Z. Abbas

On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet

In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.

Unsteady flow of a second grade fluid film over an unsteady stretching sheet

In this article, the flow problem in a thin liquid film of second grade fluid over an unsteady stretching surface is investigated. By means of suitable transformations, the governing nonlinear partial differential equation has been reduced to the nonlinear ordinary differential equation. The developed nonlinear equation is solved analytically by using the homotopy analysis method (HAM). An expression for analytic solution is derived in the form of a series. The convergence of the obtained series is shown explicitly through numerical computations. The effects of various parameters on the velocity components are shown through graphs and discussed. The values of the skin-friction coefficient for different emerging parameters are also tabulated.

Radiation and Mass Transfer Effects on the Magnetohydrodynamic Unsteady Flow Induced by a Stretching Sheet

This investigation deals with the influence of radiation on magnetohydrodynamic (MHD) and mass transfer flow over a porous stretching sheet. Attention has been particularly focused to the unsteadiness. The arising problems of velocity, temperature, and concentration fields are solved by a powerful analytic approach, namely, the homotopy analysis method (HAM). Velocity, temperature, and concentration fields are sketched for various embedded parameters and interpreted. Computations of skin friction coefficients, local Nusselt number, and mass transfer are developed and examined.

FLOW OF AN EYRING-POWELL NON-NEWTONIAN FLUID OVER A STRETCHING SHEET

This article is devoted to the study of the boundary layer flow of a non-Newtonian fluid over a stretching sheet. The non-Newtonian behavior of the fluid is characterized by the constitutive equation due to Powell and Eyring (1944). A second-order approximation of the Eyring-Powell model is used to obtain the flow equations. A local similarity solution of the governing problem is obtained numerically using an implicit finite difference scheme known as the Keller box method. The influence of pertinent non-Newtonian fluid parameters M and λ on the velocity and skin-friction coefficient is analyzed through graphical and tabular results.

STRETCHING FLOWS WITH GENERAL SLIP BOUNDARY CONDITION

General slip boundary condition is used to solve the viscous incompressible flows induced by a stretching sheet. These flow problems corresponds to the planar and axisymmetric stretching. A similarity solution is developed by shooting method using Runge–Kutta algorithm. The results are graphically displayed and discussed under the influence of slip parameter and critical shear rate. The comparison of stretching flow problem subject to Naviers boundary condition in the planar case is made with the available numerical results in the literature.

Heat transfer analysis for stretching flow over a curved surface with magnetic field

The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.

Magnetohydrodynamic Flow and Mass Transfer of a Jeffery Fluid over a Nonlinear Stretching Surface

This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of a Jeffery fluid induced by a nonlinearly stretching sheet with mass transfer. The relevant system of partial differential equations has been reduced into ordinary differential equations by employing the similarity transformation. Series solutions of velocity and concentration fields are developed by using the homotopy analysis method (HAM). Effects of the various parameters such as Hartman number, Schmidt number, and chemical reaction parameter on velocity and concentration fields are discussed by presenting graphs. Numerical values of the mass transfer coefficient are also tabulated and analyzed.

Hydromagnetic Flow and Heat Transfer of a Jeffrey Fluid over an Oscillatory Stretching Surface

Abstract The flow and heat transfer of a Jeffrey fluid over an oscillatory stretching sheet is investigated using the boundary-layer approximations. The flow is induced due to infinite elastic sheet that is stretched periodically. The number of independent variables in the governing equations was reduced by using appropriate dimensionless variables. This dimensionless system has been solved by using the homotopy analysis method (HAM) and a finite difference scheme, in which a coordinate transformation was used to transform the semi-infinite physical space to a bounded computational domain. A comparison of both solutions is provided. The effects of involved parameters are illustrated through graphs and discussed in detail.

Effects of Porosity and Mixed Convection on MHD Two Phase Fluid Flow in an Inclined Channel

The present study deals with the flow and heat transfer analysis of two immiscible fluids in an inclined channel embedded in a porous medium. The channel is divided in two phases such that a third grade fluid occupies the phase I and a viscous fluid occupies the phase II. Both viscous and third grade fluids are electrically conducting. A constant magnetic field is imposed perpendicular to the channel walls. The mathematical model is developed by using Darcys and modified Darcys laws for viscous and third grade fluids respectively. The transformed ordinary differential equations are solved numerically using a shooting method. The obtained results are presented graphically and influence of emerging parameters is discussed in detail.

Homotopy Analysis for Stagnation Slip Flow and Heat Transfer on a Moving Plate

The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous fluid over a moving plate with partial slip has been investigated. The effects of partial slip on the flow and heat transfer characteristics are considered. The equations of conservation of mass, momentum, and energy, which govern the flow and heat transfer, are solved analytically using homotopy analysis method. The convergence of the series solution is analyzed explicitly. Comparison of the present homotopy results is made with the existing numerical and asymptotic solution (Wang, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate ,” Chem. Eng. Sci., 23, pp. 7668–7672) and an excellent agreement is achieved.