The paper aims to study the combined effects of uniform magnetic field and inertia on a three-dimensional flow of a viscous fluid in a vertical channel. It is assumed that the fluid is injected into the channel through one side of the channel. The flow and heat transfer phenomena have been characterized by non-dimensional parameters R (cross-flow Reynolds number), M (magnetic parameter), Pe (Peclet number), and 𝛼𝛼 (heat generation parameter). The basic equations governing the flow and heat transfer are reduced to set of ordinary differential equations using the appropriate transformations for velocity components and temperature. These equations have been solved approximately subject to be relevant boundary conditions by employing a numerical technique. The effects of the above-mentioned parameters on the velocity and temperature distributions have been examined carefully.