Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio （width to height ratio）. These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Rant [14].

Design Optimization and Analysis of Exit Rotor with Diffuser Passage based on Neural Network Surrogate Model and Entropy Generation Method

In this paper,a diffuser passage compressor design is introduced via optimization to improve the aerodynamic performance of the exit rotor in a multistage axial compressor.An in-house design optimization platform,based on genetic algorithm and back propagation neural network surrogate model,is constructed to perform the optimization.The optimization parameters include diffusion angle of meridian passage,diffusion length of meridian passage,change of blade camber angle and blade number.The impacts of these design parameters on efficiency and stability improvement are analyzed based on the optimization database.Two optimized diffuser passage compressor designs are selected from the optimization solution set by comprehensively considering efficiency and stability of the rotor,and the influencing mechanisms on efficiency and stability are further studied.The simulation results show that the application of diffuser passage compressor design can improve the load coefficient by 12.1%and efficiency by 1.28%at the design mass flow rate condition,and the stall margin can be improved by 12.5%.According to the local entropy generation model analysis,despite the upper and lower endwall loss of the diffuser passage rotor are increased,the profile loss is reduced compared with the original rotor.The efficiency of the diffuser passage rotor can be influenced by both loss and load.At the near stall condition,decreasing flow blockage at blade root region can improve the stall margin of the diffuser passage rotor.

Total entropy generation rate minimization configuration of a membrane reactor of methanol synthesis via carbon dioxide hydrogenation

The total entropy generation rate,internal exergy loss and exergy efficiency of the membrane reactor of methanol synthesis via carbon dioxide hydrogenation are compared,and the results show that the total entropy generation rate minimization is equivalent to the internal exergy loss minimization and the exergy efficiency maximization under the fixed inlet exergy.Therefore,this paper optimizes the membrane reactor with total entropy generation rate minimization as an optimization objective under a fixed methanol production rate.The optimal temperatures curves of exterior walls for three optimal membrane reactors with different boundary conditions are obtained by using optimal control theory and nonlinear programming.The influences of other geometric and operating parameters on optimization results of optimal membrane reactors are analyzed.The results indicate that when inlet temperatures of the reaction mixture and mixture in the permeable tube are unfixed,the optimizing curve of exterior wall temperature makes the total entropy generation rate of membrane reactor reduce by 12.39%compared with the total entropy generation rate of a reference membrane reactor with a linear exterior wall temperature.Decreasing the inlet molar flow rate of sweep gas and gas hourly space velocity and increasing inlet pressure of reaction mixture,the inlet pressure of mixture in the permeable tube and heat transfer coefficients are favorable for decreasing the total entropy generation rate in the membrane reactor.As the porosity of catalyst bed and reactor length increases,the minimum total entropy generation rate decreases first and then increases.From the perspective of engineering application,this paper establishes two membrane reactors(membrane reactor heated by three-stage furnaces of the same length and membrane reactor heated by threestage furnaces of different lengths),respectively.The minimum total entropy generation rates of the two reactors are reduced by11.67%and 11.79%compared with the total entropy generation rate in the reference membrane reactor,respectively.The obtained results are beneficial to the optimal design of energy-efficient membrane reactors.

Application of Metaheuristic Algorithms for Optimizing Longitudinal Square Porous Fins

The objectives of this study involve the optimization of longitudinal porous fins of square cross-section using metaheuristic algorithms.A generalized nonlinear ordinary differential equation is derived using Darcy and Fourier’s laws in the energy balance around a control volume and is solved numerically using RFK 45 method.The temperature of the base surface is higher than the fin surface,and the fin tip is kept adiabatic or cooled by convection heat transfer.The other pertinent parameters include Rayleigh number(100≤Ra≤10^(4)),Darcy number,(10^(−4)≤Da≤10^(−2)),relative thermal conductivity ratio of solid phase to fluid(1000≤kr≤8000),Nusselt number(10≤Nu≤100),porosity(0.1≤φ≤0.9).The impacts of these parameters on the entropy generation rate are investigated and optimized using metaheuristic algorithms.In computer science,metaheuristic algorithms are one of the most widely used techniques for optimization problems.In this research,three metaheuristic algorithms,including the firefly algorithm(FFA),particle swarm algorithm(PSO),and hybrid algorithm(FFAPSO)are employed to examine the performance of square fins.It is demonstrated that FFA-PSO takes fewer iterations and less computational time to converge compared to other algorithms.

Second Law Analysis and Optimization of Elliptical Pin Fin Heat Sinks Using Firefly Algorithm

One of the most significant considerations in the design of a heat sink is thermal management due to increasing thermal flux and miniature in size.These heat sinks utilize plate or pin fins depending upon the required heat dissipation rate.They are designed to optimize overall performance.Elliptical pin fin heat sinks enhance heat transfer rates and reduce the pumping power.In this study,the Firefly Algorithm is implemented to optimize heat sinks with elliptical pin-fins.The pin-fins are arranged in an inline fashion.The nature-inspired metaheuristic algorithm performs powerfully and efficiently in solving numerical global optimization problems.Based on mass,energy,and entropy balance,three models are developed for thermal resistance,hydraulic resistance,and entropy generation rate in the heat sink.The major axis is used as the characteristic length,and the maximum velocity is used as the reference velocity.The entropy generation rate comprises the combined effect of thermal resistance and pressure drop.The total EGR is minimized by utilizing the firefly algorithm.The optimization model utilizes analytical/empirical correlations for the heat transfer coefficients and friction factors.It is shown that both thermal resistance and pressure drop can be simultaneously optimized using this algorithm.It is demonstrated that the performance of FFA is much better than PPA.

Multi-objective optimization for membrane reactor for steam methane reforming heated by molten salt

A membrane reactor for steam methane reforming heated by molten salt(MS-SMRMR)is studied based on finite time thermodynamics for decreasing carbon emissions and improving hydrogen production rate(HPR).Effects of flow directions of sweep gas and molten salt on MS-SMRMR are researched.Profiles of temperatures,HPR,and local entropy generation rates(EGRs)of MS-SMRMR are analyzed.Hybrid particle swarm optimization algorithm is utilized to obtain the minimum of specific EGR(SEGR),ratio of EGR to HPR.Multi-objective optimization about HPR maximization and EGR minimization is performed by utilizing NSGA-II.The EGR caused by the mass transfer process is the largest among all irreversible processes in the MS-SMRMR.The membrane length should be slightly shorter than the reactor length when the flow direction of sweep gas is different from that of reaction mixture.When flow directions of molten salt and sweep gas are opposite to that of reaction mixture,SEGR is the smallest.Compared with SEGR calculated by utilizing initial parameters,SEGRs after primary,twice and triple optimizations reduce by 1.2%,5.5%and 5.7%,respectively.SEGR can be further decreased by adjusting other operating parameters.Pareto front provides many optimization results,and it contains SEGR minimization.In Pareto front,an optimum decision point is obtained based on decision-making of TOPSIS,and its EGR and HPR,respectively,increase by 7.12%and13.24%,compared with those obtained by using initial parameters.The results have certain theoretical guiding significance for optimization designs of MS-SMRMR.