Approximate Solutions for the Flow and Heat Transfer due to a Stretching Sheet Embedded in a Porous Medium with Variable Thickness, Variable Thermal Conductivity and Thermal Radiation using Laguerre Collocation Method

In this article, a numerical approach is given for studying the flow of a Newtonian fluid over an impermeable stretching sheet 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 Laguerre expansion of functions. An approximate formula of the integer derivative is introduced. The introduced method converts the proposed equations by means of collocation points to a system of algebraic equations with Laguerre coefficients. Thus, by solving this system of equations, the Laguerre 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 skin-friction and Nusselt numbers are presented. Comparison of obtained numerical results is made with previously published results in some special cases. The results attained in this paper confirm the idea that the proposed method is powerful mathematical tool and it can be applied to a large class of nonlinear problems arising in different fields of science and engineering.