Abstract: Two-dimensional steady-state buoyancy driven flows of thermo-dependent shear-thinning power-law fluid confined in a square cavity, submitted to cross uniform heat fluxes, has been conducted numerically using a finite difference technique. The
parameters governing the problem are the thermo-dependence number (0 £ m £ 10) and the ratio between the heat flux imposed on the vertical walls and that imposed on the horizontal ones represented by a (0 £ a £1) , while the flow behavior index n is fixed at
(n = 0.6) and the Rayleigh number at (Ra = 5. 103) . The effects of these parameters on the flow structure and heat transfer characteristics have been analyzed.

Key words: Heat transfer; Natural convection; Non-Newtonian fluids; Numerical study; Square cavity.