Laminar Natural Convection of Power-Law Fluids in a Square Enclosure With Differentially Heated Sidewalls Subjected to Constant Wall Heat Flux

Abstract

Two-dimensional steady-state laminar natural convection of inelastic power-law non-Newtonian fluids in square enclosures with differentially heated sidewalls subjected to constant wall heat flux (CHWF) are studied numerically. To complement the simulations, a scaling analysis is also performed to elucidate the anticipated effects of Rayleigh number (Ra), Prandtl number (Pr) and power-law index (n) on the Nusselt number. The effects of n in the range 0.6 ≤ n ≤ 1.8 on heat and momentum transport are investigated for nominal values Ra in the range 103–106 and a Pr range of 10–105. In addition the results are compared with the constant wall temperature (CWT) configuration. It is found that the mean Nusselt number Nu¯ increases with increasing values of Ra for both Newtonian and power-law fluids in both configurations. However, the Nu¯ values for the vertical walls subjected to CWHF are smaller than the corresponding values in the same configuration with CWT (for identical values of nominal Ra, Pr and n). The 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 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 Pr are shown to be essentially negligible in the range 10–105. New correlations are proposed for the mean Nusselt number Nu¯ for both Newtonian and power-law fluids.