General Solutions for Some MHD Motions of Second-Grade Fluids between Parallel Plates Embedded in a Porous Medium

General solutions are established for an initial boundary value problem by means of the integral transforms. They correspond to isothermal MHD unidirectional motion incompressible second-grade fluids between infinite horizontal parallel plates embedded in a porous medium. The fluid motion, which some situations becomes symmetric with respect median plane, is generated two that apply time-dependent arbitrary shear stresses fluid. Closed-form expressions both velocity and corresponding non-trivial stress. Using important remark regarding governing equations stress, exact general developed similar motions same when move their planes velocities. results have been obtained here can generate any technical relevance this type correctness being proved comparing them numerical solution or known from existing literature. Consequently, problems these stress on completely solved.