The incompressible Poiseuille flow and heat transfer of a power-law fluid across an inclined long square cylinder confined in a two-dimensional channel is investigated numerically in the steady laminar flow regime. The effects of inclination angle, alpha, and power-law index, n, on the non-dimensional pumping power and the Nusselt number are studied for the conditions: 1 <= Re <= 40, 0 <= alpha <= 45, 0.4 <= n <= 1.8, Pr = 50 and blockage ratio beta = 1/4. It is verified that the flow is steady in these ranges of conditions and the vortex shedding occurs only for n = 0.4 and alpha= 45 at Re >= 33. In the steady flow regime the results show that the total drag coefficient on the cylinder increases with an increase in the power-law index and the maximum total lift coefficient occurs at alpha = 15. Moreover, a decrease in the power-law index and/or an increase in the inclination angle increase the Nusselt number and decrease the non-dimensional local pumping power. Simple correlations are also introduced for drag coefficient, local pressure drop and Nusselt number as functions of n, alpha and Re. (C) 2011 Elsevier B.V. All rights reserved.