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Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

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Chinese Physics B 2013年第2期22卷 314-319页

作者： Krishnendu Bhattacharyya Tasawar Hayat Ahmed alsaedi Department of Mathematics The University of BurdwanBurdwan-713104West BengalIndia Department of Mathematics Quaid-I-Azam University 45320Islamabad 44000Pakistan Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is *** similarity transformations,the governing equations are converted to an ordinary differential equation and then solved *** introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet *** similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the *** stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.

关键词： magnetohydrodynamic boundary layer Casson fluid stretching/shrinking sheet wall mass transfer analytic solution

MHD three dimensional flow of viscoelastic fluid with thermal radiation and variable thermal conductivity

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Journal of Central South University 2014年第10期21卷 3911-3917页

作者： SHEHZAD S A HAYAT T alsaedi a Department of Mathematics Comsats Institute of Information Technology Department of Mathematics Quaid-i-Azam University

The objective of the present work is to model the magnetohydrodynamic(MHD) three dimensional flow of viscoelastic fluid passing a stretching surface. Heat transfer analysis is carried out in the presence of variable thermal conductivity and thermal radiation. Arising nonlinear analysis for velocity and temperature is computed. Discussion to importantly involved parameters through plots is presented. Comparison between present and previous limiting solutions is shown. Numerical values of local Nusselt number are computed and analyzed. It can be observed that the effects of viscoelastic parameter and Hartman number on the temperature profile are similar in a qualitative way. The variations in temperature are more pronounced for viscoelastic parameter K in comparison to the Hartman number M. The parameters N and ε give rise to the temperature. It is interesting to note that values of local Nusselt number are smaller for the larger values of ε.

关键词： three dimensional flow viscoelastic fluid variable thermal conductivity thermal radiation

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

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Applied Mathematics and Mechanics(English Edition) 2014年第6期35卷 717-728页

作者： T.HAYAT S.ASAD A.alsaedi Department of Mathematics Quaid-i-Azam University Islamabad 44000 Pakistan Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.

关键词： Casson fluid thermal radiation variable thermal conductivity inclined stretching cylinder

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

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Chinese Physics B 2014年第12期23卷 289-292页

作者： Krishnendu Bhattacharyya Tasawar Hayat Ahmed alsaedi Department of Mathematics The University of Burdwan Department of Mathematics Quaid-I-Azam University Department of Mathematics Faculty of Science King Abdulaziz University

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.

关键词： dual solutions boundary layer flow Maxwell fluid porous shrinking sheet

Melting effect and Cattaneo-Christov heat flux in fourth-grade material flow through a Darcy-Forchheimer porous medium

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Applied Mathematics and Mechanics(English Edition) 2021年第12期42卷 1787-1798页

作者： T.HAYAT K.MUHAMMAD A.alsaedi department of mathematics quaid-i-azam universityislamabad 44000pakistan nonlinear analysis and applied mathematics(naam)research group department of mathematicsfaculty of scienceking abdulaziz universityjeddah 80203saudi arabia

The melting phenomenon in two-dimensional(2 D)flow of fourth-grade material over a stretching surface is *** flow is created via a stretching surface.A Darcy-Forchheimer(D-F)porous medium is considered in the flow *** heat transport is examined with the existence of the Cattaneo-Christov(C-C)heat *** fourth-grade material is electrically conducting subject to an applied magnetic *** governing partial differential equations(PDEs)are reduced into ordinary differential equations(ODEs)by appropriate *** solutions are constructed analytically through the optimal homotopy analysis method(OHAM).The fluid velocity,temperature,and skin friction are examined under the effects of various involved *** fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter,porosity parameter,and Forchheimer *** fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number,magnetic parameter,and thermal relaxation ***,the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters,thermal relaxation parameter,and Forchheimer number.

关键词： melting heat Darcy-Forchheimer(D-F)porous medium magnetohydrodynamics(MHD) Cattaneo-Christov(C-C)heat flux fourth-grade fluid optimal homotopy analysis method(OHAM)

Solitary Wave Solutions of Some Nonlinear Physical Models Using Riccati Equation Approach

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 401-418页

作者： Zaid ODIBAT Ahmed alsaedi Tasawar HAYAT School of Basic Sciences and umanities German Jordanian UniversityAmman 11180Jordan Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics Quaid-I-Azam UniversityIslamabad 44000Pakistan

Riccati equation approach is used to look for exact travelling wave solutions of some nonlinear physical *** wave solutions are established for the modified KdV equation,the Boussinesq equation and the Zakharov-Kuznetsov *** generalized solitary wave solutions with some free parameters are *** obtained solutions,which includes some previously known solitary wave solutions and some new ones,are expressed by a composition of Riccati differential equation solutions followed by a *** employed approach,which is straightforward and concise,is expected to be further employed in obtaining new solitary wave solutions for nonlinear physical problems.

关键词： solitary wave solution Riccati equation the modified KdV equation the Boussinesq equation the Zakharov-Kuznetsov equation

Flow of Burgers' fluid over an inclined stretching sheet with heat and mass transfer

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Journal of Central South University 2015年第8期22卷 3180-3188页

作者： T.Hayat Sadia Asad A.alsaedi Department of Mathematics Quaid-i-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Department of Mathematics Faculty of Science King Abdulaziz University

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting theη-curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time(β1 and β2) and angle of inclination(α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time(β3) and mixed convection parameter(G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number,-θ′(0), and local Sherwood number,-f′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

关键词： Burgers' fluid thermal radiation inclined stretching sheet non-uniform heat source variable thermal conductivity

Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid

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Journal of Central South University 2015年第8期22卷 3211-3216页

作者： T.Hayat M.Imtiaz A.alsaedi Department of Mathematics Quaid-I-Azam University NAAM Research Group Department of Mathematics Faculty of ScienceKing Abdulaziz University

The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method(HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter(ε) whereas it decreases by increasing the fluid material parameter(δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.

关键词： Powell-Eyring fluid boundary layer flow stretching sheet homogeneous-heterogeneous reactions

Three-dimensional mixed convection squeezing flow

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Applied Mathematics and Mechanics(English Edition) 2015年第1期36卷 47-60页

作者： T.HAYAT A.QAYYUM A.alsaedi Department of Mathematics Quaid-i-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Faculty of Science King Abdulaziz University

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations （ODEs） by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.

关键词： squeezing flow, mixed convection, vertical rotating channel unsteadystretching porous sheet