Entropy Generation Minimization Research Articles

Efficiency and cost optimization of offset Plate-Fin heat exchanger

Plate-fin heat exchangers, are also called compact heat exchangers. Due to their small size, compared to other heat exchangers they are user friendly which allow greater flexibility in plant architecture. The heat exchanger is made by stacking up fin surfaces which are separated by a sheet. With the increase in the area of the offset fin structure, the heat transfer also increases. But on the other end total annual cost and entropy generation is also affected by geometric variables. In the present work, seven geometric variables of the heat exchanger are investigated for the optimization of effectiveness, total annual cost and entropy generation minimization. Genetic algorithm is implemented for the optimization. Finally, parametric analysis is also performed to investigate the effect of design variables on the optimized results.

Matrixed modeling method and entropy generation minimization analysis of heat supply system based on standard thermal resistance

AbstractComplex implicit expressions and many intermediate parameters are not conducive to the application of entropy generation optimization to the performance of thermal and energy systems from component and system perspectives. In this paper, we derived matrix heat transport equations of three primary heat exchanger networks according to the heat current method. Based on the matrix equations, we established the matrixed model of a typical heat supply system and obtained the corresponding matrix equation reflecting the power topology structure of the system. Moreover, we derived and reconstructed a single heat exchanger's entropy generation rate expression based on the standard thermal resistance, which was only related to inlet temperatures, structural parameters, and operating parameters. The total system entropy generation rate was then derived and minimized by the Lagrange multiplier method. The optimization results provided the optimal distribution of the mass flow rate of each fluid. Besides, the influence of the heat transfer rate and outer loop inlet temperature on the optimization results revealed that local equipment parameters and conditions could affect the system's minimum entropy generation. The total entropy generation rate decreases by 17.5% when the outer loop inlet temperature was increased from 274 to 280 K. In conclusion, the matrixed modeling and entropy generation analysis are feasible for thermal system modeling and optimization.

Integer programming topology optimization for subsonic compressible flows with geometry trimming

The incompressibility hypothesis is successfully applied in a broad range of engineering problems simulated via computational fluid dynamics (CFD) codes. However, depending on the Mach number, the effects of compressibility are no longer negligible. Recently, the first papers about topology optimization considering compressible flows were published. All of them use the continuous design variables method which has some known drawbacks. The present work proposes topology optimization considering the compressible Navier-Stokes equations and discrete variables with a step of geometry trimming. This approach constrains the design variables to a binary set and solves the problem by using sequential integer linear programming, being a feasible alternative to classic density-based methods. Additionally, the solid regions are trimmed out from the physics analysis. A material model is inserted in the governing equations in such a way that, it is possible to calculate the sensitivity and, at the same time, guarantee the adiabatic condition. In this work, it is observed that the minimization of entropy generation as the objective function tends to converge to an undesired trivial solution. Alternatively, this work proposes the maximization of mass flow rate as the objective function to, indirectly, minimize the entropy. Furthermore, it is proposed the use of a new set of inlet boundary conditions. Three optimization cases are solved: the double-pipe, the pipe-bend, and an entropy maximization problem. The optimized solutions for the pipe-bend and double-pipe problems present geometries where the constraints are satisfied with the minimum entropy generation. Using the double-pipe example, it is conducted a study to understand the impacts of TOBS-GT parameters in the solutions. The results evidenced that, in some conditions, the implementation is prone to fall in a local minimum. In the third example, entropy maximization subjected to volume constraint is successfully solved. Moreover, a minimization case is also solved to aid in the interpretation of the results.

Heat transportation performance and entropy generation analysis of Iron (II, III) oxide microparticles on Taylor Couette flow over a slit wall

Despite the significance of Taylor Couette flow over a slit wall in industries, little is known about the impact of Iron (II, III) oxide (Fe3O4) microparticle on the dynamics and heat transfer properties of Taylor-Couette flow. This study aims to investigate the effect of solid particles on heat transfer performance of Taylor-Couette flow over a slit wall. The trajectory of particles in the flow field is described utilizing Eulerian-Lagrangian method in this report. The Fe3O4-water suspension with particle size dp = 1μm, 5μm and particle volume fraction φ = 0.5 % , 1.0 % , 1.5% are considered. Results reveal that the heat transfer performance of Taylor vortex is remarkable enhanced by adding the solid particles inside the annular gap compared to pure water. Solid particles in the annular gap show the movement of migration from inner to outer cylinders due to the interaction with fluid, which causes more disordered flow field around the inner cylinder. The addition of particles could significantly thin the velocity and temperature boundary layers. Frictional and thermal entropy generation display a reverse tendency with increasing particle volume fraction and size. Thermal entropy generation appears obviously higher than frictional entropy generation. Suspension with φ = 1.5% and dp = 1μm makes optimal performance of Taylor vortex because of the minimum entropy generation and boundary layers.

Numerical simulation and artificial neural network prediction of hydrodynamic and heat transfer in a geothermal heat exchanger to obtain the optimal diameter of tubes with the lowest entropy using water and Al2O3/water nanofluid

Since the world is facing an energy crisis, and the emission of carbon-based fuel combustion is causing global warming, more research has been devoted to studying renewable energies. Due to the broad use of geothermal heat exchangers in central air-conditioning systems and also as a direct source of energy, in the present study, we have conducted a simulation of a geothermal heat exchanger and investigated the optimal diameter and nanoparticle concentration in order to minimize entropy generation. The fluid flow is turbulent, and SST K−ε is utilized as the turbulence model. The results show that as the thermal resistance of the inner wall increases, the outlet temperature rises. The effects of thermal resistance and diameter are thoroughly investigated, and the results have been used for selecting the least entropy generation. The results showed that the diameter in which the entropy is minimized increases by increasing the inner wall's thermal resistance. The best case is high thermal resistance in the outer walls and meager resistance in the inner walls. Using inner walls with high thermal resistance can decrease the adverse effects of entropy generation in large diameters. Also, the addition of nanoparticles is investigated, and the average Nusselt number and entropy generation, respectively, increased and decreased by almost 10%. Artificial neural network models are proposed to predict Nusselt number and entropy generation based on numerical results. The models are able to achieve MAE of lower than 3% and R2 higher than 0.95.

Optimal piston motion paths for a light-driven engine with generalized radiative law and maximum ecological function

Searching optimal piston motion path (OPMP) by using optimal control theory for various thermal cycles is an important task in finite time thermodynamics. Some optimization objectives have been used in this type of researches, including maximum work output (MWO) and minimum entropy generation (MEG). This paper introduces maximum ecological function (MEF) into OPMP problem for light-driven engine (LDE) with generalized radiative heat transfer law (HTL) [q∝Δ(Tn)]. The LDE is with working fluid of reacting system [A]⇌[B] and irreversibilities of piston friction and heat conduction. Numerical examples of OPMPs at MEF with Newtonian (n=1), linear phenomenological (n=−1) and radiative (n=4) HTLs are provided. The results are compared with those obtained by MWO and MEG objectives as well as different HTLs. Utilizing MEF as objective can effectively accomplish entropy generation reduction with a little decrease in work output. Time-parametrized piston velocity, working fluid temperature and piston position for MEF are situated between those for MEG and MWO. Moreover, OPMPs for MEF with different HTLs are also quite different. Although all of the values of ecological function are negative for three special HTLs, work output and ecological function decrease with the increase in n, and entropy generation increases when n increases.

Entropy generation minimization of higher-order endothermic/exothermic chemical reaction with activation energy on MHD mixed convective flow over a stretching surface

The present investigation aims to analyze higher-order endothermic/exothermic chemical reactions with activation energy by considering thermophoresis and Brownian motion effects on MHD mixed convective flow across a vertical stretching surface. The influence of velocity slip, thermal slip, and concentration slip along with an inclined external magnetic field is also considered. The governing coupled non-linear partial differential equations are transformed into ordinary differential equations using similarity transformation. The resulting system of non-linear ODEs is solved by the Newton Raphson shooting technique using the RK-4 algorithm. The impact of various physical parameters discovered in the problem viz. endothermic/exothermic reaction variable, thermophoresis parameter, activation energy parameter, Brownian motion parameter, chemical reaction parameter have been analyzed on velocity profile, temperature profile, and concentration profile. The effects of these parameters on skin-friction coefficient, Nusselt number, and Sherwood number are displayed in tabular form as well as surface plots. The impact of various physical parameters that appeared in the entropy generation is shown using surface and contour plots. The numerical findings are in good agreement with the previously published results. It is observed that an increment in thermophoresis and Brownian motion parameters results in a declination of entropy profiles, whereas an increment in Bejan number profiles is observed. A small region near the surface exhibits an inclination in concentration profiles with an increase in the order of the chemical reaction. In contrast, the opposite effect is analyzed near the boundary layer. Also, the contour and surface plots are displayed to portray real-world applications in industrial and technical processes and the physical depiction of flow characteristics that arise in the current study.

Entropy generation minimization of an advanced two-bed adsorption refrigeration system

This article presents the thermodynamic assessment of an advanced adsorption chiller with an aim towards entropy generation minimization through the selection of appropriate operating strategies, temperatures, and design modifications. The present study carries out a second law analysis of a two-bed silica gel water pair-based adsorption cooling system, with a focus on the under-explored aspects of a heat recovery strategy and auxiliary consumption-reducing measures. A second law performance index, viz. specific irreversibility, is introduced for effectively incorporating the entropy generation, auxiliary electricity consumption, and cooling capacity, and it has been further verified to be an indicator of second law efficiency. The performance of the system has been numerically evaluated under the normal and passive heat recovery strategies, where it is found that the passive heat recovery strategy offers a lower entropy generation by 63%. The study further investigates the second law efficiency impact of adopting a capillary-assisted evaporator for auxiliary electricity consumption reduction. It is observed that the specific irreversibility could reduce by up to 22% over a conventional falling film design. The analysis and results presented in this study are anticipated to increase the effectiveness of adsorption chillers for heat recovery applications.

Optimal thermal conductivity design for the volume-to-point heat conduction problem based on adjoint analysis

Volume-to-point (VP) problem is a classic prototype of heat conduction optimization and benefits important applications such as electronic devices thermal management. However, many studies employ various optimization principles without verifying their applicability; some other studies rashly apply a single principle on different cases but ignore influences of various objectives and boundary conditions. Here, a novel optimization principle for VP problems is derived by applying adjoint analysis, where the minimization of average temperature is considered as an example. The derived optimization principle reads the optimal thermal conductivity distribution maximizes the synergy between temperature gradient and adjoint temperature gradient fields. Relations among the proposed principle and three common ones are clarified rigorously, and reasons of why the latter cannot give optimal results are revealed. A one- and a two-dimensional cases are numerically optimized to validate the proposed principle, and results show that it gives the lowest average temperature as expected. For instance, the average temperature after optimization by using the proposed principle can be lower than that obtained from entropy generation minimization by around 25 and 10 K in the one- and two-dimensional cases studied, respectively. The presented derivation also applies to other objectives for obtaining corresponding optimization principle, showing its flexibility.

Energy analysis of a phase change material embedded heat exchanger for air conditioning load reduction in different Indian climatic zones

Air conditioning (AC) systems for tropical countries like India account for sixty percent of the total energy needs of a building. With the onset of COVID-19, the increase of fresh air ventilation rate has been recommended by various guidelines for indoor spaces which increase the load on the AC system. The present study attempts to reduce this burden through retrofitting a phase change material (PCM) embedded pin fin heat exchanger into an air-conditioning system. The heat exchanger is designed to cater to the peak load fluctuations for cities in three hot climatic zones of India, viz., Jaisalmer, Kolkata, and Delhi. Dodecanol with a melting temperature of 24 °C, is chosen as the appropriate PCM material for these locations. The optimal pin fin diameters are estimated through an entropy generation minimization analysis for the three locations. A heat transfer analysis of the PCM embedded heat exchanger is further presented through an analytical approach to estimate the PCM mass requirement and energy savings potential. The masses of the PCM estimated for Jaisalmer, Kolkata, and Delhi are 11.36 kg, 22.42 kg, and 19.35 kg, respectively for their respective peak load fluctuations of 0.25 kW, 0.28 kW and 0.48 kW. Energy savings of up to 4.7 % for Delhi, 2 % for Kolkata, and 2.75 % for Jaisalmer are identified with the PCM embedded heat exchanger incorporation. The results show the potential of such PCM thermal storage in reducing the peak energy demands of buildings amidst various environmental and health concerns.

Numerical Chebyshev finite difference examination of Lorentz force effect on a dissipative flow with variable thermal conductivity and magnetic heating: Entropy generation minimization

AbstractThis work presents the computational analysis of entropy generation minimization in a dissipative flow of viscous fluid. The flow is produced by a non‐linearly elastic surface under the influence of the variable magnetic field. The non‐isothermal boundary condition is chosen such that all the embedding flow control parameters are free from the space variables. It is supposed that the working fluid's thermal conductivity is temperature‐dependent. The heating term corresponding to the magnetic dissipation effect is also added to the energy equation. The governing energy and momentum equations are simplified by similarity transformations and numerically solved using Chebyshev Finite Difference Scheme (ChFDS). Volumetric entropy generation in dimensionless form is also obtained via similarity transformations. The obtained solutions are also utilized for calculating entropy and Bejan numbers. It has been noticed that the production of entropy is highest at the surface of the elastic boundary. The temperature and entropy have increasing relation with the Eckert number and magnetic parameter. Further, an inverse relation is observed between the entropy generation and temperature difference parameter. The consequences of relevant parameters on the velocity, temperature, entropy and Bejan number are visually described and discussed.

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.

Dynamics of Colloidal Mixture of Cu-Al2O3/Water in an Inclined Porous Channel Due to Mixed Convection: Significance of Entropy Generation

The unavailability of energy has become a major challenge to industry in the last years, as an important percentage of the generated energy is dissipated as heat in transport. Since heat transfer processes are irreversible, the role of entropy generation minimization in nanofluid flow and heat transfer cannot be neglected. The present paper was dedicated to the study of entropy generation for the problem of steady mixed-convection flow in a porous inclined channel filled with a hybrid nanofluid (Cu-Al2O3/water). A symmetrical uniform heat flux was considered at the walls and a constant flow rate was given through the channel. The mathematical model, consisting of a system of equations with given boundary conditions, was transformed in terms of dimensionless variables and the proposed analytical solution was found to be valid for all the cases of the inclined channel. The solution was validated by comparison with previously published results. The behavior of the velocity and temperature of the hybrid nanofluid were studied together with the entropy generation inside the channel by considering the influence of different important parameters, such as the nanoparticle volume fraction, the mixed-convection parameter and the inclination angle of the channel from horizontal. The results were focused to prevent the dissipation of energy by calculating the maximum thermal advantage at a minimum entropy generation in the system.

Hydrothermal Performance Maximisation and Entropy Generation Minimisation of Different Perforated Pinned Heat Sink Designs for Electronic Cooling

Abstract To quantify the benefits of reducing entropy production and improving hydrothermal performance with varied thermal air characteristics through different perforated heat sinks, a numerical study was conducted. Various numbers of circular perforations are studied from 0 perforations to 5 perforations. In addition, perforation configuration is considered, such as circular (3CP), square (3SP), elliptic (3EP), and triangular (3TP) perforated pinned heat sinks, as well as three slotted pinned heat sinks (SPHSs) (3S, 6S, and 10S) and four notched pinned heat sinks (NPHSs) (3S, 6S, and 10S) (2.5 N, 5 N, 7.5 N, and 10 N). The numerical results showed that the 5-circular perforations heat sink model (5CP) generates the minimum entropy generation and the maximum hydrothermal performance (HTP), around 17% and 1.2, respectively compared to the zero-perforation model, while the circular perforated pinned heat sink (3CP) model produces the maximum reduction in entropy generation, generally around 13% with moderated HTP of 1.1. Moreover, when comparing slotted and notched pinned heat sinks, the 10S slotted and 10 N notched pinned heat sinks achieve 1.45 of HTP.

Entropy generation minimization in the Blasius–Rayleigh–Stokes nanofluid flow through a transitive magnetic field with bioconvective microorganisms

The goal of this study is to underscore the attributes of nanofluid by discussing the Blasius-Rayleigh-Stokes (BRS) nanofluid flow with effects of modified Fourier law with gyrotactic microorganisms influenced by the transitive magnetic field past a moving semi-infinite plate. The proposed flow is supported by the non-uniform heat sink/source and radiation with zero mass flux at the surface. Analysis of entropy generation is also a part of this study. The most notable aspect of the presented model is that it discusses the entire problem using the Blasius-Rayleigh-Stokes flow. The envisioned model is reflected in the form of a system of PDEs that is transformed into a highly nonlinear system of ODEs engaging the boundary layer approximations and handled numerically. Graphical illustrations are designed for the arising parameters versus the associated profiles. It is comprehended that the thermal profile lowers for the thermal relaxation parameter. The results also disclosed that the motile density profile declines for Peclet number, and microorganism concentration difference parameter. Furthermore, the mass transfer rate is reduced by rising the chemical reaction parameter. Entropy generation upsurges versus heat generation absorption coefficients. A check for the validation of the presented model is also added to the problem.

Irreversibility analysis of the MHD Williamson fluid flow through a microchannel with thermal radiation

The heat transport and non-Newtonian fluid (Williamson fluid) flow through a micro-channel are considered to analyze the entropy generation minimization using the thermodynamic second law. The energy equations have been modeled with the addition of joule heating, heat source, and thermal radiation. The use of suitable dimensionless transformation helps to convert the modeled flow equations into non-dimensional coupled ODEs. The numerical simulations are done via the Finite Element Method. The current outcomes are constructed to examine the behavior of various flow parameters and presented via graphs. It is found that the rise of heat source and Reynolds number Re decays/boosts the entropy rate Ns and the Bejan number Be profile near the left/right plate, and reverse behavior is noticed for the thermal radiation parameter.

Analysis of Entropy Generation and Potential Inhibition in an Aeroengine System Environment

From a system perspective, the entropy generation of an aeroengine is directly related to the thermal efficiency when the Brayton cycle pressure ratio and maximum temperature remain constant. The lower the entropy generation of the engine is, the higher the thermal efficiency. However, the secondary air system of the engine generates a large quantity of entropy compared to the components of the main flow channel, because the irreversible losses of the internal flow and heat exchange between the air system components generate considerable entropy within the system. In this study, the theoretical method is used to build entropy generation model for different characteristics of air system components during the aerothermal process. In this basis, an integrated model of the whole engine is introduced to identify the key components for entropy generation in the system environment. The results show that the labyrinth at outlet of unloading cavity is recognized as the one that generates the most entropy in the entire aeroengine system, and the total entropy generation of the system is highly related to this component. Besides, in the system environment, entropy generation is the sum of the local entropy generated by the components and the total entropy generated by mixing of airflows in each component. High local entropy generated by components does not necessarily result in a high system entropy production, and vice versa. Therefore, when the minimum system entropy generation is the design goal, the most critical operations for entropy generation should be identified according to the corresponding sensitivity and parameter variation range, and the design should be improved accordingly.

The analysis and modeling of the binary reactive flow of the Carreau–Yasuda fluid with thermal and solutal stratifications and Soret and Dufour effects

Thermal and mass transport in the Carreau Yasuda fluid stagnation point MHD flow is addressed through a stretchable surface in this study. Thermal and solutal stratifications are analyzed. They occur due to temperature and concentration variation. The activation energy in the mass transfer is used to enhance the results. It is the initial input of energy due to which reaction proceeds. The velocity slip effect is implemented at the boundary for the momentum equation. Soret and Dufour’s impact on a given flow is also studied. The entropy generation rate is computed mathematically and the results are presented through different plots for pertinent flow parameters. The governing PDE system is changed into an ordinary one by appropriate transformations. The obtained system is tackled through the ND-Solve MATHEMATICA for numerical results. It is seen that the concentration, temperature, and velocity distributions are diminished against rising values of thermal and solutal stratified parameters and slip. Also, we have seen that stratification is very useful in entropy generation minimization.

Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer.

The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs.

Numerical Investigation on the Heat Transfer Characteristics of Liquid Lithium Metal in a Bent Tube and Its Structure Optimization

Abstract Liquid lithium is expected to be the promising coolant for the next generation of space nuclear reactor power sources, and pipe structures have critical impacts on the flow and heat transfer characteristics, whereas related studies are still incomplete. In this work, a steady-state non-isothermal heat transfer model with modified turbulent Prandtl number is developed for the turbulent flow of liquid lithium in elbows with different bends. The results demonstrate that liquid lithium has best performance in a 90 deg bend in the Pe range of 320–955, which has the highest heat transfer performance per unit pressure drop and exhibits the lowest entropy generation. Due to the difference in flow velocity between the inner and outer sides of the pipe, a high-temperature region exists in the inner-wall area from the pipe bend and migrates from the wall side to the center area in the exit area. When decreasing the flow velocity and increasing the wall heat flow density, a more significant increase in the percentage of the high-temperature region is demonstrated on the inner wall side of the pipe in the exit area of the bend. Under a given total length of L, the inlet length H with the H/L ratio of 0.025 has the minimum entropy generation within the unit pressure drop, and is the best U-tube structure. This work provides comprehensive investigations on flow and heat transfer characteristics of liquid lithium in bends and U-tubes and inspires practical applications.