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The effects of aspect ratio AR (ratio of enclosure height to length) on Rayleigh–Bénard convection of inelastic non-Newtonian fluids obeying the power-law model of viscosity within rectangular enclosures have been numerically analysed where the horizontal walls are subjected to constant wall temperatures with the bottom wall at higher temperature. Simulations have been undertaken for the range of aspect ratio 0.25 ⩽ AR ⩽ 4 , nominal Rayleigh number range 10 3 ⩽ Ra ⩽ 10 5 ( Ra defined based on the enclosure height) for a single representative value of nominal Prandtl number ( Pr = 10 3 ). It is found that convection weakens with increasing aspect ratio and the heat transfer takes place purely due to thermal conduction for tall enclosures (i.e. AR > 2 ) for all values of Ra and n considered here. Additionally, the flow pattern for AR ⩽ 2 has been found to be dependent not only on Ra and n but also on the choice of initial condition used for the simulation. Although viscous resistance weakens with decreasing power-law exponent for a given set of values of Ra , AR and Pr , the mean Nusselt number Nu ‾ does not exhibit a monotonic increase with decreasing n for AR ⩽ 2 because of the change in flow pattern (i.e. number of convection rolls/cells) within the enclosure. Accordingly, it has been found that the flow pattern and the mean Nusselt number Nu ‾ are dependent on initial conditions and it is possible to obtain different steady-state solutions for different initial conditions. Furthermore, it is possible to obtain a steady solution for shear-thinning (i.e. n < 1 ) fluids only for some initial conditions, whereas other initial conditions may yield unsteady flow patterns. The key simulation results have been explained based on scaling arguments and the scaling relations have been utilised to identify different regimes of natural convection of power-law fluids accounting for aspect ratio effects. [ABSTRACT FROM AUTHOR]