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A new numerical investigation of some thermo-physical properties on unsteady MHD non-Darcian flow past an impulsively started vertical surface

Motsa Sandile Sydney (University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Science, Scottsville, Pietermaritzburg, South Africa)
Animasaun Isaac L. (Federal University of Technology, Department of Mathematical Sciences, Akure, Ondo State, Nigeria)

The behaviour of unsteady non-Darcian magnetohydrodynamic fluid flow past an impulsively started vertical porous surface is investigated. The effect of thermophoresis due to migration of colloidal particles in response to a macroscopic temperature gradient is taken into account. It is assumed that both dynamic viscosity and thermal conductivity are linear functions of temperature. The governing equations are non-dimensionalized by using suitable similarity transformation which can unravel the behaviour of the flow at short time and long time periods. A novel iteration scheme, called bivariate spectral local linearization method is developed for solving the corresponding systems of highly non-linear partial differential equations. The results of the numerical solutions obtained are presented graphically and analyzed for the effects of the various important parameters entering into the problem on velocity, temperature, and concentration field within the boundary layer.

Keywords: bivariate Lagrange interpolation, variable thermal conductivity, unsteady flow, non-Darcian flow, impulsive stretching sheet, thermophoresis