Entropy Generation Minimization Approach Research Articles

Entropy Generation Minimization for Boiling Flow Inside Evaporator Tube With R32 and R410A Refrigerants: A Comparison of Different Two-Phase Flow Models

AbstractThe objective of the present work is to find out the optimal mass flux of two common refrigerants, R32 and R410A, undergoing boiling in an evaporator tube based on the entropy generation minimization approach. An entropy generation model is developed for two-phase boiling flow based on the drift flux approach. The distinct terms for entropy generation due to heat transfer and pressure drop are developed. The optimal solutions of the present model under a practical range of parametric conditions are compared with that obtained from the existing homogeneous and separated flow-based model. Analysis reveals that increasing the evaporator diameter and heat flux increases the optimal mass flux at minimum entropy generation for both refrigerants. On the other hand, increasing the evaporator length decreases the optimal mass flux. It is observed that the optimal mass flux data for all parametric conditions deviate within 10–15% on the positive and negative sides for drift flux and homogeneous models, respectively, compared to separate flow model. The present analysis also reveals that the overall deviation of data of the drift flux model and homogeneous flow model indicates a standard deviation of 1.95–1.98%, respectively.

Entropy generation minimization-based heat transfer and mass transfer study of rectangular packed-bed filled with spherical particles

The study focuses on tritium-extraction and heat-extraction characteristics of the lead lithium ceramic breeder (LLCB) blanket module, an Indian tritium breeding blanket concept design in the International Thermonuclear Experimental Reactor (ITER). The present study focuses on the mass transfer phenomenon and entropy generation minimization (EGM)-based heat transfer analysis of the packed bed of a fusion reactor considering tritium isotopes in helium gas. For temperature-dependent convection-diffusion of tritium in helium gas and its permeation through the solid structure, a multi-region model in OpenFOAM using the locally varying porous medium approach is developed for studying the coupled multi-physics phenomena. For heat extraction behavior, a parametric study-based analysis is done using the EGM approach that involves irreversibility due to heat transfer, mass transfer, viscous, porosity effect, and heat generation rates. It is found that a lower Reynolds number (Re), and higher non-dimensional heat generation number (β), and non-dimensional species generation number (ϛ) result in a higher tritium extraction. In contrast, due to minimum total entropy generation, higher Re, and lower β and ϛ are preferred. Random packing arrangement as compared to BCC and FCC arrangements gives better tritium extraction and uniformity. However, the FCC arrangement is found as a better choice based on entropy minimization. Diagonally-opposite as compared to same-side inlet-outlet configuration extracts tritium more effectively and also found to be a better configuration from the EGM approach. The present work is significant since, for the breeder blanket, it presents the implementation of Sievert law boundary conditions and the EGM model for the first time in the literature.

Irreversibilities in a triple diffusive flow in various porous cavities

Entropy generation minimization approach is a very good method allowing to analyze the engineering systems to exclude technical failure. The present study deals with computational analysis of triple diffusive flow, energy transference and entropy production in different porous cavities from square to triangular through trapezoidal shape. The formulated boundary-value problem has been worked out using the finite element technique and non-primitive variables. The developed computational code has been verified using numerical results of other researchers. Analysis of entropy production due to energy and mass transport, motion friction, and porous material has been performed for different chamber's shapes. Entropy generation analysis in chambers of various geometries under the triple-diffusive flow is a novelty of the present research, where different entropy production mechanisms have been scrutinized for one complex problem. It has been ascertained that average total entropy generation strength raises with buoyancy ratios, Lewis and Rayleigh numbers, but it has the minimum value for the square chamber in comparison with triangular and trapezoidal shapes. Moreover, obtained results characterize a neglecting influence of motion friction on the total entropy generation.

Circular Microchannel Heat Sink Optimization Using Entropy Generation Minimization Method

Abstract The performance of the microchannel heat sink (MCHS) in electronic applications needs to be optimized corresponding to the number of channels (N). In this study optimization of the number of channels corresponding to the diameter of the microchannel ( D N {D_{N}} ) using an entropy generation minimization approach is achieved for the MCHS used in electronic applications. The numerical study is performed for constant total heat flow rate ( q ˙ t o t ) ({\dot{q}_{tot}}) and total mass flow rate ( m ˙ t o t ) ({\dot{m}_{tot}}) . The results indicate that the dominance of frictional entropy generation ( S g e n , F r {S_{gen,Fr}} ) increases with the reduction in diameter. However, the entropy generation due to heat transfer ( S g e n , H T {S_{gen,HT}} ) decreases with the reduction in diameter. Therefore, the optimum diameter ( D ∗ {D^{\ast }} ) is calculated corresponding to the minimum total entropy generation ( S g e n , t o t a l {S_{gen,total}} ) for the optimum number of channels ( N ∗ {N^{\ast }} ). Furthermore, the entropy generation number ( N S {N_{S}} ) and Bejan number ( B e Be ) are also calculated.

Thermo-hydraulic analysis and optimization of CuO/water nanofluid inside helically dimpled heat exchangers

The use of dimple technology and the use of nanofluids in different heat exchanging systems are known as powerful tools for improving heat transfer and fluid flow conditions. This work aims to prepare a comprehensive thermo-hydraulic parametric study and optimization of CuO/water nanofluid flow inside dimpled heat exchangers. The modeling procedure is based on the combination of the heat and mass transfer, fluid flow characteristics as well as the second law of thermodynamics. The parametric study is done for evaluating three thermo-hydraulic criteria (i.e., entropy generation number, Bejan number and irreversibility distribution ratio) with changing some of the most important fluid conditions (namely Reynolds number, average flow temperature and nanofluid concentration) as well as pitch ratio of the heat exchanger. Finally, the optimization is done through the combination of entropy generation minimization approach and genetic algorithm method. The results indicate that among the decision parameters, the average flow temperature and the pitch ratio have the lowest and highest effect on the entropy generation, respectively. From the optimization process, the optimum values of Reynolds number, dimensionless average flow temperature, nanofluid concentration and pitch ratio are 4610.428, 1.077, 0.000216 and 0.00326, respectively.

Optimal design with entropy generation minimization approach in combined natural convection with surface radiation in a two‐dimensional enclosure

AbstractAnalysis of combined natural convection with surface radiation in a two‐dimensional enclosure is carried out. To search the optimal location of the heat source, the entropy generation minimization approach and conventional heat transfer parameters are used and compared. Air is considered as an incompressible fluid and transparent media filling the enclosure with a steady and laminar regime. The enclosure internal surfaces are also gray, opaque, and diffused. The governing equations are solved using the finite difference approach. The results show that with increase in emissivity, entropy generation decreases, and as the Rayleigh number increases, the rate of entropy generation increases. Furthermore, optimum design with the maximum dimensionless temperature and convective Nusselt number confirms the applicability of the second law for optimal design.

Optimizing chevron plate heat exchangers based on the second law of thermodynamics and genetic algorithm

The aim of the current work is to determine optimal geometries and flow conditions of the chevron plate heat exchangers based on entropy generation minimization approach (a combination of the second law of the thermodynamics and heat transfer and fluid-flow equations). The optimization process is carried out by considering the entropy generation as target function. The all effective parameters are taken into account including chevron angle (30° ≤ β ≤ 60°), surface enlargement factor (1.1 ≤ ϕ ≤ 1.4), dimensionless plate width (19 ≤ $${\mathcal{W}}$$ ≤ 79), Prandtl number (2.6 ≤ Pr ≤ 6.4) and Reynolds number (1000 ≤ Re ≤ 8000). The results indicate that for each surface enlargement factor, there is an optimum chevron angle. Also, by increasing chevron angle, the optimum values of dimensionless plate width, working fluid Prandtl number and Reynolds number decrease. After presenting a comprehensive sensitivity analysis, the genetic algorithm is utilized to find optimum conditions at (a) designing and (b) operating situations. In the first situation, the optimization process reveals optimum chevron angle, surface enlargement factor, dimensionless plate width, Prandtl number and Reynolds number. For the second situation, a useful and practical correlation is developed for obtaining optimum Reynolds number as a function of the geometrical parameters.

Exergy Analysis of a Domestic Refrigerator

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between its hot and cold thermal conductances. Nine types of condensers were used according to its internal surface area and thermal conductance, in order to reach the minimum entropy generation in the refrigerator. The results showed that the compressor has the lowest exergy efficiency of 25%. The expansion device was the second component after the compressor with exergy efficiency of 92%, followed by the condenser with an efficiency of 93%. The evaporator was found to have an exergy efficiency of 98 %. The experimental tests were repeated for the nine condensers sizes with three different ambient temperatures 25℃, 30℃ and 35℃. The exergy analysis showed that the design of the refrigerator mainly depends on thermal conductance calculations rather than the surface inner area estimation.

Heat transfer and entropy generation of the nanofluid flow inside sinusoidal wavy channels

Corrugating channel walls is a way to enhance heat transfer in heat exchangers. In the current investigation, the entropy generation minimization approach has been employed to optimize heat transfer and fluid flow within a wavy channel. A numerical method has been built to compute entropy generation rate in a sinusoidal wavy-wall channel with copper-water (Cu-water) nanofluid flow. The governing equations have been discretized using finite volume method for a two-dimensional steady flow. The effects of geometrical and flow parameters, including nanoparticles volume fraction (0.01 < ϕ < 0.05), Richardson number (0.1 < Ri < 10), wave amplitude ratio (0.1 < α < 0.3) and wave length ratio (1 < λ < 3), have been investigated. Results reveal that increasing nanoparticle volume fraction within investigated Richardson number will increase Nusselt number. In addition, the maximum entropy generation rate declines as Richarson number increases. The optimal wave amplitude ratio (corresponding to lowest entropy generation), for wave length ratios of λ = 1 and λ = 2, found to be α = 0.2. Also, for wave length ratio of λ = 3, the minimum entropy generation approximately occurs at α = 0.1.

Using artificial neural network and quadratic algorithm for minimizing entropy generation of Al2O3-EG/W nanofluid flow inside parabolic trough solar collector

Abstract Entropy generation minimization approach, quadratic optimization algorithm and artificial neural network (ANN) have been applied to find optimal condition of the turbulent Al2O3-60:40% EG/W nanofluid flow inside the absorber tube of a parabolic trough solar collector (PTSC). A three-input ANN has been employed for predicting optimal volume fraction ( ϕ opt ). The process is carried out for optimizing nanoparticle concentration, nanoparticle diameter, nanofluid average flow temperature and Reynolds number. Results show that the rate of the entropy generation decreases by decreasing volume fraction, increasing particle diameter and increasing average flow temperature. Adding the nanoparticles to the base-fluid increases frictional entropy generation and decreases thermal entropy generation. It causes an improvement in heat transfer but an increase in viscous irreversibility too. Finally, it was observed that for each particle sizes and average flow temperatures, there is a specific amount of optimal volume fraction, ϕ opt ; which is not dependent on the Re number. There is an optimal volume fraction for all Re numbers at constant particle size and mean flow temperature. Also, the optimum values of nanoparticle size, nanofluid average flow temperature and Reynolds number are found to be 90 nm, 360 K and 4000, respectively.

Optimizing flow properties of the different nanofluids inside a circular tube by using entropy generation minimization approach

The use of nanofluids as working fluid is one of the represented methods in efficiency enhancement of various systems. One of the most important subjects in nanofluid utilization is finding the optimal conditions. In this study, the efforts have been made to find optimal condition of forced convection nanofluid flow inside a circular tube. The flow is assumed turbulent, and optimization process is carried out for two metallic oxide nanoparticles (Al2O3, CuO) and one nonmetallic oxide nanoparticle (SiO2), dispersed in a 60:40% ethylene glycol/water base fluid. The optimization process has been performed based on the second law of thermodynamic and entropy generation minimization approach. The process has been focused on finding the optimal values for volume fraction, Reynolds number, diameter of particles and average flow temperature. Results show that two metallic oxide nanofluids generate less entropy compared with nonmetallic oxide nanofluid. In addition, comparing these two metallic oxide nanofluids, the maximum amount of total entropy generation is 20% lower when CuO nanoparticles added to the base fluid instead of Al2O3.

Tube-in-tube helical heat exchangers performance optimization by entropy generation minimization approach

There are several different types of heat exchangers that are used for various applications. Helically coiled heat exchanger is one of widely used types of heat exchangers in industrial applications as it offers certain advantages, such as smaller size, higher heat transfer rate, efficient performance in high pressure and temperature differentials and lower cost. This study aims at finding the optimal geometry and operational conditions of helically coiled heat exchangers for both laminar and turbulent flows based on the second law of thermodynamics. In order to fulfill the main goals of this work, first, a dimensionless function for entropy generation number comprising four dimensionless variables, i.e. Prandtl number (Pr), Dean number (De), the ratio of helical pipe diameter to the tube diameter (δ) and the duty parameter of heat exchanger, is derived. Next, the entropy generation number is minimized to develop analytical expressions for the optimal values of δ, De number (for laminar flow) and Reynolds number (Re, for turbulent flow) of the heat exchangers.

Estimation of a tube diameter in a ‘church window’ condenser based on entropy generation minimization

Abstract The internal diameter of a tube in a ‘church window’ condenser was estimated using an entropy generation minimization approach. The adopted model took into account the entropy generation due to heat transfer and flow resistance from the cooling-water side. Calculations were performed considering two equations for the flow resistance coefficient for four different roughness values of a condenser tube. Following the analysis, the internal diameter of the tube was obtained in the range of 17.5 mm to 20 mm (the current internal diameter of the condenser tube is 22 mm). The calculated diameter depends on and is positively related to the roughness assumed in the model.

Performance assessment of longitudinal flow through rod bundle arrangements using entropy generation minimization approach

Longitudinal flow through central subchannel structures in an array of fuel rods in a nuclear reactor plays an important role in removing the heat generated inside the fuel rods. In this paper, an entropy generation analysis has been carried out for assessment of the performance of an infinite triangular as well as a square subchannel for single-phase forced turbulent flow. The performance is evaluated with the objective function being the overall entropy generation in a central subchannel. Various constraints such as dimensionless flow area subtended by the array of rods, pitch to diameter ratio for the configuration of rod bundles and volumetric heat generation to power density ratio of the subchannel imposed by power restrictions have been considered. The parameters include the dimensionless wall heat flux, duty parameter, length to diameter ratio for fuel rods, Reynolds number etc. It has been observed that for a pitch to diameter ratio constraint the square subchannel generates lesser amount of entropy and thus more acceptable compared to triangular structure. For the same constraint the optimum Reynolds number shifts towards higher value compared to triangular one. For dimensionless flow area constraint, on the other hand, the analysis reveals completely reverse phenomenon.

Finite Element Simulation with Heatlines and Entropy Generation Minimization during Natural Convection within Porous Tilted Square Cavities

A complete finite element analysis on the effect of the Darcy number for heat-flow visualization (via heatlines) and entropy generation due to heat transfer (Sθ) and fluid friction (Sψ) within inclined porous cavities is presented. Heatlines are obtained via solution of the Poisson equation using the finite element method. Strong features on conductive and convective heat fluxes were found for high Darcy number flows. Generalized formulations on finite element basis functions are used to calculate all derivatives (Sθ and Sψ) for entropy generation within tilted cavities for all tilted angles (φ). On the basis of the entropy generation minimization approach, it has been concluded that the cavities with inclination angles φ ≤ 30° for lower Pr fluid (Pr = 0.025) and φ = 15° for higher Pr (Pr = 998) may be an efficient strategy for optimal thermal processing.

Entropy generation due to natural convection in discretely heated porous square cavities

Optimization of industrial processes for higher energy efficiency may be effectively carried out based on the thermodynamic approach of entropy generation minimization (EGM). This approach provides the key insights on how the available energy (exergy) is being destroyed during the process and the ways to minimize its destruction. In this study, EGM approach is implemented for the analysis of optimal thermal mixing and temperature uniformity due to natural convection in square cavities filled with porous medium for the material processing applications. Effect of the permeability of the porous medium and the role of distributed heating in enhancing the thermal mixing, temperature uniformity and minimization of entropy generation is analyzed. It is found that at lower Darcy number ( Da), the thermal mixing is low and the heat transfer irreversibility dominates the total entropy generation. In contrast, thermal mixing is improved due to enhanced convection at higher Da. Friction irreversibility is found to dominate the total entropy generation for higher Prandtl number ( Pr) fluids at higher Da, whereas the heat transfer irreversibility dominates the total entropy generation for lower Pr fluids. Based on EGM analysis, it is established that larger thermal mixing at high Darcy number may not be always recommended as the total entropy production is quite large at high Darcy number. Overall, it is found that the distributed heating methodology with multiple heat sources may be an efficient strategy for the optimal thermal processing of materials.

Entropy Generation Minimization Versus Thermal Mixing Due to Natural Convection in Differentially and Discretely Heated Square Cavities

Uniform temperature distribution is a key parameter in many thermal processing applications. A considerable amount of additional energy is used to enhance the fluid mixing in order to maintain the temperature uniformity, but that affects the overall efficiency of the process. In this article, an alternate approach is proposed for maintaining uniform temperature via various distributed/discrete heating strategies while maintaining the minimal entropy generation. The system of laminar natural convection in differentially and discretely heated square cavities filled with various materials (molten metals, air, aqueous solutions, oils) is considered, and finite element simulations are performed for a range of Rayleigh numbers (Ra = 103–105). Entropy generation is evaluated using finite-element basis sets for the first time in this work, and the derivatives at particular nodes are estimated based on the functions within adjacent elements. Analysis of entropy generation in each case is carried out and a detailed investigation of entropy production due to local heat transfer and fluid friction irreversibilities is presented. It is found that a high thermal mixing may not be the optimal situation for achieving uniform temperature distribution based on entropy production. A greater degree of temperature uniformity with moderate thermal mixing may correspond to minimum entropy generation with distributed heating. Further, based on entropy generation minimization approach, it has been thermodynamically established that the distributed heating methodology with multiple heat sources may be the energy efficient strategy for attaining adequate uniform temperature distribution with minimum entropy generation.

Second law analysis of a magnetohydrodynamic plasma generator

The performance of an MHD generator utilizing plasma as working fluid has been assessed from the viewpoint of the second law of thermodynamics. The plasma flow in the generator linear duct has been solved by dividing the channel cross-section to an inviscid core region and the viscous boundary layers in the vicinity of the walls. The Hall effect has been taken into account and equilibrium ionization has been assumed. The dependence of the plasma properties such as Hall parameter, the coefficients of thermal and electrical conductivity, and viscosity on the plasma state has also been considered. Using the information obtained on the plasma behaviour in the generator, the entropy generation minimization approach is applied to improve the conversion efficiency. In addition to seeking the optimal working conditions, the nature of the irreversibilities occurring in the generator has been inspected and the relative importance of the phenomena of fluid friction, heat transfer and Ohmic dissipation and their contribution to the rate of destruction of useful available work has been compared. These studies reveal notable contrasts between the nature of irreversibilities in the liquid metal generators considered earlier and the more common plasma generators studied in the present work.