Minimum Entropy Generation Rate Research Articles

Role of entropy generation minimization in thermal optimization**Project supported by the National Natural Science Foundation of China (Grant No. 51376101) and the National Natural Science Fund for Creative Research Groups, China (Grant No. 51621062).

Thermal optimization is very important for improving the performances of thermal systems. In engineering, the entropy generation minimization (EGM) has been widely used to optimize and evaluate the performances of thermal systems. However, the consistency between the EGM and the optimization objective should be specified when the EGM is used. In this paper, we discuss the view angle of irreversibility of entropy generation, and show that entropy generation directly reflects the exergy destruction or the ability loss of doing work. As the design objective in a thermal system is not often consistent with the view angle of irreversibility of entropy generation, the EGM may not lead to the optimal value of the design objective. In heat transfer and heat-work conversion, the inconsistence between the design objectives and the EGM is shown with some examples, and the applicability of the EGM is found to be conditional. The “entropy generation paradox” in heat exchanger analyses is also discussed, and it is shown that there is no direct monotonic relation between the minimum entropy generation rate and the best heat transfer performance of heat exchangers.

Entropy generation minimization of steam methane reforming reactor with linear phenomenological heat transfer law

This paper investigates a class of tubular plug flow steam methane reforming reactor coupling among heat exchange, fluid flow and chemical reaction, in which the heat transfer between the heat reservoir outside the conversion tube and the reactants inside the tube is assumed to obey the linear phenomenological heat transfer law [ q ∝ Δ ( T − 1 ) ]. Under the condition that all of the hydrogen production rate, the inlet pressure, the total inlet molar flow rate, the inert gas (N2) molar flow rate are given, and the reservoir temperature is assumed to be controllable completely, both the minimum entropy generation rate of the process and the corresponding optimal reservoir temperature profile are obtained for minimizing the total entropy generation due to heat transfer, fluid flow and chemical reaction and by applying the theory and method of finite time thermodynamics with the help of nonlinear programming method. The obtained results are also compared with other two classes of reference reactors under the heat transfer strategies of constant and linear reservoir temperature operations and the optimization results for the minimum entropy generation of the case with Newtonian heat transfer law [ q ∝ Δ ( T ) ]. The results show that compared to the two classes of the reference reactors, optimizing the reservoir temperature profiles could reduce the entropy generation by more than 58%, which is mainly due to the decrease in the entropy generation caused by heat transfer; a shorter reactor may perform equally well, and the optimal path shows immediate regions of either a constant thermal force or a constant chemical force; heat transfer laws have significant effects on the optimal temperature configurations of both the heat reservoir and the reaction mixture for the minimum entropy generation of the chemical reactor.

The entropy generation rate minimization for a proposed air ejector for the carpet industry

In this study, a numerical model is developed to simulate an air ejector pump that is proposed for the carpet industry. Simulations have been performed by solving the compressible, steady-state, two-dimensional Reynolds-averaged Navier–Stokes equations, and k–e Realizable model is used to simulate a turbulent flow. A comparison of the computed results with the published experimental data is presented. The total entropy generation rate distribution provides designers with useful information about the causes of the flow irreversibility. As an objective, the total entropy generation rate is introduced as a design criterion parameter for an air ejector and compared with the entrainment ratio criterion. Results are shown, the main sources of entropy are mixing, and normal shock is developed in the mixing chamber and diffuser. The optimum ejector geometry parameters of an air ejector, based on the maximum entrainment ratio and the total entropy generation rate minimization, are in agreement, and the optimal converging angle of the mixing chamber, length of the mixing chamber, diameter of primary nozzle, and outlet diameter of the diffuser are θ = 2.8°, L m = 40 mm, d p = 1 mm, and d d = 12.6 mm, respectively.

Optimization of heat sink of thermoelectric cooler using entropy generation analysis

In the present study, an optimization model is developed for a thermoelectric cooler (TEC) based on the entropy generation minimization method. In the model, the total entropy generation rate, the entropy generation number and the exergetic efficiency are proposed as optimization objective functions, respectively, while the number of transfer units of the heat sink is considered as a constraint. The heat capacity rate of cooling fluid in the heat sink is optimized under other given conditions. The results show that a minimum total entropy generation rate and a minimum entropy generation number can be achieved by optimally selecting the heat capacity rate of the cooling fluid. In addition, the minimum total entropy generation rate and corresponding optimal heat capacity rate of the cooling fluid are both dominated by the number of transfer units and the electrical current. Furthermore, the effects of the heat capacity rate of cooling fluid and the electric current in terms of the exergetic efficiency are also evaluated.

Entropy Generation Analysis of Natural Convection in Square Enclosures with Two Isoflux Heat Sources

This study investigates entropy generation resulting from natural convective heat transfer in square enclosures with local heating of the bottom and symmetrical cooling of the sidewalls. This analysis tends to optimize heat transfer of two pieces of semiconductor in a square electronic package. In this simulation, heaters are modeled as isoflux heat sources and sidewalls of the enclosure are isothermal heat sinks. The top wall and the non-heated portions of the bottom wall are adiabatic. Flow and temperature fields are obtained by numerical simulation of conservation equations of mass, momentum and energy in laminar, steady and two dimensional flows. With constant heat energy into the cavity, effect of Rayleigh number, heater length, heater strength ratios and heater position is evaluated on flow and temperature fields and local entropy generation. The results show that a minimum entropy generation rate is obtained under the same condition in which a minimum peak heater temperature is obtained.

EDITORIAL

The editorial of Engenharia Térmica of this issue continues the discussion on scientific research needs in vital areas in which thermal engineering has important participation. The main goal is to motivate the readers, within their specialties, to identify possible subjects for their future research. Extensive research efforts have been devoted to the development of high performance heat sinks, and numerous geometric designs and fin arrangements as well as materials have been proposed to achieve higher heat dissipation rates. Previous studies have deduced different fin geometries and arrangements based on minimum entropy generation or maximum heat transfer rate, subject to various constraints such as available space, material, or cost. Consequently, many fin shapes and arrangements exist in literature ranging from elliptical cylinders to rhombus, and from pin to flared fin, respectively. According to the literature review, however, helical fins have not yet been explored as an alternative design owing to its complex geometry that restricts the analysis to 3D space. Therefore, a 3D helical fin model still needs to be developed to investigate its feasibility and performance as an alternative fin design. In addition, a helical fin arrangements optimization study shall be conducted for minimum pressure drop and maximum heat transfer. The mission of Engenharia Térmica is to document the scientific progress in areas related to thermal engineering (e.g., energy, oil and renewable fuels). We are confident that we will continue to receive articles’ submissions that contribute to the progress of science.

Effect of Conjugate Heat Transfer on Entropy Generation in Slip-Driven Microflow of Power Law Fluids

ABSTRACTWe analyze the entropy generation characteristics in a non-Newtonian microflow under the influence of interfacial slip as modulated by the conjugate transport of heat. We consider power law model to represent the constitutive behavior of the non-Newtonian fluid. In this analysis, we analytically solve the transport equations employing the thermal boundary condition of the third kind at the exterior wall surface accounting for the effect of conjugate heat transfer. We demonstrate that the slip flow–driven alteration in convective transport of heat and its nonlinear interaction with viscous dissipation, as modulated by fluid rheology and conjugate transport of heat, gives rise to a minimum entropy generation rate of the system. We determine the optimum value of the geometrical parameter—that is, the channel wall thickness and the thermophysical parameters, such as the Biot number and Peclet number—leading to a minimum entropy generation rate in the system. The results of this analysis could be of helpful in designing microsystems/devices typically used for electronic cooling, micro-heat pipes, and micro-heat exchangers.

Determining the Optimum Inner Diameter of Condenser Tubes Based on Thermodynamic Objective Functions and an Economic Analysis

The diameter and configuration of tubes are important design parameters of power condensers. If a proper tube diameter is applied during the design of a power unit, a high energy efficiency of the condenser itself can be achieved and the performance of the whole power generation unit can be improved. If a tube assembly is to be replaced, one should verify whether the chosen condenser tube diameter is correct. Using a diameter that is too large increases the heat transfer area, leading to over-dimensioning and higher costs of building the condenser. On the other hand, if the diameter is too small, water flows faster through the tubes, which results in larger flow resistance and larger pumping power of the cooling-water pump. Both simple and complex methods can be applied to determine the condenser tube diameter. The paper proposes a method of technical and economic optimisation taking into account the performance of a condenser, the low-pressure (LP) part of a turbine, and a cooling-water pump as well as the profit from electric power generation and costs of building the condenser and pumping cooling water. The results obtained by this method were compared with those provided by the following simpler methods: minimization of the entropy generation rate per unit length of a condenser tube (considering entropy generation due to heat transfer and resistance of cooling-water flow), minimization of the total entropy generation rate (considering entropy generation for the system comprising the LP part of the turbine, the condenser, and the cooling-water pump), and maximization of the power unit’s output. The proposed methods were used to verify diameters of tubes in power condensers in a200-MW and a 500-MW power units.

Non-linear drag induced irreversibility minimization in a viscous dissipative flow through a micro-porous channel

We focus on the entropy generation minimization analysis associated with the thermo-fluidic transport of a Newtonian fluid through a hyper-porous channel formed between two asymmetrically heated parallel plates. Employing an analytical method, which is consistent with the perturbation analysis, we solve the governing transport equations taking the effects of nonlinear Forchheimer drag and conjugate heat transfer into account. We also invoke to the thermal boundary conditions of third kind at the outer boundaries of channel for the conjugate analysis of heat transfer. We bring out the alterations in the entropy generation rate in the system as attributable to the nonlinear interactions between the heat transfer rate as modulated by the fluid temperature, temperature gradient, the dissipative heat originating from the non-linear Forchheimer drag, Darcy frictional effect and the viscous shearing stress in the flow field. Also, we unveil optimum values of wall thickness, wall to fluid conductivity ratio and other thermophysical parameters, leading to a minimum entropy generation rate in the system for a given set of the other different parameters considered. We believe that the inferences obtained from this analysis may improve the design and optimization of thermodynamic systems/devices typically used in different engineering applications.

Analysis of Entropy Generation Minimization in Radial Heat Sink

Background/Objective:In this paper, an entropy generation rateof a radial flow type heat sink model has been investigated and its minimization is the primary aim of this study to exhibit the overall performance of the model. Methods/Statistical Analysis: The entropy generation method (EGM), which is one of the best modeling and optimization approach, has been used to optimize the parametric variable of the heat sink. In this study, a numerical iterative technique of Newton-Raphson method has been employed to solve the multiple nonlinear equation system which occurred in the analysis. Findings:The optimization was conducted to study the effects of the number of fins, thermal resistance of the heat sink and the approach velocity on the rate of entropy generation for the heat sink model. From the optimized results of the model, the number of fins, N ≈ 55 was estimated for the minimization of entropy generation rate, and its effect on the thermal resistance of the heat sink was also observed. The variation of the entropy generation rate and the number of fins at a different approach velocity were reported in this analysis, and also,three-dimensional surface plotis created by the surf command in MATLAB software. Application/Improvements: The entropy generation minimization method was employed to exhibit the overall performance of the optimized heat sink model and its application is more advantageous in the illumination industry.

Constructal entropy generation rate minimization for cylindrical pin-fin heat sinks

Optimization of in-line cylindrical pin-fin heat sinks (PFHS) is carried out by using constructal theory and entropy generation minimization (EGM) theory for fixed total heat sink volume and fin-material volume. The optimal constructs of cylindrical pin-fin are obtained by taking the minimum entropy generation rate (MEGR) as objective, and the influences of fin-material fraction, heat transfer load (HTL) of the heat sink and the fluid velocity on the optimization results are studied. It is shown that there exists optimal diameters makes the EGR minimized for the fixed shape of the heat sink; the MEGR decreases, the corresponding optimal diameter and number of cylindrical pin-fin increase as the fin-material fraction increases; the MEGR increases, the corresponding optimal diameter and number of cylindrical pin-fin decrease as the HTL and the fluid velocity increase, respectively; when the shape of the heat sink can be morphed freely, the MEGR increases as the aspect ratio of the heat sink increases, and the corresponding optimal geometric parameters are different, which means there is no quadratic optimal constructs for the heat sink by taking MEGR as optimal objective. That is the less MEGR can be obtained by choosing the more fin-material fraction, the lower fluid velocity and the smaller aspect ratio of the heat sink in allowed range. The results can provide theoretical support for the MEG optimization design of in-line cylindrical PFHS.

Selecting the cooling water mass flow rate for a power plant under variable load with entropy generation rate minimization

The paper deals with selecting the mass flow rate of cooling water under variable load of a power unit such that optimum operating parameters of the unit can be achieved. The change in the cooling water mass flow rate influences the resistance to flow (on the cooling water side) and the pressure of the condensing steam. A higher cooling water mass flow rate increases the resistance to flow and power supplied to the cooling water pump, but it also results in a drop in the condensing steam pressure and an increase in the power generated in the LP (low-pressure) part of the turbine. Since the change in the mass flow rate affects the performance of the condenser, the LP part of the turbine, and the cooling water pump, a system comprising these components was analyzed. The cooling water mass flow rate was chosen via minimization of the total entropy generation rate in these components and a change in the unit's power output defined as a difference between the power outputs of the LP part of the turbine and the cooling water pump. The aim of this paper is to find the optimum value of the mass flow rate of cooling water under variable load of the power plant.

Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation

Combined effects of hydrodynamic slip, magnetic field, suction/injection, thermal radiation, nanoparticle volume fraction and convective boundary conditions on the heat transfer and global entropy generation in a viscous electrically conducting nanofluid flow through a microchannel with permeable plates are studied. Analytical solutions of the momentum and the energy equations are obtained in closed form. Particularly, considering the radiative term, joule heating and viscous dissipation in the energy equation, the temperature field of the nanofluid is derived analytically. Influences of pertinent parameters on global entropy generation are discussed in detail and depicted graphically. Analysis of our results indicates that entropy generation minimization can be achieved by appropriate combination of the geometrical and physical parameters of the system. It is possible to determine optimum values of radiation parameter, nanoparticle volume fraction, Hartmann and Biot numbers which lead to a minimum global entropy generation rate. The Nusselt number is also calculated and explored for different conditions. Optimum values of nanoparticle volume fraction and magnetic field strength that maximize heat transfer are derived.

The equivalence of minimum entropy production and maximum thermal efficiency in endoreversible heat engines

The objective of this study is to investigate the thermal efficiency and power production of typical models of endoreversible heat engines at the regime of minimum entropy generation rate. The study considers the Curzon-Ahlborn engine, the Novikov’s engine, and the Carnot vapor cycle. The operational regimes at maximum thermal efficiency, maximum power output and minimum entropy production rate are compared for each of these engines. The results reveal that in an endoreversible heat engine, a reduction in entropy production corresponds to an increase in thermal efficiency. The three criteria of minimum entropy production, the maximum thermal efficiency, and the maximum power may become equivalent at the condition of fixed heat input.

Maximum production rate optimization for sulphuric acid decomposition process in tubular plug-flow reactor

A sulphuric acid decomposition process in a tubular plug-flow reactor with fixed inlet flow rate and completely controllable exterior wall temperature profile and reactants pressure profile is studied in this paper by using finite-time thermodynamics. The maximum production rate of the aimed product SO2 and the optimal exterior wall temperature profile and reactants pressure profile are obtained by using nonlinear programming method. Then the optimal reactor with the maximum production rate is compared with the reference reactor with linear exterior wall temperature profile and the optimal reactor with minimum entropy generation rate. The result shows that the production rate of SO2 of optimal reactor with the maximum production rate has an increase of more than 7%. The optimization of temperature profile has little influence on the production rate while the optimization of reactants pressure profile can significantly increase the production rate. The results obtained may provide some guidelines for the design of real tubular reactors.

Constructal entropy generation rate minimization for asymmetric vascular networks in a disc-shaped body

Based on constructal theory, the vascular networks with asymmetric pairing in a disc-shaped body are optimized by taking the minimizations of the dimensionless entropy generation rate and dimensionless entropy generation ratio as optimization objectives, respectively. The results show that there exist optimal tube lengths and angles which lead to the minimum dimensionless entropy generation rate and dimensionless entropy generation ratio of the vascular networks with two and three levels of asymmetric pairing, respectively. The optimal constructs of the vascular networks based on asymmetric and symmetric designs are different. For the specified heat flow per unit length on each tube surface, when the number of outlets N=24 and the dimensionless mass flow rate M1∗=10-2, the dimensionless entropy generation rate with two levels of pairing based on asymmetric design is decreased by 7.80% than that based on symmetric design; when the number of outlets N=24 and the dimensionless pumping power W̃2∗=1, the dimensionless entropy generation rate with three levels of pairing based on asymmetric design is decreased by 6.78% than that based on symmetric design. Moreover, the performance improvements of the vascular networks with asymmetric design can also be found for the specified heat flux on each tube surface. The optimization results of the vascular networks based on minimum flow resistance are special cases of those based on minimum entropy generation rate in this paper.

Energy and Entropy-Based Optimization of a Single-Stage Water–Lithium Bromide Absorption Refrigeration System

Thermodynamic optimization of single-stage water–LiBr absorption system was performed earlier both from first- and second-law points of view. However, a realistic comparison between the two approaches is essential to identify the superior one. Hence a theoretical model is developed to optimize the absorption chiller for identifying conditions corresponding to maximum system coefficient of performance (COP) and minimum entropy generation rate. Optimum generator temperature for minimum entropy generation is found to be lower than that corresponding to maximum COP, with absorber having a dominant role in enhancing irreversibility in system. Optimal generator temperature decreases with increasing evaporator temperature and decreasing condenser temperature. Thus, it is possible to identify optimum value for any combination of condenser and evaporator temperature from both the energy and entropy points of view. Concerned contour maps are presented. Adoption of an entropy-optimized map is suggested, owing to higher sensitivity of entropy generation to the changes in condition compared to COP.

Entransy analyses of thermal processes with variable thermophysical properties

Entransy method is developed for the analyses of thermal processes with variable thermophysical properties. The entransy and enthalpy entransy balance equations for thermal processes with variable thermophysical properties are derived based on the definitions of differential entransy and enthalpy entransy. The definitions of the entransy and enthalpy entransy for an object are presented. The optimization principles for heat transfer and heat-work conversion processes with variable thermophysical properties are discussed with the concept of entransy. Entransy analyses for a two-stream heat exchanger and a closed Brayton cycle with variable thermophysical properties are conducted and compared with the entropy generation analyses. For the heat exchanger, the results show that both the minimum entransy-dissipation-based thermal resistance and the minimum revised entropy generation number correspond to the maximum heat exchanger effectiveness when the inlet condition of the heat exchanger is prescribed, but the minimum entropy generation rate and the minimum entropy generation number do not. For the closed Brayton cycle, the results show that both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum output power and both the maximum entransy loss coefficient and the minimum entropy generation number correspond to the maximum heat-work conversion efficiency when the inlet conditions of the streams and the environmental temperature are prescribed. When the inlet temperature of the hot stream increases, larger entransy loss rate and larger entransy loss coefficient still correspond to larger output power and larger heat-work conversion efficiency respectively.

Entropy analysis on MHD pseudo-plastic nanofluid flow through a vertical porous channel with convective heating

This paper is concerned with the entropy generation in a magnetohydrodynamic (MHD) pseudo-plastic nanofluid flow through a porous channel with convective heating. Three different types of nanoparticles, namely copper, aluminum oxide and titanium dioxide are considered with pseudo-plastic carboxymethyl cellulose (CMC)–water used as base fluids. The governing equations are solved numerically by shooting technique coupled with Runge–Kutta scheme. The effects of the pertinent parameters on the fluid velocity, temperature, entropy generation, Bejan number as well as the shear stresses at the channel walls are presented graphically and analyzed in detail. It is possible to determine optimum values of magnetic parameter, power-law index, Eckert number and Boit number which lead to a minimum entropy generation rate.

“Disc-point” heat and mass transfer constructal optimization for solid–gas reactors based on entropy generation minimization

Based on constructal theory, the disc-shaped solid–gas reactors combined heat and mass transfer are investigated in this paper. Radial- and branched-pattern of the discs are considered, and the two pattern discs are optimized based on entropy generation rate minimization. The results show that there exist a minimum value of the entropy generation rate and the corresponding optimal construct of the reactor. The minimum entropy generation rate increases with the increase in the radius of the first order disc; therefore, a proper radius of the first order disc should be adopted according to the practical demand of the reactor. The performance of the reactor can be improved by increasing the material amount of the integrated collector or reducing the number of elemental tributaries and the thermodynamic parameter η. The design pattern of the disc depends on the relationship of the critical radius and disc radius. Moreover, the heat transfer or mass transfer models are special cases of the heat and mass transfer model in this paper.