Numerical investigation of steady state laminar natural convection of power-law fluids in side-cooled trapezoidal enclosures heated from the bottom
Sean P. Malkeson, S. Alshaaili, Nilanjan Chakraborty
Abstract
Laminar, steady-state, natural convection of power-law fluids in 2-D trapezoidal enclosures with a heated bottom wall, adiabatic top wall and cooled inclined sidewalls has been analyzed for the first time based on numerical simulations for a range of different values of nominal Rayleigh number (i.e. 103≤Ra≤105), power-law index (i.e. 0.6≤n≤1.8), nominal Prandtl number (i.e. Pr=10, 102,103) and sidewall inclination angle (i.e. 30°≤ϕ≤60°). It has been found that the mean Nusselt number Nu¯ increases with increasing nominal Rayleigh number Ra (up to a 187% increase for n=0.6 and up to 2.3% increase for n=1.8 between Ra=103 and 105) and decreasing power-law index n (up to a 4.1% increase for Ra=103 and up to 193% increase for Ra=105 between n=0.6 and 1.8) due to the strengthening of advective transport. Moreover, an increase in the sidewall inclination angle ϕ leads to a decrease in Nu¯ (approximately 44% decrease for Ra=103 across values of n and up to 33% decrease for Ra=105 across values of n) due to an increase in the area for heat loss from the cavity. It has been found that Nu¯ does not vary significantly with the values of Pr considered in the current study. Furthermore, a new correlation for the mean Nusselt number Nu¯ in this configuration has been identified which provides adequate approximation of the corresponding values obtained from the simulations.