This paper is devoted to introduce a numerical simulation
with a theoretical study for flow of a Newtonian fluid over an impermeable
stretching sheet which embedded in a porous medium with a power
law surface velocity and variable thickness in the presence of thermal
radiation. The flow is caused by a non-linear stretching of a sheet. Thermal
conductivity of the fluid is assumed to vary linearly with temperature.
The governing PDEs are transformed into a system of coupled
non-linear ODEs which are using appropriate boundary conditions for
various physical parameters. The proposed method is based on replacement
of the unknown function by truncated series of well known shifted
Legendre expansion of functions. An approximate formula of the integer
derivative is introduced. Special attention is given to study the convergence
analysis and derive an upper bound of the error of the presented
approximate formula. The introduced method converts the proposed
equation by means of collocation points to a system of algebraic equations
with shifted Legendre coefficients. Thus, by solving this system of
equations, the shifted Legendre coefficients are obtained. The effects of
the porous parameter, the wall thickness parameter, the radiation parameter,
thermal conductivity parameter and the Prandtl number on the
flow and temperature profiles are presented. Moreover, the local skinfriction
and Nusselt numbers are presented. Comparison of obtained
numerical results is made with previously published results in some special
cases, and excellent agreement is noted. The results attained in this
paper confirm the idea that proposed method is powerful mathematical
tool and it can be applied to a large class of linear and nonlinear
problems arising in different fields of science and engineering.