generation rate of 100 kg/s and a fixed circuit volume of 47 m3, increasing the heat flux from 36 to 50 kW/m2 shifts the EGM point from an evaporator diameter of 62 mm to 84 mm, respectively. On the other hand, the minimum point shifts to a diameter of 43 mm when the heat flux is decreased to 25 kW/m2. The present study concludes that the selection of the constraint volume for designing the evaporator downcomer circuit for a target steam generation rate should be done based on the available furnace heat flux to choose the most efficient design.
In order to reduce size and cost, the heat transfer (HT) capacity of conventional heat exchanger (HE) must be increased. Addition of nanoparticles (NPs) into parent fluids is a potentially effective method of improving HT at a manageable pressure drop. The present study was focused on the comparative analysis of thermal performance factor (TPF) between CuO–water nanofluid (NF) and ZnO–water nanofluids on double-pipe heat exchanger (DPHE) at four volume fractions (0.005%, 0.02%, 0.04%, and 0.07%) in the Reynolds number (Re) range of 5500–15000. The experiment was performed for single-phase fully developed flow in turbulent regime. The maximum enhancement in Nusselt number (Nu) for CuO–water NF was observed as 12.58% higher than ZnO–water NF for volume fraction (VF) of 0.07% at Re = 5000. Maximum augmentation in friction actor was recorded for CuO–water NF as 14.55% superior than ZnO–water NF for VF of 0.07% at lowest Re of 5500. At a Re of 5500, the maximum TPF value for CuO–water NF was found to be 2.61% greater than ZnO–water NF for 0.07% of VF. In order to develop better understanding of the behaviour of NFs, ZnO and CuO-NPs were characterized in the laboratories using XRD, HRTEM, EDS, and FTIR analysis. An empirical correlation for both Nu and friction factor (ƒ) has been developed within the range of given parameters using regression analysis.
A printed circuit cooler for S-CO2 cycle is optimized by constructal design. First of all, a complex function composed of pumping power consumption and entropy generation rate is optimized. Volumes of cooler and heat transfer channel are fixed, which are used to achieve optimal heat transfer channel radius and minimal complex function. The optimized structural design of the cooler reduces overall pumping power consumption and complex function by 23.96% and 5.70%, respectively, and e entropy generation rate is increased by 12.55%. There is an optimal number of plate layers that can yield a bi-minimum complex function. Secondly, the NSGA-II is used for multi-objective optimization (MOO), dense distribution of optimal channel radius () is between 0.8 and 1.0 mm, whereas that of optimal plate layer number () is between 100 and 160. The smallest deviation index obtained by LINMAP or TOPSIS decision-making method is 0.088. In this case, and are and 144, respectively. This result can be considered the best alternative for MOO design scheme of printed circuit cooler with the objectives of entropy generation rate and overall pumping power consumption. Theoretical guidance for structure designs of printed circuit coolers can be served from constructal optimization results obtained herein.
This study investigates the heat transfer, thermal hydraulic performance, and entropy generation of turbulent flow in a horizontal double pipe heat exchanger. The heat exchanger is integrated with wire coil inserts, featuring various combinations of pitch ratios (P/Dc) and wire diameters (d), using numerical analysis. The RNG k-ε model and the finite volume technique have been utilized to solve the equations, and experimental data from published studies have been used to validate three-dimensional simulations. The computational findings have been obtained for a range of Reynolds numbers (Re) 5500 ≤ Re ≤ 11,500 using three different types of wire diameter (d = 1 mm, d = 1.5, and d = 2 mm) and pitch ratios P/Dc in the range of (3.125–0.625) for a heat flux of 5000 W m-2. The effect of these parameters on the Nusselt number, friction factor (ƒ), entropy generation number, and thermal performance factor (TPF) are investigated and compared with those of plain pipe under similar conditions. The incorporation of wire coil inserts significantly improves fluid mixing by creating a swirling flow pattern. The Nusselt number showed its highest enhancement at 111.11%, coupled with a substantial 347.8% increase in friction factor penalty with P/Dc = 0.625 and d = 2 mm at the highest Re as compared to plain tube. The highest value of the TPF recorded during the investigation was 1.36, observed at P/Dc = 0.625 and d = 2 mm, with a Re of 5500. This study also compares numerical results with experimental findings, revealing variations within a range of ± 10%.
To address energy problems in thermodynamic installations, the authors of the paper propose a working methodology in which the determining role of the exergetic aspects of the processes is especially emphasized. One of these energy problems, addressed in many papers in recent years, is of particular importance in the fight to reduce chemical and thermal pollution of the environment: the problem of storing excess energy and energy from renewable or residual sources. Approaching this issue as well from this point of view, the authors propose a series of solutions by which they seek to use the most of the exergy extracted from the available energy sources. The solutions proposed here are based on the use of an own invention, the isothermalizer , a particularly powerful tool, able to bring highly effective solutions to many of the problems that concern researchers determined to create a cleaner planet. Designers and users of thermodynamic systems now have the possibility of an initial choice and subsequent changes (with the change of external conditions), of their energy and exergetic efficiency, as well as the possibility of calculating the material and energy costs necessary to achieve the proposed objective. In any gas compression/expansion problem, the energy efficiency is established precisely, by choosing the isothermal speed of the process (so of the isothermal temperature), and the power density, by choosing the total surface of the thermal sponge, the flow rate and the mode of distribution of the cooling agent. As the isothermalizer is equipped with a processor that controls and modifies the isothermal speed in such a way that the exergy consumption is optimized, the energy storage processes become processes of extracting thermal energy from a tank and transferring it to another tank, a process accompanied by consumption/supply of mechanical energy.
The objective of this study is to determine the irreversible losses and associated entropy generation within a fluid system, considering the combined effects of magnetic field, convective boundaries, and porous media. It accomplishes this objective by a thorough investigation into the second law analysis and entropy generation of a magnetohydrodynamic (MHD) Eyring–Powell fluid flowing through a symmetric porous medium. To achieve this, the governing equations for the Eyring–Powell fluid are formulated using the conservation laws of mass, momentum, and energy, while incorporating the magnetic field’s effects. In order to account for the porous character of the medium, the equations are coupled with the Darcy model. Using appropriate computational techniques, the resulting system of partial differential equations is numerically solved. The local irreversibility ratio calculates the system’s entropy generation number, revealing its distribution. The Hartmann number and Eyring–Powell fluid parameters are also studied. The primary findings indicate that [Formula: see text] enhances velocity and diminishes temperature and entropy, while [Formula: see text] has the opposite effect. Entropy is also increased by Hartmann and Brinkman numbers, which are a result of the enhanced heat transfer and stronger magnetic fields. The findings emphasize the need and importance of studying irreversible losses and improving fluid system energy efficiency.
Purpose
Analyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.
Design/methodology/approach
The dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.
Findings
The numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.
Originality/value
This study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.
Due to the continuously increasing power density of electronic devices, the improvement of the temperature uniformity and the reduction of the irreversible energy losses became crucial in these studies on enhanced cooling capacity of the heat sinks. In this paper, a jet impingement microchannel heat sink with airfoil fins (AF‐JIMHS) is proposed. The AF‐JIMHS with reversed fins arrangement has very high comprehensive heat transfer performance. The increase of the internal tangent circle radius and chord length of fin can improve the temperature uniformity of the AF‐JIMHS bottom surface and reduce the irreversible energy losses, at the expense of reducing its comprehensive heat transfer performance. Although the increase of the tangent arc length of fin reduces the temperature uniformity and increases the irreversible energy losses of the AF‐JIMHS, it improves the comprehensive heat transfer performance in a specific parameter range. The increase of fin height improves temperature uniformity of the AF‐JIMHS, while reducing its irreversible energy losses and improving its comprehensive heat transfer performance. Compared with the AF‐JIMHS with uniform height fins, the one with decreasing height fins has higher comprehensive heat transfer performance and lower irreversible energy losses. Moreover, the AF‐JIMHS with increasing height fins has better temperature uniformity.
Se abordan las técnicas de optimización para la generación de energía en hidroturbinas, con un enfoque en algunos de los métodos metaheurísticos y el método de generación de entropía local. Entre los métodos metaheurísticos se incluyen los que se basan en las aplicaciones del algoritmo genético, el enjambre de partículas, recocido simulado, entre otros. Se discuten las ventajas y desventajas de cada método y se analiza su rendimiento en diferentes estudios en contraste con el método de generación de entropía local con el objetivo de determinar cuál método resulta el más apropiado para su utilización en una metodología de diseño.
To minimize energy loss in a greenhouse environmental system, analyzing the entropy generation within the system is crucial. Based on the established mathematical model of the greenhouse environment, entropy generation in the greenhouse environment system is analyzed, and the irreversible energy loss in the greenhouse environment system is determined by viscous flow, heat and mass transfer. In the closed greenhouse environment at night, internal temperature change is small, and total entropy generation rate is small. Under different ventilation conditions during the day, the entropy generation is mainly concentrated near the ventilation window, with larger ventilation areas leading to higher entropy generation rates.
The primary objective of the present study is to explore the novelty in the analysis of entropy generation introduced in the oscillatory flow of Jeffrey fluid through an asymmetric tapered wavy channel subjected to Lorentz force and thermal radiation. It has diverse applications in a range of disciplines: automotive elastomers in the material selection process, soft tissue mechanics modeling in biomechanics, extrusion and injection molding optimization in polymer processing, rheological test design and data interpretation in rheology. The unique nature of the tapered wavy shape in the channel and its influence on the velocity profile of MHD oscillatory Jeffrey fluid flow represents a novel element that has not been extensively explored previously. The governing equations are transformed into a system of nonlinear differential equations using non-similarity transformations. The transient system of dimensionless partial differential equations (PDEs) is solved using an implicit finite difference numerical scheme called the Crank-Nicolson method. Incorporating relevant parameters, the exact behavior of the flow with respect to velocity, temperature and volumetric rate of entropy generation is graphically depicted. The increase in entropy generation with a higher Brinkman number implies that the enhanced influence of the porous structure leads to greater irreversibility in the Jeffrey fluid flow. A comparative study is carried out to characterize Newtonian and Jeffrey fluid behavior by analyzing the velocity and temperature profiles. Finally, the findings of the current study have been compared to those of earlier studies. The comparison is seen to bear a good agreement with the existing literature.
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.
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.
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.
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.