Thermal analysis in an electrically conducting fluid with multiple slips and radiation along a plate: A case study of Stokes' second problem

Stoke's problems significantly impact several domains, including industrial manufacturing, geophysical flows, chemical engineering, and heat conduction. Stoke's second problem deals with the movement of a semi-infinite viscous incompressible fluid caused by an oscillating flat plate. Thus, this work examines Stoke's second problem for an unsteady hydromagnetic surface-driven flow along an infinite flat plate in the presence of thermal radiation and heat dissipation. The governing momentum and energy equations form an emerging nonlinear system of partial differential equations through dimensionless proxies. MAPLE 2022 is employed to solve the resulting system of nonlinear partial differential equations that control the flow both analytically and numerically in specific situations. The analytical solutions are displayed graphically, along with variations of skin friction and Nusselt number at the plate. It has been observed that momentum and thermal slips significantly diminished the flow characteristics to cause damping flow rate and temperature distributions. Rising the values of Magnetic and velocity slip parameters, an oscillatory motion is observed in skin friction. This is due to the periodic and wavy nature of the boundary wall. Furthermore, a rise in the Prandtl number and radiation value correspondingly boosted the wall heat gradient profiles. Finally, this study will assist industry and engineering in understanding the sensitivity of their working fluids to parameter variations and for the exact prediction of their base fluids.