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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 applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

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Communications in Theoretical Physics 2021年第9期73卷 37-50页

作者： Aamar Abbasi Waseh Farooq M Ijaz Khan Sami Ullah Khan Yu-Ming Chu Zahid Hussain M Y Malik Department of Mathematics University of Azad Jammu and Kashmir Muzaffarabad13100 Pakistan Department of Mathematics and Statistics Riphah International University I-14Islamabad 44000Pakistan Department of Mathematics COMSATS University IslamabadSahiwal 57000Pakistan Department of Mathematics Huzhou UniversityHuzhou 313000China Department of Mathematics College of SciencesKing Khalid UniversityAbha 61413Saudi Arabia

entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation due to magnetic field,nonlinear thermal radiation,viscous dissipation,thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk.The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow,heat and mass transfer,while the second law of thermodynamics is used to analyze the entropy and irreversibility.The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method.The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks.The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks.Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks.The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion.The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant.It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip.The current results present many applications in the lubrication phenomenon,heating processes,cooling of devices,thermal engineering,energy production,extrusion processes etc.

关键词： entropy generation viscoelastic fluid lubricated surface nonlinear thermal radiation Joule heating Keller box method

entropy generation of MHD natural convection heat transfer in a heated incinerator using hybrid-nanoliquid

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Propulsion and Power Research 2021年第2期10卷 143-154页

作者： Bouchmel Mliki Mohamed Ammar Abbassi Materials Energy and Renewable EnergiesFaculty of Sciences of GafsaB.P.19ZarrougGafsa2112Tunisia

The present study explores magnetic hybrid-nanoliquid(Al_(2)O_(3)-Cu/H_(2)O)natural convection in a heated incinerator shaped cavity by using the lattice Boltzmann method(LBM).Numerical results are presented in the form temperature contours,stream function and local entropy generation.Complex interaction between various physical phenomena characterizing this problem including the natural convection and the magnetic field has been observed.Influences of Rayleigh number(Ra=10^(3)-10^(6)),volumetric fraction of nanoparticles(ϕ=0-0.04),and Hartmann number(Ha=0-90)are clarified in details through graphical portraits.Results depict that the average Nusselt number(Nu_(m))and average entropy generation(S_(gen,A))increases with an increase of the Rayleigh number while are decreased by applying a magnetic field.In addition,it is found that the average Nusselt number(Nu_(m))increases with the rise of volumetric fraction of nanoparticles for all Rayleigh and Hartmann numbers.Conversely,an opposite effect is obtained by an increase in volumetric fraction of nanoparticles on the average entropy generation(S_(gen,A)).Finally,the numerical results demonstrate that the effect of Lorentz force is reduced when the heat transfer regime conduction is considered.

关键词： Incinerator entropy generation Natural convection Hybrid-nanoliquid Magnetohydrodynamic(MHD)

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

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 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 under the influence of radial magnetic field and viscous dissipation of generalized Couette flow in an annulus

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Propulsion and Power Research 2018年第4期7卷 342-352页

作者： Taiwo S.Yusuf Michael O.Oni Department of Mathematics Ahmadu Bello UniversityZariaNigeria

This paper investigates the combined effect of radial magnetic field and viscous dissipation on entropy generation in horizontal co-axial cylinders of generalized Couette flow.The analytical solutions for velocity and temperature profiles are obtained and utilized to compute the entropy generation,Bejan number as well as the average entropy generation number.The effect of relevant parameters on temperature field,velocity field,entropy generation,average entropy and Bejan number are portrayed graphically and discussed.We isoflux heating near the inner surface of the fixed outer cylinder with higher dominance in the case of isoflux heating.The reverse is seen on the moving inner cylinder.

关键词： Radial magnetic field Viscous dissipation Generalized Couette flow Isothermal Isoflux entropy generation

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

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