Novel insights into the computational techniques in unsteady MHD second‐grade fluid dynamics with oscillatory boundary conditions

Abstract

AbstractThis study presents mechanisms for the investigation of an unsteady magnetohydrodynamic second‐grade fluid flow between two periodically oscillating plates. The flow characterization is given in three forms, that is, Couette flow, Poiseuille flow, and a combination flow of both of them. A mathematical system is generated to design the problems, which are solved in an analytical way with two novel procedures, namely Adomian decomposition method (ADM) and optimal homotopy asymptotic method (OHAM). The numerical comparison, absolute errors, and residuals of OHAM and ADM solutions are evaluated. Results obtained from these two methods are studied comparatively in the form of numbers and graphs. A good agreement between the respective data is obtained. The influences of flow parameters like frequency parameter, non‐Newtonian fluid parameter, magnetic field parameter, pressure gradient parameter, and time variable on velocity have been analyzed.