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Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid

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Applied Mathematics and Mechanics(English Edition) 2021年第8期42卷 1205-1218页

作者： Tiehong ZHAO M.R.KHAN Yuming CHU A.ISSAKHOV R.ALI S.KHAN Department of Mathematics Hangzhou Normal UniversityHangzhou 311121China LSEC and ICMSEC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 1001900China School of Mathematical Science University of Chinese Academy of SciencesBeijing 1001900China Department of Mathematics Huzhou UniversityHangzhou 313000Zhejiang ProvinceChina Department of Mathematical and Computer Modeling Al-Farabi Kazakh National UniversityAlmaty 050040Kazakhstan Department of Mathematical and Computer Modeling Kazakh British-Technical UniversityAlmaty 050000Kazakhstan School of Mathematics and Statistics Central South UniversityChangsha 410083China

This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic(MHD)stagnation point flow across a stretchable *** heat transport process is investigated with respect to the viscous dissipation and thermal radiation,whereas the mass transport is observed under the influence of a chemical *** irreversibe factor is measured through the application of the second law of *** established non-linear partial differential equations(PDEs)have been replaced by acceptable ordinary differential equations(ODEs),which are solved numerically via the bvp4 c method(built-in package in MATLAB).The numerical analysis of the resulting ODEs is carried out on the different flow parameters,and their effects on the rate of heat transport,friction drag,concentration,and the entropy generation are *** is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number,although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter,*** entropy generation augments with boosting values of the Brinkman number,and decays with escalating values of both the radiation parameter and the Weissenberg number.

关键词： tangent hyperbolic fluid magnetohydrodynamic(MHD) viscous dissipation stagnation point flow heat generation/absorption thermal radiation

MHD stagnation point flow towards heated shrinking surface subjected to heat generation/absorption

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Applied Mathematics and Mechanics(English Edition) 2012年第5期33卷 631-648页

作者： T.HAYAT M.HUSSAIN A.A.HENDI S.NADEEM Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Physics Faculty of ScienceKing Saud UniversityRiyadh 11321Saudi Arabia

The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature （PST） and the prescribed heat flux （PHF）, are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presenta- tion of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.

关键词： stagnation point flow micropolar fluid shrinking sheet convergence ho-motopy analysis method

Magnetohydrodynamic stagnation point flow of a Maxwell Nanofluid with Variable Conductivity

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Communications in Theoretical Physics 2019年第12期71卷 1493-1500页

作者： M.Irfan M.Khan W.A.Khan M.Alghamdi Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Department of Mathematics Faculty of ScienceKing Khalid UniversityAbha 61413Kingdom of Saudi Arabia

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell *** Buongiorno’s theory has been established to picture the inducement of Brownian and thermophrotic diffusions ***,the aspect of heat sink/source is *** homotopic analysis method(HAM)has been worked out for the solution of nonlinear *** behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and *** attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration *** is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion ***,for the confirmation of our study comparison tables are reported.

关键词： Maxwell nanofluid stagnation point flow magnetohydrodynamic(MHD) variable conductivity chemical reaction

MHD stagnation point flow of Williamson Fluid over a Stretching Cylinder with Variable Thermal Conductivity and Homogeneous/Heterogeneous Reaction

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Communications in Theoretical Physics 2017年第6期67卷 688-696页

作者： M.Bilal M.Sagheer S.Hussain Y.Mehmood Department of Mathematics Capital University of Science and Technology

The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity *** system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.

关键词： stagnation point flow homogeneous/heterogeneous reaction Williamson fluid stretching cylinder variable thermal conductivity thermal stratification

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

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Communications in Theoretical Physics 2020年第12期72卷 71-82页

作者： Z H Khan M Usman T Zubair M Hamid R U Haq State Key Laboratory of Hydraulics and Mountain River Engineering College of Water Resource and HydropowerSichuan UniversityChengdu610065China BIC-ESAT College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering SciencePeking UniversityBeijing 100871China Institute of Ocean Research Peking UniversityBeijing 100871China School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mechanics and Engineering Science Fudan UniversityShanghai 200433China Department of Electrical Engineering Bahria UniversityIslamabad CampusIslamabad 44000Pakistan

This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching *** influence of thermophoresis and Brownian motion is also considered in transport *** nonlinear ODE set is obtained from the governing nonlinear equations via suitable *** numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme(RK-4)is available to show the credibility of the Galerkin *** numerical exploration is carried out for various governing parameters,namely,Brownian motion,steadiness,thermophoresis,stretching ratio,velocity slip,concentration slip,thermal slip,and fluid parameters,and Hartmann,Prandtl and Schmidt *** velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing,but the behavior is reversed for assisting *** Brownian motion and thermophoresis parameters cause an increase in temperature for both cases(assisting and opposing).The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis *** the outcomes and the behavior of emerging parameters are illustrated *** comparison analysis and graphical plots endorse the appropriateness of the Galerkin *** is concluded that said method could be extended to other problems of a complex nature.

关键词： Eyring-Powell fluid stagnation point flow Brownian motion and thermophoresis Galerkin method

Non-axisymmetric Homann MHD stagnation point flow of Al2O3-Cu/water hybrid nanofluid with shape factor impact

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Applied Mathematics and Mechanics(English Edition) 2020年第8期41卷 1125-1138页

作者： M.KHAN J.AHMED F.SULTANA M.SARFRAZ Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan Department of Basic Sciences University of Engineering and TechnologyTaxila 47050Pakistan

The heat transfer of Homann flow in the stagnation region of the Al2 O3-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical *** effects of the nanoparticle shape,the viscous dissipation,and the nonlinear radiation are *** governing equations are obtained by using similarity transformations,and the numerical outcomes for the flow and the temperature field are noted by bvp4 c on *** numerical solutions of the flow field are compared with the asymptotic behaviors of large shear-to-strain-rate *** effects of variations of parameters involved are inspected for both nanofluid and hybrid nanofluid flows,temperature profiles,local Nusselt numbers,and skin *** is concluded that the velocity and temperature fields in the hybrid nanophase function more rapidly than those in the nanofluid phase.

关键词： cylindrical disk hybrid nanofluid magnetic field non-linear thermal radiation stagnation point flow viscous dissipation

Nonlinear radiative heat transfer in magnetohydrodynamic(MHD)stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

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Propulsion and Power Research 2015年第4期4卷 230-239页

作者： Wubshet Ibrahim Department of Mathematics Ambo UniversityP.O.Box 19AmboEthiopia

Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is *** paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic(MHD)stagnation point flow past a stretching sheet with convective *** of zero normal flux of nanoparticles at the wall for the stretched flow is *** nanoparticle fractions on the boundary are considered to be passively *** solution for the velocity,temperature and nanoparticle concentration depends on parameters *** number Pr,velocity ratio parameter A,magnetic parameter M,Lewis number Le,Brownian motion Nb,and the thermophoresis parameter ***,the problem is governed by temperature ratio parameter Nr¼Tf T1and radiation parameter *** transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential *** equations were numerically solved using the function bvp4c from the matlab software for different values of governing *** results are obtained for velocity,temperature and concentration,as well as the skin friction coefficient and local Nusselt *** results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A *** local Nusselt number-θ0(0)decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr ***,radiation has a positive effect on temperature and concentration profiles.

关键词： Nonlinear radiative effect Stretching sheet stagnation point flow Convective boundary condition Passive control of nanoparticles

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

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Propulsion and Power Research 2016年第2期5卷 164-175页

作者： Wubshet Ibrahim Department of Mathematics Ambo UniversityP.O.Box 19AmboEthiopia

The present study examines the effect of induced magnetic field and convectiveboundary condition on magnetohydrodynamic(MHD)stagnation point flow and heat transfer dueto upper-convected Maxwell fluid over a stretching sheet in the presence of *** layer theory is used to simplify the equation of motion,induced magnetic field,energyand concentration which results in four coupled non-linear ordinary differential *** takes into account the effect of Brownian motion and thermophoresis *** equations and their associated boundary conditions are initially cast into dimensionlessfonm by similarity *** resulting system of equations is then solved numerically usingfourth order Runge-Kutta-Fehlberg method along with shooting *** solution for thegoverning equations depends on parameters such as,magnetic,velocity ratio parameter B,Biotnumber Bi,Prandtl number Pr,Lewis number Le,Brownian motion Nb,reciprocal of magnetic Prandtl number A,the thermophoresis parameter Nt,and Maxwell parameter β.The numerical results are obtained for velocity,temperature,induced magnetic field andconcentration profiles as well as skin friction coefficient,the local Nusselt number andSherwood *** results indicate that the skin friction coefficient,the local Nusseltnumber and Sherwood number decrease with an increase in B and M ***,local Sherwood number-φ'(O)decreases with an increase in convective parameter Bi,but the local Nusselt number-φ'(0)increases with an increase in *** results are displayed both ingraphical and tabular form to illustrate the effect of the governing parameters on thedimensionless velocity,induced magnetic field,temperature and *** numericalresults are compared and found to be in good agreement with the previously published resultson special cases of the problem.

关键词： Nanofluid stagnation point flow Heat transfer Convective boundarycondition Induced magneticfield Upper-convected Maxwell fluid

Magnetohydrodynamic(MHD)boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting

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Propulsion and Power Research 2017年第3期6卷 214-222页

作者： Wubshet Ibrahim Department of Mathematics Ambo UniversityP.O.Box 19AmboEthiopia

The paper examines the melting heat transfer in magnetohydrodynamic(MHD)stagnation point flow of a nanofluid past a stretching *** layer theory is employed to simplify the system of partial differential equations of motion,energy and concentration to three coupled non-linear ordinary differential *** non-linear ordinary differential equations and their boundary conditions are changed into dimensionless form by using suitable similarity variables before numerically solved using fourth order Runge-Kutta-Fehlberg method along with shooting *** effect of pertinent parameters on different flow fields are determined and discussed in detail through several plots and *** numerical results are obtained for velocity,temperature and concentration *** is found that the skin friction coefficient and Sherwood number decrease with an increase in B and M ***,the local Nusselt number-θ′(0)increases with an increase in B and ***,the results are compared and found to be in good agreement with the previously published results in limiting cases of the problem.

关键词： Nanofluid Magnetohydrodynamic(MHD) stagnation point flow Melting heat transfer