Abstract

FINITE DIFFERENCE SOLUTION FOR MAGNETOHYDRODYNAMICS THIN FILM FLOW OF A THIRD GRADE FLUID DOWN INCLINED PLANE WITH OHMIC HEATING

Lawal Oluwafemi Waheed, Loyinmi Adedapo Chris, Hassan Anthony Rotimi

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Abstract. This study investigates the numerical solution of Magnetohydrodynamic (MHD) thin film flow of a third grade fluid down inclined plane with heat transfer. This problem has been studied by Aiyesimi, Okedayo and Lawal [1] using the traditional and homotopy perturbation methods. In this present study, the governing non-linear ordinary differential equations are reduced to a system of non-linear algebra using implicit finite difference schemes and then solved using damped-Newton method. Also, the solutions obtain in [1] are only valid for the weak non-linearity. However the numerical solutions obtained in this study is valid for all values of the physical parameter and their effects on the velocity and temperature profile are presented graphically. Keywords: Third grade fluid, Magnetohydrodynamics flow, Thin film flow, Finite difference method, Ohmic heating.

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