Numerical investigations are conducted into steady laminar combined convection flows of a power taw fluid between vertical parallel plates with constant wall temperatures. The parabolic boundary layer equations are written in an implicit finite difference form and are then solved using a marching technique. The governing parameters are Gr/ Re, Pr, and the non-Newtonian power law index n. Various values of Gr/Re and n are considered, including the forced convection solution, Gr/Re = 0, and the Newtonian case, n = /. Pr is set at a value of unity in order to present the numerical method. Under certain circumstances, reverse flow regions appear, either at the center or adjacent to the wall of the duct, and these are dealt with using an iterative technique. Results are presented in terms of velocity profiles, local and average Nusselt numbers, and friction factors.