Azeem Shahzad

A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet

This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.

On the Exact Solution for Axisymmetric Flow and Heat Transfer over a Nonlinear Radially Stretching Sheet

We investigate the boundary-layer flow and heat transfer of a magnetohydrodynamic viscous fluid over a nonlinear radially porous stretching sheet within a porous medium. The flow is generated due to a nonlinear stretching sheet and influenced by a continuous suction/blowing of the fluid through the porous sheet. The governing momentum and thermal boundary layer equations are converted into ordinary differential equations by appropriate similarity transformations. The exact solution for the velocity and the temperature fields are derived in the form of an incomplete Gamma function. Also analytic solutions are found by the homotopy analysis method. The graphical results for velocity and temperature fields are presented and discussed. Further, the numerical values of the skin friction coefficient and the Nusselt number are calculated and discussed.

Analytic and numerical solutions for axisymmetric flow with partial slip

This article deals with the slip effects on the axisymmetric flow of an electrically conducting viscous fluid in the presence of a magnetic field over a non-linear radially stretching sheet. By introducing new similarity transformations, the governing partial differential equations are reduced to an ordinary differential equation. The resulting ordinary differential equation is then solved analytically using the homotopy analysis method and numerically by shooting method to show the accuracy of the analytical solution. The significant effects of various parameters on velocity field are discussed in detail. The shear stress at the wall together with some other physical parameters is tabulated and compared with existing literature, which shows an excellent agreement.

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.

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.

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.

Analytic approximate solutions for time-dependent flow and heat transfer of a Sisko fluid

Purpose – The purpose of this paper is to find analytic approximate solutions for time-dependent flow and heat transfer of a Sisko fluid. Design/methodology/approach – The homotopy analysis method is used to find a family of travelling wave solutions of the governing non-linear problem. Findings – The effects of different parameters on the velocity and temperature profiles are shown graphically. Originality/value – The analytic solutions of the system of non-linear ordinary differential equations are constructed in the series form for various values of the power index.

Falkner–Skan Boundary Layer Flow of a Sisko Fluid

In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.

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.