Abstract
In this article, the semi-analytical technique of the Hybrid Analytical and Numerical Method (the HAN Method) is used to study the non-transient forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion that is constrained between two plates. The magnetic field is also present in this model. The governing equations are in the PDE form and by using the Von Kármán similarity variables, they transformed into a set of ODEs. The HAN-method is applied to solve the ODEs and their associated boundary conditions, analytically. In addition, for the validation, the HAN solution results were compared with the HPM and numerical technique of Runge-Kutta results. And finally, new results were extracted from the HAN solutions in a quantitative form.