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Applied Mathematics and Mechanics(English Edition) 2024年第6期45卷 1051-1070页

作者： P.S.REDDY P.SREEDEVI Department of Mathematics Rajeev Gandhi Memorial College of Engineering and TechnologyNandyal 518501India

The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.

关键词： volume fraction of nano-encapsulated phase change material(NEPCM) radiation Stefan number heat capacity ratio entropy generation

entropy generation for mixed convection flow in vertical annulus with two regions hydromagnetic viscous and Cu-Ag water hybrid nanofluid through porous zone: a comparative numerical study

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Propulsion and Power Research 2022年第3期11卷 401-415页

作者： T.Rahim J.Hasnain N.Abid Z.Abbas Department of Mathematics The Islamia University of BahawalpurBahawalpur63100Pakistan Department of Computer Sciences Bahria UniversityIslamabad44000Pakistan

The primary determination of this study is a numerical investigation of the entropygeneration (EG) in the steady two-region flow of viscous fluid and hybrid nanofluid (NF) in along-infinite vertical annulus having a clear region as well as porous media. Stoke’s and single-phase NF models are used to study the viscous fluid and hybrid nanofluid (HNF) heat transferdevelopments, respectively. Two types of nanoparticles are taken, such as copper (Cu) and sil-ver (Ag) within base fluid water to make it a HNF. Darcy-Brinkman law is also used to examinethe flow through the porous zone in the annulus. Necessary quantities have been used in thesystem of equations to transfer them into non-dimensional forms. For momentum and energytransport, the numerical results are evaluated for various model parameters and are examinedvia the shooting method in MATHEMATICA. It is noted that the momentum and energy trans-port are more significant when two immiscible fluids in a clear vertical annulus are taken. Thefindings also indicate that two-phase momentum and heat flow are greater when a NF is used in Region-II and lower when a HNF is used. The temperature (in Region-II) falls with a high na-nomaterials volume fraction (see Figure 4) while it is increased when the Hartman number isincreased. Moreover, velocity declines with increment in nanomaterials volume fraction. Thus,higher thermal conductivity can be accomplished by using a magnetic field.

关键词： Two-phase flow Hybrid nanofluid Viscous fluid Porous zone Vertical annulus entropy generation

entropy generation Analysis around Airfoil using Multi-Block Lattice Boltzmann Method

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Advances in Applied Mathematics and Mechanics 2022年第3期14卷 777-798页

作者： Wei Wang Jun Wang Zhiang Li Zhiliang Lin School of Energy and Power Engineering Huazhong University of Science and TechnologyWuhanHubei 430074China Foshan City Nanhai Jiuzhou Popula Fan Co.Ltd FoshanGuangdong 528222China

This present paper proposes aerodynamic forces and entropy generation characteristics on theﬂow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theﬂow loss mechanism.The block mesh reﬁnement was adopted in which a higher accuracy was needed in parts of the domain characterized by complexﬂow.The interpolated bounce-back method was used to treat the irregular curve.This numerical method can effectively solve the complexﬂowﬁeld simulation problems with reasonable accuracy and reli-ability by simulatingﬂow around plate and airfoil.Based on second law of thermo-dynamics,an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of theﬂowﬁeld at any position.After that,a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 air-foil as the research object.For unsteady condition,entropy generation rate and the drag force are not linearly related any more.Losses due to steady effects mainly con-sider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shed-ding vortex.

关键词： Loss mechanism entropy generation ﬂow past airfoil lattice Boltzmann method multiple-relaxation-time block mesh reﬁnement

An optimization method for enhancement of gas–liquid mass transfer in a bubble column reactor based on the entropy generation extremum principle

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Chinese Journal of Chemical Engineering 2023年第1期53卷 83-88页

作者： Chao Zhang Youzhi Liu Weizhou Jiao Hongyan Shen Xigang Yuan Shengkun Jia Shanxi Province Key Laboratory of Higee-Oriented Chemical Engineering North University of ChinaTaiyuan 030051China State Key Laboratory for Chemical Engineering School of Chemical Engineering and TechnologyTianjin UniversityTianjin 300072China

In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can be maximized with the increase of mass transfer rate,based on which the velocity field can be optimized.The oxygen gas–liquid mass transfer is the major rate–limiting step of the toluene emissions biodegradation process in bubble column reactor,so the entropy generation due to oxygen mass transfer is used as the objective function,and the conservation equations of the gas–liquid flow and species concentration are taken as constraints.This optimization problem is solved by the calculus of variations,the optimal liquid flow pattern is obtained and the relationship of the maximum mass transfer enhancement on viscous dissipation is revealed,which can be used to improve the design of internal structure of the bubble column reactor.

关键词： entropy generation Bubble column reactor Optimization Biodegradation Flow field

Turbulent Double-Diffusive Natural Convection and entropy generation within an Inclined Square Cavity

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Fluid Dynamics & Materials Processing 2022年第6期18卷 1619-1629页

作者： Khaled Said Ahmed Ouadha Amina Sabeur Laboratoire des Sciences et Ingénierie Maritimes Facultéde Génie MécaniqueUniversitédes Sciences et de la Technologie Mohamed BOUDIAF d’OranOran El-MnouarAlgérie

The present study deals with double-diffusive convection within a two-dimensional inclined cavity filled with an air-CO_(2) binary gas mixture.The left and the right vertical walls are differentially heated and subjected to different locations of(CO_(2))contaminants to allow for the variation of the buoyancy strength(N).However,the horizontal walls are assumed adiabatic.The simulations are conducted using the finite volume method to solve the conservation equations of continuity,momentum,energy,and species transport.Good agreement with other numerical results in the literature is obtained.The effect of multiple parameters,namely,buoyancy ratio(N),thermal Rayleigh number(Ra),and inclination angle(α)on entropy generation rate is analyzed and discussed in the postprocessing stage,while considering both laminar and turbulent flow regimes.The computations reveal that these parameters considerably affect both the heat and mass transfer performances of the system.

关键词： CFD entropy generation double diffusive convection inclination angle CO_(2) turbulent regime

entropy generation and Thermal Radiation Effects on Nanofluid over Permeable Stretching Sheet

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Journal of Mathematical Research with Applications 2022年第5期42卷 523-538页

作者： S.K.ASHA G.MALI Department of Mathematics Karnatak University

In the present paper, effects of entropy generation and nonlinear thermal radiation on Jeffery nanofluid over permeable stretching sheet with partial slip effect were analyzed. The suitable similarity transformation is utilized for the reduction of a set of governing equations,which are solved by using Differential Transformation Method(DTM) with the help of symbolic software MATHEMATICA. The accuracy of impact of slip parameter on coefficient of skin friction by using DTM and numerical method(Shooting technique with fourth-order RungeKutta) is illustrated and good agreement is found. Further, velocity, temperature, nanoparticle volume fraction and entropy generation profiles are shown graphically and studied in detail for various physical parameters. We notice that, as slip parameter rises the velocity and entropy generation profile rises. Enhancement in the effect of nonlinear thermal radiation reduces the entropy generation.

关键词： stretching sheet partial slip permeable nonlinear thermal radiation entropy generation Jeffrery nanofluid

entropy generation in bypass transitional boundary layer flows

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Journal of Hydrodynamics 2014年第5期26卷 669-680页

作者： GEORGE Joseph OWEN Landon D. XING Tao MCELIGOT Donald M. CREPEAU John C. BUDWIG Ralph S. NOLAN Kevin P. Department of Mechanical Engineering College of EngineeringUniversity of IdahoMoscowIdaho 83843USA University of Idaho Idaho FallsIdaho 83402USA University of Idaho BoiseIdaho 83702USA Imperial College London London SW7-28ZUK

The primary objective of this study is to evaluate the accuracy of using computational fluid dynamics （CFD） turbulence models to predict entropy generation rates in bypass transitional boundary layers flows under zero and adverse pressure gradients. entropy generation rates in such flows are evaluated employing the commercial CFD software, ANSYS FLUENT. Various turbulence and transitional models are assessed by comparing their results with the direct numerical simulation （DNS） data and two recent CFD studies. A solution verification study is conducted on three systematically refined meshes. The factor of safety method is used to estimate the numerical error and grid uncertainties. Monotonic convergence is achieved for all simulations. The Reynolds number based on momentum thickness, Reo, skin-friction coefficient, Cf, approximate entropy generation rates, S, dissipation coefficient, Cd , and the intermittency, y, are calculated for bypass transition simulations. All Reynolds averaged Navier-Stokes （RANS） turbulence and transitional models show improvement over previous CFD results in predicting onset of transition. The transition SST k - ω 4 equation model shows closest agreement with DNS data for all flow conditions in this study due to a much finer grid and more accurate inlet boundary conditions. The other RANS models predict an early onset of transition and higher boundary layer entropy generation rates than the DNS shows.

关键词： entropy generation bypass transition Reynolds averaged Navier-Stokes （RANS） transitional boundary layer turbulence models

entropy generation analysis for the peristaltic flow of Cu-water nanofluid in a tube with viscous dissipation

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Journal of Hydrodynamics 2017年第1期29卷 135-143页

作者： Noreen Sher Akbar Adil Wahid Butt DBS&H CEMENational University of Sciences and TechnologyIslamabadPakistan DBS&H MCENational University of Sciences and TechnologyIslamabadPakistan

The purpose of the current investigation is to examine the influence of different physical parameters on the entropy gene- ration. The entropy generation number due to heat transfer and fluid friction is formulated. The velocity and temperature distributions across the tube are presented along with pressure attributes. Exact analytical solution for velocity and temperature profile is obtained. It is found that the entropy generation number attains high values in the region close to the walls of the tube, while it falls to low values near the center of the tube.

关键词： entropy generation heat transfer nanofluid Cu-water uniform robe

entropy generation analysis of thermally developing forced convection in fluid-saturated porous medium

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Applied Mathematics and Mechanics(English Edition) 2008年第2期29卷 229-237页

作者： K.Hooman A.Ejlali F.Hooman School of Engineering The University of QueenslandBrisbaneAustralia Fix Equipment Lead Engineer Namavaran Delvar Engineering and Construction CompanyTehranIran Chemical Engineering Department Sharif University of TechnologyTehranIran

entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates is investigated analytically on the basis of the Darcy flow model where the viscous dissipation effects had also been taken into account. A parametric study showed that decreasing the group parameter and the Peclet number increases the entropy generation while for the Brinkman number the converse is true. Heatline visualization technique is applied with an emphasis on the Br 〈 0 case where there is somewhere that heat transfer changes direction at some streamwise location to the wall instead of its original direction, i.e., from the wall.

关键词： entropy generation porous media heatline energy flux vectors forced convection

entropy generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

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Computers, Materials & Continua 2020年第1期62卷 37-59页

作者： Mohamed Abd El-Aziz A.M.Aly Department of Mathematics Faculty of ScienceKing Khalid UniversityAbha61411Saudi Arabia Department of Mathematics Faculty of ScienceHelwan UniversityHelwan-Cairo11795Egypt Department of Mathematics Faculty of ScienceSouth Valley UniversityQena83523Egypt

In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(nentropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.

关键词： Boundary layer entropy generation exponentially stretching surface magnetic field sisko-fluid