Hybrid numerical solution for unsteady state of constant accelerated MHD in a third-grade fluid with a rotation

Abstract

The aim of this research is to investigate the problem related to the constant accelerated of unsteady MHD third grade fluid in a rotating frame. New numerical approach will be used in order to solve the problem. Hybrid numerical approach of finite difference method and asymptotic interpolation method is introduced. This method is suitable for solving unbounded domain where the domain of the problems tends to infinity. Validation has been made with other analytical method; Homotopy Analysis Method to show that this hybrid method is acceptable. The equation of unsteady state MHD third grade fluid in a rotation about z-axis is derived. The nonlinear equation will be discretized by using finite difference method and couple with asymptotic interpolation to fulfil the unbounded domain of boundary condition. The effect of various values of parameters such as MHD, rotation, time, second and third grade are being tested and discussed. This study concludes that the velocity of distribution decreased when the value of MHD and rotation increased. Meanwhile a contrary result occurs when the factor of time increased. The velocity profile for real part also will be increased and imaginary part will be decreased when the parameter of second and third grade increased.