Combined Porous and Magnetic Effects on Some Fundamental Motions of Newtonian Fluids Over an Infinite Plate

General expressions for the dimensionless velocity and shear stress fields and the skin friction coefficient corresponding to the motion due to a moving plate are used to provide new interesting solutions for the second problem of Stokes. As a novelty, the solutions corresponding to the motion induced by cosine oscillations of the plate reduce to the classical solutions of Stokes' first problem if the frequency of the plate oscillations becomes or tends to zero. Porous and magnetic effects are taken into consideration and, for the first time in the literature, their combined influence is graphically underlined and discussed for some motions with engineering applications. As an application, exact solutions are developed for motions induced by an arbitrary time-dependent shear stress on the boundary. In both cases, characteristics of hydromagnetic motion of Newtonian fluids over an infinite plate embedded in a porous medium do not depend on magnetic and porous parameters independently and a two-parameter approach is superfluous or even misleading both physically and computationally.