Asif Munir

Flow and heat transfer in Sisko fluid with convective boundary condition.

In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index , magnetic parameter , stretching parameter , generalized Prandtl number Pr and generalized Biot number are presented graphically. It is found that temperature profile increases with the increasing value of and whereas it decreases for . Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results.

Flow and Heat Transfer to Sisko Nanofluid over a Nonlinear Stretching Sheet

The two-dimensional boundary layer flow and heat transfer to Sisko nanofluid over a non-linearly stretching sheet is scrutinized in the concerned study. Our nanofluid model incorporates the influences of the thermophoresis and Brownian motion. The convective boundary conditions are taken into account. Implementation of suitable transformations agreeing with the boundary conditions result in reduction of the governing equations of motion, energy and concentration into non-linear ordinary differential equations. These coupled non-linear ordinary differential equations are solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting technique. The effects of the thermophoresis and Brownian motion parameters on the temperature and concentration fields are analyzed and graphically presented. The secured results make it clear that the temperature distribution is an increasing function of the thermophoresis and Brownian motion parameters and concentration distribution increases with the thermophoresis parameter but decreases with the Brownian motion parameter. To see the validity of the present work, we made a comparison with the numerical results as well as previously published work with an outstanding compatibility.

Convective Flow of Sisko Fluid over a Bidirectional Stretching Surface

The present investigation focuses the flow and heat transfer characteristics of the steady three-dimensional Sisko fluid driven by a bidirectional stretching sheet. The modeled partial differential equations are reduced to coupled ordinary differential equations by a suitable transformation. The resulting equations are solved numerically by the shooting method using adaptive Runge Kutta algorithm in combination with Newtons method in the domain [0,∞). The numerical results for the velocity and temperature fields are graphically presented and effects of the relevant parameters are discussed in detail. Moreover, the skin-friction coefficient and local Nusselt number for different values of the power-law index and stretching ratio parameter are presented through tabulated data. The numerical results are also verified with the results obtained analytically by the homotopy analysis method (HAM). Additionally, the results are validated with previously published pertinent literature as a limiting case of the problem.

Mixed convective heat transfer to Sisko fluid over a radially stretching sheet in the presence of convective boundary conditions

In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case.

Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden’s method in the domain. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.

MHD flow and heat transfer of a viscous fluid over a radially stretching power-law sheet with suction/injection in a porous medium

A steady boundary layer flow and heat transfer over a radially stretching isothermal porous sheet is analyzed. Stretching is assumed to follow a radial power law, and the fluid is electrically conducting in the presence of a transverse magnetic field with a very small magnetic Reynolds number. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by using appropriate similarity transformations, which are solved analytically by the homotopy analysis method (HAM) and numerically by employing the shooting method with the adaptive Runge-Kutta method and Broyden’s method in the domain [0,∞). Analytical expressions for the velocity and temperature fields are derived. The influence of pertinent parameters on the velocity and temperature profiles is discussed in detail. The skin friction coefficient and the local Nusselt number are calculated as functions of several influential parameters. The results predicted by both methods are demonstrated to be in excellent agreement. Moreover, HAM results for a particular problem are also compared with exact solutions.