Viorel Badescu's research while affiliated with Romanian Academy and other places
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Publications (383)
This paper presents the experimental and theoretical assessment of the thermal behaviour of a roll-bond evaporator in a small-scale household refrigerator using the refrigerant R600a as a working fluid. The experimental data were compared with a general correlation employed to evaluate the heat transfer convection (HTC) and radiation of vertical an...
Monthly averaged daily global solar irradiation data collected from four online platforms (NASA POWER, MERRA2, ERA5 and CAMS) are compared with ground measured data retrieved from World Radiation Data Center and Baseline Surface Radiation Network. Similarly, monthly averaged daily global solar irradiation estimated by five different Ångström-Presco...
The paper aims to compare and choose the most suitable criteria equation for the computation of the convective heat transfer coefficient on the refrigerant side of the evaporator. The comparison is carried out by considering a given air handling unit equipped with a specific evaporator operating with refrigerant R134a. A mathematical model is given...
The paper theorizes on the ultimate potential of the photovoltaic way of extracting work from thermal radiation. Two materials very well suited for photovoltaic energy conversion are considered: the constant energy bandgap and the graded energy bandgap materials, respectively. The common techniques of using these materials is described and quantifi...
The theory covers cases when the exergy concept is not fully relevant. An indicator called work content factor is used to quantify the proportion of available work in a given amount of energy. General expressions have been obtained for the flux of available work transported by particles, the rate of work deficiency and the work content factor. More...
A two-state model for short-term forecasting of PV plants output power (further referred as PV2-state) is proposed. PV2-state connects in an inventive way an empirical estimator for clear-sky photovoltaic (PV) power output with a statistical predictor for the sunshine number, a binary indicator stating whether the Sun shines or not. PV2-state shows...
A unified work extractor model is proposed, covering the four possible combinations of heat and radiation reservoirs. In case of heat driven work extractors the upper bounds of the conversion efficiency derived here have the Chambadal-Novikov-Curzon-Ahlborn efficiency as special case and the Carnot efficiency as a particular, ultimate upper bound l...
The physiological characteristics considered here are the weight carried by the user and the walking frequency. Since the input force is low frequency, the mechanical response of the piezoelectric stack may be neglected and a model based on a first order differential equation is developed. Direct optimal control techniques are used. Three objective...
The Ångström–Prescott equation defines generically the relationship between solar energy available at ground level and sunshine duration. From the very beginning in the history of the solar energy converters, the equation was extensively used to estimate the amount of collectable solar energy. In the present paper, we propose a different way of loo...
A general formalism is developed to evaluate the amount of work extractable from energy fluxes. It covers nonequilibrium cases when the concept of exergy is not relevant. The rate of work deficiency, which has been previously introduced as the total loss of exergy, is defined here as the total loss of work, which would have resulted if all the work...
The ignition delay is an important parameter which characterizes the initiation of combustion process and consequently its development in Diesel engines. This parameter mainly depends on chemical factors which are related to the fuel structure and its properties and also on physical factors which are related to the engine operating conditions. The...
The effective operation time of unglazed transpired collectors (UTCs) may be extended by double pass (descending and ascending) air flow and by energy storage in phase change materials (PCMs). The transient operation of a hybrid UTC is described by using an original 3D model. The model has been verified and calibrated against measurements obtained...
Solar cells have over 50-years of development history; many different devices and technologies are studied over this time span, and interestingly it is still a hot research topic. Although the physical mechanisms involved in photovoltaic processes are rather fundamental, the characterization and classification of the research pathways seem complica...
The complex time-dependent heat and electromagnetic energy transfer in a new type of reverse thermal engine is analyzed. The reverse thermal engine consists of a cold body, a Peltier element and an electric circuit containing an inductor with controllable inductance. This system allows cooling a body below the ambient temperature. The inductor acts...
The operational performance of small-scale refrigeration systems is mainly decided by their capillary tubes outlet parameters, wherein an accurate determination of the pressure and vapour quality is a prerequisite. Experiments have been performed for a capillary tube (CT) with specified geometry consisting of a straight, a helical and a suction lin...
A household refrigerator is a major energy consumer in all homes. The paper aims to evaluate based, on experimental data, the COP of a 65-liter household refrigerator operating with R600a. The main components and instrumentation of the experimental setup are presented. A mathematical model based on the energy balance of the refrigerated enclosure i...
The equilibrium of the electricity grid is very often changing due to demand fluctuations and it is further threatened by the fluctuation in the output of solar power plants. With the aim of increasing the share of solar electricity in the energy mix, near real-time forecasting of the solar power production represents a key issue for smart-control...
Elementary concepts about the thermodynamics of undiluted and diluted thermal radiation are introduced. Solar direct and diffuse radiation, respectively, are particular cases of the general theory. The mathematical description of reversible solar radiation concentration is developed by using a simple formalism based on the Lagrange invariant (the é...
This paper presents a mathematical model to simulate the effect of the coiling diameter, subcooling degree and internal diameter on the characteristics flow of the refrigerants R1234yf and R600a, flowing through an adiabatic helical capillary tube. The homogeneous flow model was developed in the two-phase region based on the fundamentals of conserv...
The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing sub- domain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic...
With all the progress made in atmospheric modeling, the cloud field parameterization is still a critical issue. The present study proposes a new model for the probability of a clear-line-of sight (PCLOS). The great benefit of the proposed model is in the estimation of the effective cloud field parameters (namely, the cloud aspect ratio and cloud fa...
Shape optimization of slider bearings operating with couple stress lubricants is performed here for the first time by using a novel direct optimal control approach, which defines the gradient of the film height as a control. The bearing load is maximized. One dimensional Reynolds and energy equations are used. Several constraints are taken into con...
![Figure 2: Monthly averaged day-ahead GHI forecast errors-RMSE [W/m 2 ]...](profile/Dazhi-Yang-3/publication/341466924/figure/fig1/AS:893508693016576@1590040481720/Monthly-averaged-day-ahead-GHI-forecast-errors-RMSE-W-m-2-and-nRMSE-normalized-by_Q320.jpg)
The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing subdomain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic (a...
To argue the need to extend the use of solar collectors on large-scale and integrate them into residential, industrial or industrial buildings, we start from the analysis of the solar energy for the eastern area of Europe, particularly Romania. The work analyses the global solar irradiation by average monthly values and the sunshine duration, based...
The design and steady‐state operation of a packed bed reactor with tubular geometry is optimized. Direct optimal control methods are used. Two objective functions are considered: (i) minimization of the ammonia mass fraction at reactor outlet and (ii) minimization of the heat flux necessary to reach a predefined value of the ammonia mass fraction a...
The complex time-dependent heat and electromagnetic energy transfer in a new type of cooling system is analyzed. The system consists of a cold body, a Peltier element and an electric circuit containing an inductor with controllable inductance. This system allows cooling a body below the ambient temperature without using an external reservoir of mec...
The sunshine duration data is analysed here from a new perspective, different from the traditional ones. The study is focused on pairs of periods of shining sun (called clear periods) followed by periods with the sun covered by clouds (called dark periods). Their statistical and sequential properties are illustrated by using results obtained from s...
The global trend is to increase the thermal comfort in all kinds of buildings, residential and non-residential. At the same time, minimization of energy consumption and improved building sustainability must be achieved. Only precise calculations can keep the balance between maximizing comfort and minimizing energy consumption. The PassivHaus (PH) i...
Distributed power generation may become an important segment in the energy sector in Iraq. The main objective of this paper is to estimate the potential of heat recovery from the Internal Combustion Engines (ICE) driving electric generators in Iraq. The heat recovery solution considered here is based on Organic Rankine Cycles (ORCs). A model has be...
![Figure 2.The Ryukyu pit seen on Google Earth [Google Earth software]](publication/337815012/figure/fig2/AS:833464379133954@1575724801725/The-Ryukyu-pit-seen-on-Google-Earth-Google-Earth-software_Q320.jpg)
The research purpose is to present the possibility to deposit the carbon dioxide clathrate at the ocean bottom near Japan. As it is well known, a big amount of CO 2 is produced nowadays, with a very damaging influence on the climate. These effects can already be seen all around the world. A possible solution to get rid of the CO 2 surpluses is to l...
A new type of unglazed transpired collector (UTC) incorporating phase change materials (PCMs) is presented. A time-dependent model consisting of eight 1D PDEs is derived from basic principles. Mass, momentum and energy balance equations for air flow are derived ab initio from the general transport theorem for air movement, by including mass sources...
A large number of electric generators driven by Internal Combustion Engines (ICEs) are in operation in developing countries where the national electric energy transport infrastructure is poor. An ORC-based system is considered here for heat recovery from such ICEs which in practice operate under partial load and in time-dependent conditions. A crit...
This study is focused on modeling the morphological properties of cloud fields by the instrumentality of the probability of a clear line-of-sight (PCLOS). Depending on the assumed effective cloud geometry, PCLOS is expressed by different power functions of zenithal angle and cloud field parameters. Generally, the equations are very complicated and...
The paper presents an analysis of the solar irradiation and the stability of the solar radiative regime, available for Bucharest and the southern area of Romania. The study is based on meteorological data measured at 3.6 seconds, on several consecutive days of each season, in the years 2017 and 2018. Data acquisition was performed at Technical Univ...
The first objective of this paper is to prove that for the same amount of incident solar irradiation, the amount of useful heat provided by a solar air collector is different during time intervals with stable and unstable radiative regimes, respectively. A simple one-node model is used to analyze the performance of two solar air collectors with sim...
The paper deals with waste heat recovery (WHR) from internal combustion engines (ICE) using organic Rankine cycle based systems (ORC), due to its ability to operate with moderate temperature differences. The waste heat source is flue gas from an ICE that drives a stationary electric generator. The configuration of the ORC system is the basic one. T...
Proper knowledge of the I-V characteristics of a PV module is a key requirement for accurate estimation and forecast of energy production. By using the scarce information provided in the manufactures’ datasheet (short circuit current, open circuit voltage and the maximum power point), the mathematical description of the I-V characteristic is always...
Controlled autoignition delay is considered a very promising new technology, having the potential of combining low fuel consumption with low pollutant emissions. In this study, the effect of pure diesel fuel and biodiesel B20 (20% rapeseed oil mixed with 80% diesel fuel, by volume) on ignition delay period, at different engine speeds, under full lo...
This paper presents models/strategies for optimum performance of solar collector in closed loop systems. These models aim to maximize the obtained energy by thermal conversion of solar energy. The mass flow rate of the fluid from the primary circuit of the system is the control parameter. The semi empirical models and optimal control methods are in...
Solar radiation at ground level may be modeled as diluted thermal radiation. Two upper bounds are obtained for the efficiency of converting the energy of diluted radiation into work. They depend on the dilution factor and the geometric factor of the radiation reservoir and on the nature of the absorber (i.e. absorptance, emittance, geometric factor...
Adaptive thermal comfort refers to the ability that the occupants of a building have to accustom themselves to specific thermal conditions. The notion of human thermal comfort (HTC) is therefore introduced and defined by a simple mathematical equation. In the evaluation process of actual buildings and in the design of new ones, adaptive HTC equatio...
![Cloud shade (CS) vs point cloudiness (PC¯\documentclass[12pt]{minimal}...](publication/318159860/figure/fig5/AS:960317349711872@1605968906066/Cloud-shade-CS-vs-point-cloudiness-PCdocumentclass12ptminimal_Q320.jpg)
Clouds play a key role in establishing the Earth’s climate. Real cloud fields are very different and very complex in both morphological and microphysical senses. Consequently, the numerical description of the cloud field is a critical task for accurate climate modeling. This study explores the feasibility of retrieving the effective cloud field par...
This study aims to integrate in constructal networks of heat exchangers (HEXs) two ways of optimization: entropy generation minimization and thermoeconomics. We obtained a complete (non-simplified) analytic solution of the entropy generation along of the HEX that allows exact evaluation of the irreversible processes in smooth or augmented tubes. By...
The objective of this paper is to investigate the effect of simultaneous using of nanofluid and selective absorber on the improvement of work extraction by a solar flat-plate collector (FPC). Applying a precise model for the exergy factor of solar incident, it is found that the maximum power generation is higher and lower than that by the Petela-Land...
A new formula has been proposed for the Landsberg–Tonge function \chi (\varepsilon ) entering the entropy density flux of the diluted blackbody radiation of dilution factor ε . Two models have been proposed for the conversion of diluted blackbody radiation energy into work. The Carnot and Petela–Landsberg–Press relationships do not provide accurate...
This article considers a new type of air infiltration through building envelopes caused by the barometric pressure variation. This process is independent from wind action or stack effect. A new building–atmosphere differential equation of air exchange is established. Based on the solution of the differential equation of air exchange, we propose the...
As long as human activity requires much energy, a large amount of CO2 is produced. The World Meteorological Organization announced that in 2016 the CO2 concentrations in atmosphere reached a new record. This is the highest growth in the last 30 years, based on measurements performed in 51 countries. The growth concentration is with 50% higher than...
This paper is focused on modeling the morphological properties of the cloud fields in terms of the probability of a clear line of sight (PCLOS). PCLOS is defined as the probability that a line of sight between observer and a given point of the celestial vault goes freely without intersecting a cloud. A variety of PCLOS models assuming the cloud sha...
The ignition delay period for a compression ignition engine fueled alternatively with pure diesel and with biodiesel B20 has been experimentally and numerically investigated. The engine was operated under full load conditions for two speeds, 1400 rpm speed for maximum brake torque and 2400 rpm speed for maximum brake power. Different parameters sug...
The focus of this study is on the properties of consecutive intervals consisting of pairs of clear periods (the Sun is shining) and dark periods (the Sun is obscured by clouds). Namely, the distribution of the duration length of clear and dark periods is studied and illustrated with results obtained for the climatic regime of Timisoara (Romania, Ea...
National and international adaptive thermal comfort (ATC) standards gain now wider acceptance. These standards propose adaptive comfort equations derived from specific databases. New ATC equations are developed worldwide, under different latitudes and climates. A field survey has been performed in 2013–2014 in six naturally ventilated buildings loc...
The aim of this work is to analyse the performance of a solar energy collector system for water and air heating in real working conditions. Two coupled mathematical models have been developed. One of them describes the thermal behaviour of the Hybrid Solar Collector (HSC) and the second one describes the simultaneous operation of the HSC and of a f...
Biodiesel is one of the biodegradable and renewable fuels, which is originated from vegetable oil or animal fats. Rapeseed biodiesel is a kind of biofuel which is gaining acceptance in the market due to many environmental and economic benefits. It can be used alone or in a blend with Diesel fuel, directly in compression ignition engines, without...
An experimental and numerical study was performed to investigate the impact of Biodiesel B20 (blends 20% Rapeseed methyl ester with 80 % Diesel volumetric fraction) and different energetic fractions of hydrogen content (between 0 and 5%) on the mixture formation, combustion characteristics, engine performance and pollutant emissions formation. Expe...
This study aims to integrate in constructal networks of heat exchangers (HEXs) two ways of optimization represented by entropy generation minimization and thermoeconomics. We obtained a complete (non-simplified) analytic solution of the entropy generation along of the HEX that allows exact evaluation of the irreversible processes in smooth or augme...
This paper refers to recovering waste heat from the hot gases exhausted by internal combustion engines (ICEs) driving electric generators (EGs) at full and partial load. The topic is of particular interest for developing countries where electric grids are underdeveloped or missing and electricity is generated locally by using classical fuels. The h...
Ground-based meteorological observations are used here as proxy data, as well as aerosol reanalysis estimates
for training, to reconstruct aerosol optical depth (AOD) time series over Romania during a multidecadal period (1961–2015).
The approach uses sunshine duration fraction (SDF) data computed for cloudless summer days (identified from 6-hourly...
This paper proposes a new extended power law (EPL) of air infiltration in buildings as an alternative in certain cases to the widely used power law (PL) and quadratic law (QL). Specifics: it separates the airflow rates in laminar and turbulent components; improves the estimation of the leakage area; new evaluation of the airflow rate at low pressur...
This paper makes an analysis of the optimal operation of the systems with flat solar collectors in closed circuit, to convert the solar energy in thermal energy - hot water (DHW – domestic hot water), by comparing the various models from the literature. To improve the performance of thermal solar collectors, we follow to maximize the energy as: (i)...
This chapter presents a number of concepts and methods of differential calculus which are important by themselves, being, however, applicable both in variational calculus and in optimal control theory. Only the case of functions of real variables is considered here. Natural and exact sciences are based on functional relationships between different...
Direct and indirect optimal control methods are used. Two different objective functions are considered. First, the transferred heat flux is maximized and the resulting optimal pin fin shape is a cylinder. Second, the pin volume is minimized for given value of the heat flux. Then, the optimum pin fin profile consists of two regions. In the first reg...
This chapter refers to thermal energy storage (TES) systems based on fully mixed and stratified liquid storage tanks. The performance indicator adopted here is the minimum exergy destruction. All relevant irreversibility sources are considered. Every operation regime has an optimum charging time, which increases by decreasing the hot gas inlet temp...
Dynamic programming is a popular optimization method. It can be used to solve a large diversity of issues, ranging from common optimization problems to complex optimal control problems. A brief introduction into dynamic programming is presented in this chapter.Dynamic programming
is one of the most popular optimization methods. Its wide usage is ex...
This chapter makes the transition from classical variational calculus to optimal control. Section 4.1 defines a set of often used general notions. Section 4.2 shortly presents various ways of formulating optimal control problems and the main methods used to solve them. Some qualitative characteristics of these methods, accompanied by comparisons an...
A general method able to meet the technical requirements of the process control has been developed between 1956 and 1960 by L.S. Pontryagin and his collaborators. The theory based on this method is presently considered the most powerful mathematical tool that can be used to solve optimal control problems with constraints expressed by ordinary diffe...
Variational calculus (also called calculus of variations) deals with extremization of those maps whose definition domain is a space of infinite size, sometimes called curves space or functions space. The maps of this type are called functionals. In general, functional is called any mapping of the functions space on the real straight line. This chap...
Endoreversible heat engines are endoreversible heat machines which convert heat into work. An optimal control model is presented in this chapter for a class of endoreversible heat engines.
Two procedures to derive the optimal steady state operation of heat exchangers are presented. The first procedure, which is based on the calculus of variations, can be used in case the optimization criterion is minimum entropy generation. The second procedure can be used in principle for any optimization criterion. Both procedures show that, whatev...
Closed loop flat-plate solar collector systems are considered. The water storage tank operates in fully mixed regime. An indirect optimal control technique based on Pontryagin’s maximum principle is implemented. The optimal operation strategy involves two-steps up and down jumps between zero and a maximum allowable fluid flow rate in the primary ci...
Optimal slider bearing profiles for maximum bearing load are studied by using direct constrained optimal control techniques. Technological constraints such as the maximum lubricant pressure and temperature and the minimum lubricant film thickness are included into the model. The realistic problem considered here yields optimal bearing profiles whic...
A rather involved flat-plate solar collector model is used. The width and thickness of fins is optimized by minimizing the cost per unit useful heat flux. Fins of both uniform and variable thickness are considered. In case of fins with uniform thickness, the optimum distance between tube centre decreases by increasing the operation temperature, whi...
The main difficulty that arises in practice is that the optimal control is not expressed as a function of the measurable state variables of the system. A practical way of implementing the strategy of optimal flow control is discussed in this chapter.
The gradient method
belongs to the
direct optimization methods
, characterized by the fact that the extreme is found without any prior indication of the necessary existence conditions. Several results which refer to the first order approximation of the gradient method are presented in this chapter. The complexity of the treatment is gradually incre...
Three solar energy applications are considered. Procedures for sizing and optimizing the structure of solar collection systems are proposed. Four economical indices, including net present value and internal return rate, are given as examples of objective functions. In the case of solar collectors with uniformly distributed parameters, the procedure...
The optimal control of Diesel engines is shortly treated in this chapter. The forces of friction, the heat losses and the fuel burning at finite speed are taken into consideration. The piston movement that leads to maximum power supply is determined, for both bounded and unbounded acceleration.
The best operation strategies for open loop flat-plate solar collector systems are considered. A detailed collector model and realistic meteorological data from both cold and warm seasons are used in applications. The maximum exergetic efficiency is low (usually less than 3%), in good agreement with experimental measurements reported in literature....
Four objective functions are shortly presented and minimized. They include the consummated cooling fluid mass and some dissipation measures, such as the entropy generation and the lost available work. Cooling processes are wildly used in metallurgy, chemical industry and other activities traditionally covered by thermal engineering, but also in ele...
In this chapter the piston motion of a Daniel cam engine is optimized. Piston acceleration is taken as a control. The objective is to maximize the net output work during the compression and power strokes. A thermally insulated cylinder is considered and a realistic model taking into account the cooling system is developed. The sinusoidal approximat...
Seasonal accumulation of solar thermal energy (i.e. the storage in summer for consumption during winter) shows great advantages at large latitudes. Such seasonal storage systems are characterized by the solar collector type, its surface orientation and its efficiency, the heating requirements of the user, the storage capacity, the soil properties a...
In this chapter a system of uniform temperature in contact with a thermal bath must be heated in a fixed time interval. Several ways of defining the lost work associated with the heating process are presented. The minimum entropy generation is generally not equivalent to the minimum lost available work. Two optimal control problems are defined and...
Photochemical engines are based on the existence of a working fluid in which photochemical reactions take place. In this chapter, an engine model based on a bi-molecular photochemical reaction is presented.
The paper focuses on a Joule cycle reciprocating Ericsson engine (JCREE) coupled with a solar parabolic trough collector (PTC). A small scale application located at mid Northern Hemisphere latitude (44°25″N) is considered. A new dynamic (time-dependent) model is developed and used to design the geometry and estimate the performance of the PTC-JCREE...
A parametric model of the pin fin shape has been developed. The pin fin profile optimization is performed without adopting the “length-of-arc” approximation. The model is based on the accurate treatment of the arc length. The heat transfer coefficient h is not constant but variable along the length of the pin fin. The objective is to minimize the p...
The dependence of the daily photothermal conversion performance on the stability of the radiative regime has been rarely treated in literature and only for systems based on water collectors. The objective here is to estimate whether the daily performance of solar air collectors is dependent on the radiative regime characteristics other than the lev...
Human thermal comfort (HTC) embraces two major approaches, Fanger or classical theory and an adaptive one. Adaptive HTC equations make up parts of the worldwide recognized thermal comfort standards. The balance between thermal comfort and energy saving is held by the adaptive approach of thermal comfort. The use of adaptive HTC equations in the eva...
Two advanced models for forecasting the output power of photovoltaic plants are discussed in details: a black-box Takagi-Sugeno fuzzy model and a physically inspired, semiparametric statistical model (Generalized Additive Model, GAM) based on smoothing splines. The structure of the two models, their strengths and weaknesses, are presented. The mode...
Biodiesel produced from rapeseed oil considered one of promising option in Romania for compression ignition engines due to the higher level of productions and environmental friendliness. In this work, biodiesel B20 is prepared from rapeseed oil (blends 20% Rapeseed methyl ester with 80 % Diesel volumetric fraction). The fuel is tested on a direct i...
In the current study, the ignition delay period for a compression ignition engine fueled with Diesel and biodiesel B20 at engine speeds 1400 rpm and 2400 rpm under full load operating conditions has been experimentally identified. The experimental results of Diesel fuel are compared with the ignition delay predict by four known correlations, while...
In this paper we investigate whether, and to what extent, the radiative regime has an influence on the performance of a solar domestic hot water system. We compared the results of two mathematical models (a more accurate model with stratification in the storage tank and a simple, less accurate, fully mixed model), simulating the dynamic behaviour o...
In times of great transition of the European construction sector to energy efficient and nearly zero energy buildings (nZEBs), a market observation containing qualitative and quantitative indications should help to fill out the enormous information gaps concerning the EU 2020 carbon targets. Next to the economic challenges, there are equally import...
This paper presents a review of exergy analysis of solar thermal collectors and processes. It includes not only various types of solar collectors, but also various applications of solar thermal systems. Initially the fundamentals of second law analysis are briefly presented as well as the exergy of solar radiation, which is the input to any solar s...
This study proposes engine model to predicate the performance and exhaust gas emissions of a single cylinder four stroke direct injection engine which was fuelled with diesel and palm oil methyl ester of B7 (blends 7% palm oil methyl ester with 93% diesel by volume) and B10. The experiment was conducted at constant engine speed of 3000 rpm and diff...
Entropy generation of 3D cross sections circular, square, and hexagon shapes microchannel heat sinks (MCHS) were numerically performed. The governing equations (continuity, momentum and energy) along with the boundary conditions and the study state conjugate heat transfer problem were solved using the finite volume method (FVM). The Reynolds number...