Free convection of power-law fluids in enclosures with partially heating from bottom and symmetrical cooling from sides

Abstract

Steady-state laminar free convection of power-law fluids in a square enclosure with partial heating from below and symmetrical cooling from sides has been investigated based on numerical simulations. The partially heating is conducted by a centrally heated heat source on the bottom wall for different values of normalised heat source length IA (ranging from 0.2 to 0.8); power-law index n (from 0.6 to 1.8); nominal Rayleigh number (Ra) (from 10(3) to 10(6)) and nominal Prandtl number Pr (from 10 to 10(3)). An increase in the power-law index n leads to weakening of thermal advection owing to the augmentation of viscous resistance. This is reflected as an increment in the mean Nusselt number (Nu) over bar with decreasing value of n. Additionally, (Nu) over bar increases with an increase in Ra and IA for shear thinning (i.e. n < 1), Newtonian (i.e. n = 1) and shear thickening (i.e. n > 1) fluids. The observed influences of Ra, Pr, n and 1/L on (Nu) over bar have been explained by physical and scaling arguments and parameterized by a correlation for the mean Nusselt number. (C) 2019 Elsevier Ltd. All rights reserved.