This research investigates the steady, laminar Couette flow of a viscous incompressible fluid through a porous medium bounded by two infinite horizontal parallel plates. A transverse magnetic field and thermal radiation effects are typically incorporated to analyze their impact on the flow and thermal characteristics. the fluid is electrically conducting, the effects of the porosity of the medium, the surface stretching velocity, The heat generation coefficient on both the flow and heat transfer are presented. The governing partial differential equations for momentum and energy are formulated based on Darcy's law.