This paper investigated the run‐up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run‐up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed‐form solution for the velocity in the Laplace domain. Semi‐analytical result is obtained by an inversion technique based on Riemann‐sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research.

Some properties of time-dependent that modify Brinkman equations for fluid flow in a cylindrical tube filled with Bidisperse Porous Material are discussed in this article. The fluid velocities through the fracture and porous phases of the Bidisperse Porous Medium (BDPM) resulting from the application of pressure gradient are described by two coupled second-order partial differential equations. Laplace transform technique, D'Alembert and Riemann-Sum Approximation Methods are used to obtain a semianalytical solution for the model. The choice of the