Two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated vertical sidewalls subjected to both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been carried out where the enclosures are considered to be completely filled with non-Newtonian power-law fluids. The influences of the CWT and CWHF boundary conditions on the effects of aspect ratio (AR = H/L where H is the enclosure height and L is the enclosure length), in the range 0.125 <= AR <= 8, on the heat transfer characteristics have been investigated numerically for power-law index n in the range 0.6 <= n <= 1.8 for nominal values of Rayleigh number (Ra) ranging from 10(4) to 10(6) and at a nominal Prandtl number (Pr) of 10(3). A scaling analysis is performed to elucidate the anticipated effects of aspect ratio, Rayleigh number, Prandtl number and power-law index on the mean Nusselt number for power-law fluids. It is found that the mean Nusselt number (Nu) over bar follows a non-monotonic trend with aspect ratio AR for a given set of values of the Rayleigh number and Prandtl number for shear-thinning (n < 1), Newtonian (n = 1) and shear-thickening (n > 1) fluids for the CWT boundary condition whereas a monotonic increase in (Nu) over bar was obtained for increasing values of aspect ratio AR in the case of CWHF boundary condition irrespective of the value of n. This non-monotonic trend for the CWT boundary condition is caused by the competing effects of thermal convective and diffusive transports with increasing AR. New correlations are proposed for the mean Nusselt number (Nu) over bar for power-law fluids in both the CWT and CWHF boundary conditions, which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of (Nu) over bar in response to the changes in Rayleigh number, aspect ratio and power-law index. (C) 2013 Elsevier Ltd. All rights reserved.