An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium

Abstract

An implicit-Chebyshev collocation spectral method is employed in this study. This method was used to compute the problem of unsteady free convection with heat transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium, which is modeled as a power-law fluid. Boundary layer and Boussinesq approximations have been incorporated. The Darcy–Brinkman–Forchheimer model is applied to describe the flow field, where the magnetic field and the radiation effects are taken into account. Because of the non-Newtonian rheology, these problems are non-linear and must be solved numerically. The domain of the problem is discretized according to the implicit-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix and the time derivatives are computed with Crank–Nicolson implicit finite-difference method. Numerical calculations are carried out for the various parameters entering into the problem. Velocity and temperature profiles are shown in tables and graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficients approach the steady state values.