Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant temperatures

Abstract Two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated sidewalls subjected to constant wall temperatures have been carried out where the enclosures are considered to be completely filled with non-Newtonian fluids obeying the power-law model. The effects of power-law index n in the range 0.6 ⩽ n ⩽ 1.8 on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–106 and a Prandtl number (Pr) range of 10–105. It is found that the mean Nusselt number Nu ¯ increases with increasing values of Rayleigh number for both Newtonian and power-law fluids. However, Nu ¯ values obtained for power-law fluids with n 1 ( n > 1 ) are greater (smaller) than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to strengthening (weakening) of convective transport. With increasing shear-thickening (i.e. n > 1) the mean Nusselt number Nu ¯ settles to unity ( Nu ¯ = 1.0 ) as heat transfer takes place principally due to thermal conduction. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. New correlations are proposed for the mean Nusselt number Nu ¯ for both Newtonian and power-law fluids which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu ¯ in response to changes in Ra, Pr and n.

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