This investigation addresses the problem of numerically predicting the heat transfer rates between parallel surfaces of the type found in electronic equipment. This has been accomplished through a unique application of the finite-element method for transient or steady-state, two-dimensional mixed convection heat transfer with surface radiation. The approach was specifically geared toward implementation on present engineering workstations. Results are presented for mixed-convection in vertical channels using the full-elliptic form of the Navier-Stokes equations with radiation effects included. The results show that the heat transfer and flow solutions can be significantly affected when not using common approximations and simplifications.