We study the transient magnetohydrodynamic (MHD) viscous laminar flow and heat transfer in a channel containing a Darcy-Forchheimer porous medium, under a constant pressure gradient with Hall current, ionslip, transpiration, viscous and Joule heating. The dimensionless momentum and heat conservation equations are solved using the Network Simulation Method (NSM). The effects of a number of thermophysical parameters on the transport phenomena are studied including Darcy number (Da), Forchheimer quadratic drag number (Fs), Hartmann number (Ha), Hall current parameter (βe), ionslip parameter (βi) and Eckert number (Ec). The model finds applications in geophysics and MHD energy generators.