Entropy Generation Minimization Research Articles

Multi-objective performance optimization of ammonia decomposition thermal storage reactor

Heat storage technology plays an essential role in the stable operation of solar thermal power generation. In this paper, a one-dimensional model of a tubular filled bed heat absorption reactor for ammonia decomposition is established by applying finite time thermodynamics. Taking the inlet temperature, the outside diameter and the length of the reactor as optimization variables, the multi-objective particle swarm optimization is used to perform multi-objective optimization considering the maximum heat absorption rate and the minimum total entropy generation rate, and the Pareto Fronts are determined under different reactor outer wall temperatures. Finally, three optimized reactors’ design parameters and performance indicators are obtained by LINMAP, TOPSIS and Shannon Entropy decision methods, and the cross-sectional comparisonof the optimal reactors at different outer wall temperatures. Compared to the reference reactor, the three optimized reactors improve heat absorption rate by 58%-143%, while the total entropy generate rate is reduced by 26.4%-38.8%. The obtained results have some guidance for optimal designs of ammonia decomposition reactor in real engineering.

Isentropic contours of natural convection heat generated enclosures

In house CFD code, FVHT has been used to solve the dimensionless form of the governing equations of heat transfer utilizing a hybrid TDMA method within a high-order finite volume approach. Enclosures with different aspect ratios (0.25 to 8) have been studied with different heat generation rates (6 to 14) in dimensionless form. The enclosures were in natural convection heat transfer mode filled with water (Pr = 6.2) having Rayleigh number from 103 to 106. Coupled entropy and energy equations in the presence of heat generation have been solved to obtain the iso-contours of the entropy within the enclosures. The mapping is beneficial in the selection of suitable aspect ratio of the cooling enclosure for minimum entropy generation at specified operating condition (heat generation and Rayleigh number). The numerical results of the total entropy generation as function of aspect ratio, Rayleigh number and heat generation are correlated.

Design and application of a cooling device based on peltier effect coupled with electrohydrodynamics

Miniaturization has become the development trend of light-emitting diodes (LEDs), which results in a significant increase in heat flux production and operating temperature. The accumulated heat should be dissipated effectively to ensure that the chip can work properly. The conventional cooling techniques have now reached their limits in heat removal rates. A new cooling device coupled thermoelectric cooling (TEC) with corona wind cooling (CWC) was proposed and optimized experimentally based on the second law of thermodynamics and the principle of entropy generation minimization. The results indicate that a better cooling effect and a high coefficient of performance value is obtained by turning on the TEC near the heat source firstly and adjusting the CWC power at the hot side. Increasing the input power of TEC and keeping the total cooling power unchanged, another 4.7% improvement is obtained with the highest heating power of 14 W. The target temperature can be maintained at an acceptable level (＜80 °C) if the TEC and CWC are well coupled. However, the coupling effect between TEC and CWC will be worse when the input power is large. A higher output luminous flux will be obtained when the LED chip works in the constant current mode due to the good coupling between CWC and TEC. The luminescence intensity and chromaticity properties are improved significantly. The principal component analysis (PCA) also indicates excellent comprehensive performance. The results verify the feasibility of a novel cooling device coupled TEC with CWC in cooling high heat flux electronics.

Thermodynamic Analysis of a High-Temperature Latent Heat Thermal Energy Storage System

Thermal energy storage (TES) technologies are becoming vitally important due to intermittency of renewable energy sources in solar applications. Since high energy density is an important parameter in TES systems, latent heat thermal energy storage (LHTES) system is a common way to store thermal energy. Though there are a great number of experimental studies in the field of LHTES systems, utilizing computational codes can yield relatively quick analyses with relatively small expense. In this study, a numerical investigation of a LHTES system has been studied using ANSYS FLUENT. Results are validated with experiments, using hydroquinone as a phase-change material (PCM), which is external to Therminol VP-1 as a heat transfer fluid (HTF) contained in pipes. Energy efficiency and entropy generation are investigated for different tube/pipe geometries with a constant PCM volume. HTF inlet temperature and flow rate impacts on the thermodynamic efficiencies are examined including viscous dissipation effects. Highest efficiency and lowest entropy generation cases exist when when flow rates are lowest due to low viscous heating effects. A positive relation is found between energy efficiency and volume ratio while it differs for entropy generation for higher and lower velocities. Both efficiency and entropy generation decreased with decreasing HTF inlet temperature. The novelty of this study is the analysis of the effect of volume ratio on system performance and PCM melting time which ultimately proved to be the most dominant factor among those considered herein. However, as PCM solidification and melting time is of primary importance to system designers, simply minimizing entropy generation by decreasing volume ratio in this case does not lead to a practically optimal system, merely to decrease heat transfer entropy generation. Therefore, caution should be taken when applying entropy analyses to any LHTES storage system as entropy minimization methods may not be appropriate for practicality purposes.

Comments on “New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials”

The correct form of Bejan number is presented.

Nozzle design influence on the steam-driven ejector

In the present paper, a series of numerical simulations of wet steam flows within ejectors distinguished by four primary nozzle contours have been carried out with the objective to evaluate the overall ejector performance. The studied primary nozzle contours are the following: a standard Laval nozzle (LAVAL); a nozzle that is designed in order to provide Constant Expansion Rate (CER); and two nozzles (MOC_SHORT, MOC_LONG) that are designed by employing axisymmetric Method of Characteristics. At first, the wet steam flow simulation throughout solely nozzles are carried out. Within the CFD simulations routines most valuable flow parameters are compared: expansion rates, boundary layer displacement and momentum thicknesses; entropy generation rate from various thermodynamic forces; thrust and liquid mass fraction across the nozzle exit plane. A comprehensive analysis of solely nozzles revealed that the CER nozzle contour is the most aerodynamically efficient design, which provides the minimum liquid mass fraction by the nozzle exit and possess the minimum entropy generation rate. The CFD results analysis of a full ejector domain revealed that an ejector with a MOC_SHORT primary nozzle contour provides the maximum performance in terms of secondary mass flow rate. At that, the secondary mass flow rate in MOC_SHORT nozzle contour case is almost 4% greater than for the CER nozzle design case.

Can the shape influence entropy generation for thermal convection of identical fluid mass with identical heating? A finite element introspection

PurposeThis paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).Design/methodology/approachGalerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 103–105. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (Sψ and Sθ). Average Nusselt number () and average dimensionless spatial temperature () are also evaluated via the finite element basis sets.FindingsBased on larger , larger and optimal Stotal values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger , optimum Stotal) and concave (larger ). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.Practical implicationsComparison of entropy generation, intensity of thermal mixing () and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.Originality/valueThis study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of Sψ (Sψ,max), Sθ (Sθ,max) and magnitude of Stotal vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

Numerical simulation and modeling of entropy generation in Marangoni convective flow of nanofluid with activation energy

AbstractIn this article, Marangoni convective flow of nanofluid is considered. Entropy generation minimization is also considered. Equations are constructed for Buongiorno model of nanofluid. Flow is generated by rotating disk. Activation energy, nonlinear mixed convection, and MHD effects are also taken in consideration. Ordinary differential equation is formed by using appropriate variables. Results are formed by using Shooting method. Results of temperature, axial velocity, entropy, radial velocity, concentration, and Bejan number are discussed through graphs. Radial and axial velocities are increasing functions of Marangoni ratio parameter. Temperature and concentration are decreasing functions of Marangoni ratio parameter. Entropy is increasing function of Marangoni ratio parameter. Bejan number declines via Marangoni ratio parameter.

Multi-Objective Optimization of Thermal Management System in LED Bulbs Based on Entropy Generation Minimization Concept

In this paper, the thermal behavior of heat sinks with parabolic fins (convex type) in an analytical method is investigated. The considered heat sinks are used for thermal control in LED lamps. To evaluate cooling performance of these devices, the energy balance of considered heat sinks with fins is evaluated. In the derived equation, the effect of mass transfer and thermal radiation is considered and the thermal conductivity is varied with temperature. An efficient analytical method—differential transformation method—is used to the analytical solution of the governing equations. Comparison of the analytical and numerical solutions shows excellent accuracy of the selected analytical solution. Based on the proposed analytical solution, the effect of operational and geometrical parameters on the system thermal management is evaluated. Finally, a multi-objective optimization is performed to maximize the thermal efficiency and minimize the entropy generation.

Hydrothermal and entropy generation specifications of a hybrid ferronanofluid in microchannel heat sink embedded in CPUs

The objective of this numerical work is to evaluate the first law and second law performances of a hybrid nanofluid flowing through a liquid-cooled microchannel heatsink. The water-based hybrid nanofluid includes the Fe3O4 and carbon nanotubes (CNTs) nanoparticles. The heatsink includes a microchannel configuration for the flow field to gain heat from a processor placed on the bottom of the heatsink. The effects of Fe3O4 concentration (φFe3O4), CNT concentration (φCNT) and Reynolds number (Re) on the convective heat transfer coefficient, CPU surface temperature, thermal resistance, pumping power, as well as the rate of entropy generation due to the heat transfer and fluid friction is examined. The results indicated higher values of convective heat transfer coefficient, pumping power, and frictional entropy generation rate for higher values of Re, φFe3O4 and φCNT. By increasing Re, φFe3O4and φCNT, the CPU surface temperature and the thermal resistance decrease, and the temperature distribution at the CPU surface became more uniform. To achieve the maximum performance of the studied heatsink, applying the hybrid nanofluid with low φFe3O4and φCNT was suggested, while the minimum entropy generation was achieved with the application of nanofluid with high φFe3O4and φCNT.

Effect of conjugate heat transfer on the thermo-electro-hydrodynamics of nanofluids: entropy optimization analysis

We investigate, in this analysis, the entropy generation characteristics associated with the transport of nanofluid in a microfluidic channel under the combined influences of applied pressure gradient and electrical forcing. In our study, the nanofluid is subjected to an asymmetric cooling at the channel walls, while the conductive transport of heat through the channel walls is also taken into account. We show that the underlying thermo-electro-hydrodynamics of nanofluids in the channel lead to entropy generation, attributed to the irreversibilities associated with heat transfer, viscous dissipation, and Joule heating effects. We establish that a non-trivial interplay among these irreversibilities gives rise to an optimum value of the geometrical parameter, viz. the channel wall thickness ( $$ \delta $$ ), and the thermophysical parameters, viz. the thermal conductivity of the wall $$ (\gamma ) $$ , Biot number (Bi), and the modified Peclet number ( $$ \overline{\text{Pe}} $$ ), leading to a minimum entropy generation rate of the system. Also, we unveil through this study that changes in the electroosmotic parameter $$ \bar{\kappa } $$ (representative of the EDL thickness) or the composition of the fluid ( $$ \phi $$ , the volume fraction of nanoparticles agglomerates) non trivially alter the optimum values of these parameters. Inferences drawn from this analysis may have consequences in the optimum design of thermal systems/devices, typically used for thermal management in micro-heat exchangers, micro-reactors, and micro heat pipes.

Simulation study on the performance of a vapor-bypassed evaporator for heat pump applications

• A mathematical model for the vapor-bypassed evaporator is developed. • Corresponding experiments were conducted to validate the model accuracy. • Entropy generation is applied to evaluate the evaporator overall performance. • Phase separation position and channel number of the evaporator are optimized. This paper presents a simulation study on the vapor-bypassed evaporator for heat pump applications. The vapor-bypassed evaporator, in which a phase separator is set in the middle of the refrigerant circuit to bypass vapor refrigerant, can reduce the refrigerant pressure drop for enhancing the evaporator overall performance. A mathematical model for the vapor-bypassed evaporator is developed and the experiments were conducted to validate its accuracy. Based on the entropy generation minimization theory, the optimum phase separation positions and refrigerant channel numbers of the evaporator for various operation conditions are selected out. According to the simulation results, as the required heat transfer capacity ranges 4~10 kW, the vapor-bypassed (VB) mode obtains 25.6~84.6 kPa lower refrigerant pressure drop and 3.1~25.3% lower entropy generation than the conventional operation (CO) mode. Moreover, when the ambient temperature ranges 5~15°C, the entropy generation of VB mode is decrease by 22.3~11.5% than CO mode. In general, applying the vapor-bypassed technique is a promising way for improving the evaporator performance especially under high heat transfer capacity and low ambient temperature conditions.

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 generation analysis in magnetohydrodynamic Sisko nanofluid flow with chemical reaction and convective boundary conditions

The main emphasis of the present study is to analyze the novel feature of entropy generation in the flow and heat transfer of Sisko nanofluid over a stretching sheet in the presence of the magnetic field, chemical reaction, and convective boundary conditions. Buongiorno's nanofluid model is used to consider the effect of Brownian diffusion and thermophoresis. The governing Sisko nanofluid flow equations comprising the momentum, nanoparticle volume fraction, and energy are reduced to nonlinear differential equations by utilizing appropriate similarity variables. The numerical solution of nonlinear coupled differential equations is obtained using the finite difference scheme in combination with the quasilinearization technique. The impact of different physical parameters on velocity, nanoparticle volume fraction, and temperature is presented graphically. The variation in entropy generation and Bejan number with different pertinent parameters that characterize the entropy generation phenomenon for the flow of Sisko nanofluid is discussed. The obtained results indicate that the entropy generation enhances with an increase in the magnetic parameter, Brinkman number, and thermal Biot number while reduces with the Sisko material parameter. Moreover, the behavior of mass and heat transfer rates is displayed through the Brownian diffusion parameter and thermophoresis parameter. The analysis of entropy generation minimization has crucial applications in the industrial heat transfer problems, solar heat exchanger, turbomachinery designing, LED‐based spotlights, designing of air‐cooled gas turbine blades, cooling in nuclear fuel rods, rotating reactors, in chillers, air separators, and so forth. Furthermore, entropy generation with MHD flow has applications in MHD generators, nuclear reactors, flow meters, micropumps, power plants, and so forth.

Physics successfully implements Lagrange multiplier optimization.

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip-flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.

Performance assessment of longitudinal flow through rod bundle of ETRR-2 Cobalt/Iridium irradiation device

In the present paper, three dimension CFD analysis was presented for longitudinal flow through rod bundle of ETRR2 Cobalt/Iridium irradiation device. Study of optimal performance for both heat transfer and flow characteristics was performed by the determination of the conditions at which minimum entropy generation exist. The study was performed for Reynolds number (Re) in the range 2 × 104 ≤ Re ≤ 5.5 × 105, and Prandtl number (Pr) in the range 3.2 ≤ Pr ≤ 5.2 under both the conditions of uniform and non uniform (cosine shape) heat flux. Contours of fluid temperature and fluid velocity at irradiation box outlet as well as temperature contours of Ir rods at different values of inlet velocity were illustrated. Two correlations one relating the Nusselt number (Nu) with Re and Pr and the other relating skin friction factor with Re was presented in the studied range of Re and Pr. Determination of the applicability of the existing correlations for turbulent forced convection heat transfer and friction coefficient are also presented. Comparison between the flow and heat transfer characteristics through Ir rods of different locations in the irradiation box is presented.

Entropy generation minimization of a pump running in reverse mode based on surrogate models and NSGA-II

Pumps in reverse function are one of the most cost-effective industrial devices to generate power from small hydropower capacities. Due to the fact that the pump components are not inherently designed for the turbine mode, the hydraulic performance of the pump as turbine (PAT) is usually not ideal. One low-cost solution to improve the PAT performance is to redesign the pump Impeller without changing of any other components. In this study a multi-objective optimization process is applied based on the surrogate models with focus on minimizing the entropy generation rate (EGR) at 2 flow rates of the QBEP (best efficiency point) and Q1.3BEP in order to improve the hydraulic performance of the PAT over a wide range of operating points. In the optimization process, the sample space points are determined by the optimal Latin hypercube sampling (OLHS) technique. The values of the objective functions and the constraints at the sample points are specified by numerical solution of the 3D incompressible steady-state RANS equations. Kriging (KRG) surrogate models have been constructed to estimate the objective functions and constraints at the whole sample space. The blade inlet and outlet angles, the blade wrap angle, the runner inlet width and the number of blades are defined as the design variables. Finally, by using non-dominated sorting genetic algorithm II (NSGA-II), in addition to obtaining the Pareto optimal fronts (POFs), the optimal combinations of the design variables are determined. Analysis of the importance level of the design variables has been performed using the RSA surrogate model. Optimization results reveals that the maximum reduction in the EGR occurs in the optimal 8-bladed runner by approximately 50%. The decrease in the entropy production leads to a decrease in irreversible hydraulic losses and an increase in the hydraulic efficiency of the PAT, e.g. 3.8% and 5.72% increase in efficiency at the QBEP and Q1.3BEP, respectively. Flow field analysis demonstrates that the entropy generation minimization causes a reduction in flow disorders within the optimal PATs. As a result, inlet shock, flow deviation at the blade outlet, flow separation at the blade passage, backflow and swirling flow at the draft tube are dramatically reduced or completely eliminated. The optimization of the PAT with the help of surrogate models and evolutionary algorithms (EAs), from the point of view of the second law of thermodynamics, has been successfully investigated in this work and the improvement of hydraulic performance was achieved.

Entropy generation of mixed convection of SWCNT–water nanofluid filled an annulus with a rotating cylinder and porous lining under LTNE

PurposeThe purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.Design/methodology/approachThe discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.FindingsIt is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.Originality/valueTo the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

Numerical study of magnetohydrodynamic mixed convection and entropy generation of Al[formula omitted]O[formula omitted]-water nanofluid in a channel with two facing cavities with discrete heating

In this work, transient numerical simulations are carried out to investigate the effect of alumina nanoparticles with pure water as a base fluid on mixed convection with magnetohydrodynamic flow in a vertical channel with two facing identical open cubic cavities with discrete heating. The nanofluids are modeled using a single phase approach and the fluid properties are considered constant with temperature. The left and right vertical walls of the cavities are isothermal, all other bounding walls of the cavity and the channel are adiabatic, and a uniform magnetic field is applied in the horizontal direction. The governing Navier–Stokes equations in vorticity and stream function form coupled with the energy equation are solved using the control volume method on a nonuniform orthogonal Cartesian grid. A parametric study has been carried out for three different Hartmann numbers of (Ha=0;5;10) Richardson numbers of (Ri=−1;5), nanoparticle volume fractions of (φ=0.0;0.1;0.2) and Reynolds number ranging from 300 to 700. The effects of the nanoparticle volume fraction and magnetic field on hydrodynamic and thermal characteristics and entropy generation for assisting/opposing buoyancy have been assessed. In general, it has been found that in the range of parameters considered in this study, the entropy generation is dominated by irreversibilities due to heat transfer for all values of φ. The results show that the vortex dynamics, heat transfer characteristics and the magnitude of irreversibilities in the entropy generation are strongly affected by the strength of the magnetic field applied and the nanoparticle volume fraction. Moreover, these results suggest that the modulation effect of the applied magnetic field can play an important role in practical applications for entropy generation minimization.

Minimum Entropy Generation Rate and Maximum Yield Optimization of Sulfuric Acid Decomposition Process Using NSGA-II.

Based on the theory of finite-time thermodynamics (FTT), the effects of three design parameters, that is, inlet temperature, inlet pressure, and inlet total mole flow rate, of a tubular plug-flow sulfuric acid decomposition reactor on the total entropy generation rate (EGR) and SO2 yield are analyzed firstly. One can find that when the three design parameters are taken as optimization variables, the minimum total EGR and the maximum SO2 yield of the reference reactor restrict each other, i.e., the two different performance objectives cannot achieve the corresponding extremum values at the same time. Then, the second-generation non-dominated solution sequencing genetic algorithm (NSGA-II) is further used to pursue the minimum total EGR and the maximum SO2 yield of the reference reactor by taking the three parameters as optimization design variables. After the multi-objective optimization, the reference reactor can be Pareto improved, and the total EGR can be reduced by 9% and the SO2 yield can be increased by 14% compared to those of the reference reactor. The obtained results could provide certain theoretical guidance for the optimal design of actual sulfuric acid decomposition reactors.