A numerical method capable is developed for handling steady laminar now and heat transfer of a highly viscous power-law fluid whose density, viscosity, specific heat and thermal conductivity, vary with temperature. The governing equations are found to be continuity, monmentum and energy expressions. Important effects such as varying viscosity, natural convection and viscous dissipation are incorporated in the theoretical model. These equations are being attracted by employing a decoupled finite element method. Galerkin＇s principle is used to handle the momentum and continuity equations. Consistent (SU/PG) and non-consistent (SU) streamline upwind methods are employed for the energy equation. Comparison of calculated results and experimental data shows good agreement. Similar results are obtained with SU and SU/PG methods. Velocity and temperature profiles which provide insights into the process are also given.