Seripah Awang Kechil

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching flat plate is solved by using the Adomian decomposition method (ADM). The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.

Approximate analytical solutions for a class of laminar boundary-layer equations

A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a general analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.

Adomian decomposition associated with Newton-Cotes formula for solving Goursat problem

The Goursat partial differential equation is a hyperbolic partial differential equation which arises in various fields of study. Many approaches have been suggested to approximate the solution of the Goursat partial differential equation such as the finite difference method, Runge-Kutta method, finite element method, differential transform method, and modified variational iteration method. These methods traditionally focus on numerical differentiation approaches including the forward and central differences in deriving the schemes. In this paper we have developed a new scheme to solve the Goursat partial differential equation that applies the Adomian decomposition (ADM) associated with the Newton-Cotes formula for approximating the integration terms. The homogeneous linear Goursat problems are examined and the new scheme supplied quantitatively reliable results for these types of problems. The accuracy level of the results obtained indicates the superiority of these new schemes over standard scheme that a...

Magnetohydrodynamics (MHD) boundary layer flow over a stretching cylinder embedded in a porous medium

A steady axisymmetric boundary layer flow of an incompressible viscous fluid along a stretching cylinder embedded in porous medium in the presence of magnetic field is studied. The governing partial differential boundary layer equations with boundary conditions are first transformed into ordinary differential equations using similarity transformation before being solved numerically by a finite-difference method. The effects of magnetic parameter, curvature parameter, permeability parameter and Prandtl number on the characteristics of heat transfer were analyzed. It is found that the local Nusselt number decreases with increasing magnetic parameter. The velocity decreases with the increase of magnetic and permeability parameters. Both parameters present resistance to the flow, thus the flow becomes slower.

Analysis of Non-Newtonian Fluid Boundary Layer Flows Due to Surface Tension Gradient

The paper considers non-Newtonian power-law fluid flow driven by the convection of surface tension gradient in the presence of transverse magnetic field along a free-surface. The aim is to examine the effects of temperature and solute-dependent surface tension and magnetic field on the boundary layer flow of non-Newtonian fluids. The governing partial differential equations are reduced to a set of ordinary differential equations using similarity transformations. The coupled nonlinear system of equations is solved using a numerical approach known as the fourth-order finite difference scheme with shooting method. The numerical calculations were carried out for various values of fluid physical properties: power-law index, thermosolutal Marangoni number, and magnetic parameter. The results indicate that the free-surface velocity decreases with the increasing number of power-law index. As the thermosolutal Marangoni number increases, the thickness of thermal boundary layer decreases, while the surface temperature and concentration gradients increases. The magnetic field modifies the flow patterns of the non-Newtonian power-law fluid by reducing the fluid velocity at the surface.

Thermal controller effect on Marangoni instability in a fluid layer with insoluble surfactant

The effect of linear proportional feedback thermal controller on the onset of steady Marangoni instability in a horizontal fluid layer with insoluble surfactants is studied theoretically by using linear stability analysis. The exact analytical solution for the stationary modes is obtained and the effects of elasticity number, thermal controller gain, surface deformation, Galileo number, Lewis number and Biot number on the onset of Marangoni convection are determined.The elasticity number, Biot number, Galileo number and small controller gain are found to have stabilizing effects on the fluid layer but the Lewis number and large controller gain are destabilizing factors. The heat transfer mechanism and the presence of insoluble surfactant at the free surface significantly stabilize the fluid system.

Radiation effects on laminar boundary layer flow along a stretching cylinder

A steady boundary layer flow and heat transfer over a continuously stretching cylinder in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to nonlinear ordinary differential equations. Numerical solutions are obtained by employing the implicit finite difference of Keller-box scheme. The effects of radiation parameter, curvature parameter and Prandtl number on the heat transfer on the surface were discussed. It can be concluded that as the radiation parameter increases, the heat transfer decreases, while when Prandtl number or temperature exponent increases, the heat transfer at the surface increases.

Symbolic Solution to Magnetohydrodynamic Hiemenz Flow in Porous Media

A system of nonlinear ordinary differential equations governing the boundary layers of magnetohydrodynamic (MHD) Hiemenz flow in porous media is solved using a simple and efficient analytical technique of Adomian decomposition method (ADM) and Pade approximant through the computer algebra package system Maple. Several symbolic features of the Maple system are utilized to develop specific routines that compute the approximate analytical solutions of the stream, velocity and temperature functions for some exemplary prescribed parameters. Comparative study shows the well agreement of the present symbolic results with the existing numerical results.