Entropy Generation Minimization Method Research Articles

Fixed-matrix regenerators optimization with wire mesh screens using entropy generation minimization method

The thermodynamic efficiency of a wire mesh fixed matrix regenerative heat exchanger mainly depends on the regenerator’s heating performance and losses. This paper aims to increase the effectiveness and decrease the pressure loss of static regenerators with wire mesh screens as packing geometry. The entropy generated for several combinations of mesh screens is calculated by using the entropy generation minimization method (EGM), and this method helps in finding the right combination with the minimum entropy generation. The study aims to minimize entropy generation by dividing the conventional uniform mesh regenerator pack length into multiple zones by accommodating different combinations of wire mesh screens. For the sample flow condition, it is observed that 3.94 × 103 W/K entropy is generated by uniform mesh, and from 68 hybrid mesh combinations, 80–120–200 generated 2.11 × 103 W/K. By balancing pressure loss and thermal efficiency, the potential of EGM-based optimization is underscored during this study, which improves the regenerator’s performance.

Experimental investigation on the thermal and flow performance of a thermodynamically-balanced packed bed humidification system

In this paper, a packed bed humidification system filled with corrugated wire mesh was experimentally investigated to obtain a better humidification performance. To thermodynamically balance the simultaneous heat and mass transfer process, multiple water injection bypasses were fabricated at different packing heights based on the entropy generation minimization method. In addition to the inlet water temperature, the influences of the liquid–gas ratio and injection ratio on the humidification capacity, energy effectiveness, and pressure drop were respectively studied and discussed. The experimental and comparison results demonstrated that the established humidification device was robust and superior. It was summarized that raising the number of injections can significantly elevate the humidification capacity, and synchronously magnify the pressure drop for all the cases, while the effectiveness behaved a reverse trend. Additionally, a higher value of the inlet water temperature could increase the humidification capacity and effectiveness, as well as the pressure drop. And, an elevation amplitude of the humidification capacity emerged as 35.51% for the double water injections with a maximum value of 1.48 × 10−2 kgs−1 once the liquid–gas ratio increased from 1 to 1.36, while the value was 39.13% as the injection ratio raised from 0.33 to 0.7. Furthermore, it was illustrated that increasing the mass flow rate of the liquid will reduce the effectiveness when the heat capacity rate ratio is larger than 1, and the effectiveness can reach 0.97 at Twi = 70 °C. In the process of thermodynamic balancing, the increase in the pressure drop of humid air should receive more attention for the designer and researcher related to the packed bed humidifier.

Determination of the Optimum Operating Conditions and Geometrical Dimensions of the Plate Fin Heat Sinks Using Teaching-Learning-Based-Optimization Algorithm

Abstract Electronic devices must be effectively cooled for long-term reliability and safe operation. It is essential to determine operating conditions and optimum dimensions of cooling devices in terms of device weight, space, cost, and sound limits. Plate fin heat sinks (PFHSs) are frequently used for cooling electronic devices. Optimum thermal designs of PFHSs are explored in this study using a teaching-learning-based-optimization (TLBO) algorithm where entropy generation (S˙gen) minimization, profit factor (J) maximization, base plate temperature excess (θb) minimization, total mass (mass) minimization, and total volume (volume) minimization are the objective functions of the constrained single-objective optimization problems. For further investigations of the entropy generation minimization method, three different optimization problems are also studied: minimization of thermal resistance (Rth), minimization of pressure drop (ΔP), and minimization of pumping power (W˙pump). Each optimization problem is subjected to a constraint, namely, temperature excess of base plate temperature (θb) should be lower than 10 K. Four optimization variables are considered which are the number of plate fins (N), freestream velocity (Vf), the thickness of the fin (tfin), and height of the fin (Hfin). Optimum configurations belonging to the different optimization problems are compared, and the effect of each optimization variable on the objective functions is discussed in detail. It is found that one can obtain optimum operating conditions and geometrical dimensions of the PFHSs according to the design objective, i.e., minimum mass requirement, space limitation, minimum base plate requirement, etc. As a result, the optimum designs of the studied cases are different which are superior to each other in terms of design targets.

Thermal and thermodynamic optimization of the performance of a large aperture width parabolic trough solar collector using gaseous and supercritical CO2 as heat transfer fluids

• A coupled optical-thermal-fluid model of a parabolic trough collector is developed. • sCO 2 exhibits better thermal and thermodynamic performance compared to gaseous CO 2. • sCO 2 has comparable thermal performance relative to Therminol-VP1 above 80 bar. • Flow rates above 300 m 3 /h give receiver temperature gradients lower than 50°C. • New correlations for optimal thermal and thermodynamic performance are presented. The degradation of thermal-oil-based working fluids in parabolic trough solar collectors (PTSCs) systems at temperatures above 400 °C has accelerated the search for cost-effective and efficient heat transfer fluids (HTFs) for high-temperature applications. Carbon dioxide is abundant and has the potential to be used as a working fluid in PTSCs. In this work, the performance of a larger aperture width PTSC with CO 2 as the working fluid (either in gaseous or supercritical phase) is investigated. In this study, a PTSC system with an aperture width of 9 m (geometric concentration ratio of 113) was considered. The operating pressure is in the range of 40−100 bar, the HTF inlet temperatures are between 650 and 1000 K, and the flow rate varies from 32.6 to 653 m 3 /h. A thoroughly verified and validated computational model using a combination of Monte-Carlo ray tracing and computational fluid dynamics was used for the numerical study. In addition, the Realizable k- ε model was used for turbulence modeling. The results show that CO 2 at 80 bar has comparable thermal performance relative to current thermal oil-based HTFs. Results further show that supercritical CO 2 (sCO 2 ) has the best thermal performance compared to gaseous CO 2 . In addition, the entropy generation minimization method was used to determine the Reynolds number that minimizes the irreversibilities at a given operating pressure. At low pressures, much higher flow rates are required to achieve high heat transfer rates and reduce temperature gradients in the absorber tube. Furthermore, correlations have been developed for the optimal Reynolds numbers at which the entropy generation rate is minimum and the collector efficiency is maximum.

Thermal-hydraulic optimization of a steam generator by entropy generation minimization and genetic algorithm method

From the review of literature conducted in recent years, it has become clear that, despite extensive studies to obtain optimal parameters for a variety of thermodynamic systems and industrial equipment, there is still no attempt in this context on the steam generators. Hence, in this paper, we used the entropy generation equations in accordance the second law of thermodynamics, also the Drift-flux method for two-phase flow (introduced by Zuber-Findlay) and the genetic algorithm to optimize a vertical steam generator. The main goal of vertical steam generator optimization is to obtain the optimal parameters as well as to increase the steam generator efficiency and consequently to increase the efficiency of the PWRs. So the effects of all the parameters influencing on a vertical steam generator were initially separate and then simultaneously examined on entropy generation number and the exact optimal parameters for the least entropy generation number using the genetic algorithm are calculated in the MATLAB toolbox. In order to determine the two-phase flow characteristics, a thermal equilibrium mixture model with an algebraic relation between the velocities (or a slip ratio) of the two phases is used. In this study we reduced the entropy generation number value from 0.061 to 0.055 for design parameters, which represents about 10% improvement in entropy generation number. Also, the effectiveness for design parameters has increased from 0.71 up to 0.82.

Second law analysis of recharging microchannel using entropy generation minimization method

This work deals with numerical study of entropy generation in recharging and simple microchannel to explore effect of geometrical modification on thermodynamic irreversibility in a system. This work also investigates effects of geometrical and thermo-physical parameters on entropy generation in recharging microchannel system, by varying number of small channels, substrate thickness, channel wall width, channel aspect ratio, substrate material, and applied heat flux. Numerical simulations are carried out by considering water as working fluid with Reynolds number 100-500. Results reveal that recharging microchannel shows maximum 47% reduction in total entropy generation compared to simple microchannel, which indicates that thermodynamic irreversibility is lower in recharging microchannel compared to simple microchannel. Thermal entropy generation in recharging microchannel decreases with increasing number of small channels, channel aspect ratio, and substrate material thermal conductivity, whereas it increases with increasing substrate thickness, channel wall width, and applied heat flux. Moreover, frictional entropy generation in recharging microchannel is invariant with substrate thickness, channel wall width, substrate material, and applied heat flux. These parametric investigations indicate that consideration of entropy generation in microchannel solid substrate during entropy generation analysis is quite important, as it strongly influence entropy generation in a system.

Entropy and exergy analysis of a liquid-liquid air-gap hollow fiber membrane contactor

A liquid-liquid air-gap hollow fiber membrane contactor consisting of a number of hollow fiber membrane tubes forms a hollow fiber membrane absorption heat pump where the refrigerant (water) and the absorbent (LiCl solution) flow inside the tubes in a cross-flow arrangement. There are defined air-gaps between neighboring tube rows. A lumped parameter model which describes the heat and mass transfer is established by transforming the membrane contactor into a parallel-plate one. The governing equations are solved by the finite difference approach. The model is validated experimentally. The influences of various structural parameters, operation conditions, and membrane parameters on the contactor performances are analyzed. An entropy generation model and an exergy destruction model are established to solve and disclose the thermodynamic properties of the heat and mass transfer process inside the membrane contactor, which is an irreversible process. It has been found that the contactor performance can be improved by using the hollow fiber membranes with larger diffusivity or a smaller diameter of about 1.5 mm. Furthermore, the packing fraction of about 0.349 is optimal for the performance. The maximum mass transfer entropy generation rate usually corresponds to the best performance. The entropy generation minimization method is not suitable for the optimization of this membrane contactor. The optimized regions of the structural parameters, operation conditions, and membrane transport parameters with better performances and smaller entropy generation can be obtained to reduce irreversible loss in future.

Entropy generation analysis of different solar thermal systems.

The entropy generation analysis is an approach to optimize the performance ofdifferent thermal systems by investigating the related irreversibilities of the system. This paper provides a concise review of the entropy generation analysis performed for different solar thermal energy systems including solar collectors, solar heaters, solar heat exchangers, and solar stills. The mathematical formulation and the equations for calculating the entropy generation are briefly presented. Moreover, main passive techniques including the usage of nanofluids, porous materials, and inserts which are used to improve the efficiency of different solar systems are discussed. It is shown that using entropy generation minimization method is an efficient tool to find the optimaldesign of solar systems. The current review aims to motivate researchers in the field of solar energy for using entropy generation analysis to reduce the lost work and consequently improving the system performance.

Optimization of the circular microchannel heat sink under viscous heating effect using entropy generation minimization method

The present numerical study carries out the optimization of the channel dimension (DN corresponding to N-number of channels) under the consideration of viscous heating effects in entropy generation (EG) through a uniformly heated microchannel heat sink (MCHS). The numerical computations are performed for a constant total mass flow rate ṁtot and constant total heat flow rateq̇tot. In EG formulation, the partial differential equations (PDEs) are discretized by the first-order forward difference method and the temperature in the denominator is taken as the local one. The EG due to fluid friction (Sgen,FR) and heat conduction (Sgen,HT) individually as well as simultaneously is also reported. The EG due to fluid heat conduction in the radial (Sgen,HT-rad) and axial (Sgen,HT-ax) directions are also examined. The results indicate that the frictional entropy generation (Sgen,FR) is significant towards the micro dimensions of the channel. Additionally, the optimum diameter (D*) corresponding to the optimum number (N*) of the channels is designed at minimum total EG (Sgen,tot).

Optimal Design of Isothermal Sloshing Vessels by Entropy Generation Minimization Method

In this manuscript, the optimal design of geometry for a forced sloshing in a rigid container based on the entropy generation minimization (EGM) method is presented. The geometry of the vessel considered here is two dimensional rectangular. Incompressible inviscid fluid undergoes horizontal harmonic motion by interaction with a rigid tank. The analytical solution of a fluid stream function is obtained and benchmarked by Finite element results. A parameter study of the aspect ratio, amplitude, and frequency of the horizontal harmonic motion is performed. As well, an analytical solution for the total entropy generation in the volume is presented and discussed. The total entropy generation is compared with the results of the Reynolds-Averaged Navier–Stokes (RANS) solver and the Volume-of-Fluid (VOF) method). Then, the effect of parameters is studied on the total entropy generated by sway motion. Finally, the results show that, based on the excitation frequency, an optimal design of the tank could be found.

Optimization design of falling film type plate-fin condenser/reboilers by minimizing specific entropy generation rate

This paper presents an optimization model for falling film type plate-fin condenser/reboilers based on the entropy generation minimization method, which considers the irreversibilities owing to both irreversible heat transfer and pressure drop. The specific entropy generation rate, i.e. the entropy generation rate per unit total heat transfer area, is proposed as an optimization objective function. Main geometrical parameters (i.e. fin height and fin pitch) of the evaporation channel of a falling film type plate-fin condenser/reboiler are optimized. The analytical results show that under certain fin pitch, there exist different optimal fin heights corresponding to the minimum entropy generation rate and the minimum specific entropy generation rate, respectively. In addition, the value of minimum specific entropy generation rate decreases with the increase of the fin pitch, and the optimal value of the fin height varies little with the fin pitch. Effects of the heat transfer temperature difference, inlet mass flow rate of liquid to be evaporated and inlet mass flow rate of vapor to be condensed on both the minimum specific entropy generation rate and optimum values of fin parameters are also analyzed in detail.

Entropy­based methods applied to the evaluation of a real refrigeration machine

The aim of the research is the thermodynamic analysis of a real refrigerating machine with solid fouling on the heat­exchange surface of an air­cooled condenser with the help of entropy methods such as: the entropy­cycle method, the entropy­statistical method and the entropy generation minimization method. The experimental data of the refrigerating machine with solid fouling in the form of dust on the external surface of the air­cooled condenser was used for the thermodynamic analysis. The influence of irreversible losses in separate elements of the refrigerating machine caused by the presence of external solid fouling on the external heat exchange surface of the air­cooled condenser was determined according to the entropy­cycle and entropy­statistical methods. The entropy­cycle method has estimated the absolute value of energy losses in each element. The entropy­statistical method was used to determine the excessive consumption of work in the real cycle in comparison with the theoretical compression process in the compressor. The irreversible losses associated with aerodynamics and heat transfer during air motion through a finned surface in an air­cooled heat exchanger were estimated by using the entropy generation minimization theory. The influence of growing fouling on the thermal and mechanical components of the total entropy generation in the heat exchanger was determined. In addition, the fouling mass that determines the time of its cleaning was defined. Application of entropy methods for analyzing the real refrigerating machine at the design stage allows minimizing irreversible losses associated with operating conditions. Moreover, it allows predicting a maintenance schedule which contributes to energy saving

Optimization of a separator assisted two-phase thermosyphon loop by using entropy generation analysis

In this paper, an optimization model is developed for a separator assisted two-phase thermosyphon loop and basic two-phase thermosyphon loop based on the entropy generation minimization method. The total entropy generation rate of the system is proposed as an optimization objective function and the total heat transfer area of evaporator and condenser is considered as a constraint. The model takes into account the irreversibility due to both irreversible heat transfer and pressure drop. The results show that there always exists minimum total entropy generation rate of the two systems when the heat transfer area ratio varies. The optimal heat transfer area ratios corresponding to the minimum total entropy generation rate also lead to the minimum total thermal resistance of the system and achieve the lowest temperature of the cooled object. Besides, the separator assisted two-phase thermosyphon loop can gain lower total entropy generation rate than the basic two-phase thermosyphon loop. Furthermore, the effects of the heat load, the total heat transfer area, the working fluid charge, the inner diameter of the separator and the height of two-phase tube on the minimum total entropy generation rate and the corresponding area ratio are also evaluated.

Effect of Using Extra Fins on the Pin Fin Classic Geometry for Enhancement Heat Sink Performance using EGM Method

In the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins) by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height) and 4 mm (width) and triangular extra fin of 2 mm (base) 4 mm (height). The use of entropy generation minimization method (EGM) allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including a base plate and applying the conservations equations of mass and energy with the entropy balance. The dimensionless numbers used includes the aspect ratio (ε), Reynolds number (Re), Nusselt number (Nu), and the drag coefficients (CD). Fourteen different cross-section fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate. The results showed that the Nusselt number increases with increasing the Reynolds number for all employed models. The ellipse models (ET and ER-models) give the highest value in the Nusselt number as compared with the classical pin fins. The fin of the square geometry with four rectangular extra fins (SR-models) gives an agreement in Nusselt number as compared with the previous study.

Optimal Design of Thermal Radiative Heating of Horizontal Thin Plates Using the Entropy Generation Minimization Method

Thermal radiant heating through distinct heat sources is of interest for the thermal loading of thin objects as it is used in residential applications, furnaces, and insulator designs. In this paper, an optimal design for a thermal radiant system by discrete suspended heat sources is analyzed in a side open cavity used for heating the top plate, while the bottom plate is kept at a constant temperature, using the entropy generation minimization method. To avoid pressure fluctuations, the semi-implicit method for pressure linked equations method is used, which solves the continuity, Navier-Stokes, fluid energy, and surface energy equations simultaneously. The system is optimized based on the characteristic length of discrete heat sources, height of discrete heat sources from the bottom plate, the distance between discrete heat sources, the number of discrete heat sources, and the aspect ratio of the cavity that finds the optimal location of heating elements. In addition to the geometrical parameters, the effects of the thermal loading parameters on the optimal position are investigated.

Discussion on “Performance analysis of Wells turbine blades using the entropy generation minimization method” by Shehata, A. S., Saqr, K. M., Xiao, Q., Shahadeh, M. F. and Day, A.

This paper presents a critical appraisal of the paper “Performance analysis of Wells turbine blades using the entropy generation minimization method” by Shehata, A. S., Saqr, K. M., Xiao, Q., Shahadeh, M. F. and Day, A., published in Renewable Energy, volume 86, pp. 1123–1133. The discussion focuses in particular on five aspects of the work being critiqued: the set-up of the numerical experiment, the similarity of the problem studied with the large existing literature on oscillating airfoils, the estimation of entropy generation through the numerical solution of the Navier-Stokes equations, the equivalence between entropy and drag, and finally a comparison of the results presented with existing literature. From this appraisal, it is concluded that the problem studied is not representative of a Wells turbine and that the article contains a number of fundamental errors that lead to incorrect results. These mistakes would have been evident had the results been analyzed critically and compared to the existing literature on the subject. If the results had been presented in non-dimensional form, as best practice recommends, they would have been more readily comparable to those in existing literature and important discrepancies might not have been obscured.

Reply to: Discussion on “performance analysis of wells turbine blades using the entropy generation minimization method” by Shehata, A. S., Saqr, K. M., Xiao, Q., Shahadeh, M. F. and Day, A

Abstract With great interest, the authors have read the comments made by Ghisu et al. on our recent paper [1] published in Renewable Energy. The comments severely criticizes our methodology and results, which actually provide us with fortunate opportunity to discuss our work in more details to complement our work, thankfully to this available space of scientific discourse provided by Renewable Energy editors. In this reply, we show clearly that all the comments proposed by Ghisu et al. lacks sufficient understanding of Wells turbine modeling approaches, literature, and state of the art research practices. We also show that Ghisu et al. could not distinguish between fully developed turbulent flow and transitional flow around Wells turbine airfoils. It is also evidently shown that their concerns about the entropy generation calculation method are meaningless in the light of well-established practices of CFD models of entropy generation minimization principles. Our reply is structured in a point-by-point style to address the comments raised in the discussion article and help the readers understand our work in better details.

Numerical investigation on heat transfer enhancement of heat sink using perforated pin fins with inline and staggered arrangement

The current work investigates the heat transfer enhancement of heat sink using perforated pin fins with linear and staggered arrangement. Pin fins of various shapes with different perforation geometries namely circular, diamond shaped and elliptical type are considered in this analysis. Three dimensional CFD simulations have been performed to study the effects of number and shape of the fin, geometry and dimension of the perforation for both the arrangements. Results show that heat dissipation rate of perforated fins up to certain perforation number and size are always higher than the solid ones and with the variation in fin shape and perforation geometry heat transfer rate improves significantly. Moreover, better system performance is observed for staggered arrangement than inline arrangement. Conversely, pressure drop through heat sink decreases by increasing number and size of perforations though it varies with fin shape and fin arrangement. Optimization analysis using MOORA as well as entropy generation minimization method have been done to predict the best perforated fin which dissipates maximum heat transfer against minimum pressure loss. Finally, exergy analysis has been performed to calculate second law efficiencies of heat sinks using various types of perforated fins for both the arrangements.

Enhancement of performance of wave turbine during stall using passive flow control: First and second law analysis

Wells turbine is the most common type of self-rectifying air turbine employed by Oscillating Water Column (OWC) wave energy devices due to its technical simplicity, reliability, and design robustness. Because it subjected to early stall, there were many endeavors to improve the energy extraction performance of Wells turbine within the stall regime. Using the multi suction slots as a passive flow control can help obtaining a delayed stall. Two, three and four suction slots were investigated to improve the performance of Wells turbine in the stall regime. In addition the commonly used first law analysis, the present study utilized an entropy generation minimization method to examine the impact of the multi suction slots method on the entropy generation characteristics around the turbine blade. The turbine blade with optimum suction slots number and location was investigated using the oscillating water system based on the real data from the site. To achieve this purpose, two-dimension numerical models for Wells turbine airfoils under sinusoidal wave flow conditions were built and analyze using (ANSYS FLUENT) solver. It is found that the airfoil with three suction slots located at 40%, 55% and 90% from leading edge in chord percentage give the highest torque coefficient by 26.7% before the stall and 51% after the stall.

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.