Numerical investigation of steady state, laminar, natural convection of Bingham fluids in a trapezoidal enclosure heated from the bottom and cooled from the sides

Abstract

Laminar, steady-state, natural convection of Bingham fluids in trapezoidal enclosures with a heated bottom wall, cooled inclined sidewalls and an adiabatic top wall has been studied based on numerical simulations for a range of values of nominal Bingham numbers, Rayleigh numbers (i.e., 103 ≤ Ra ≤ 105), and sidewall inclination angles (i.e., 30° ≤ φ ≤ 60°) for a representative nominal Prandtl number (i.e., Pr = 103). It has been found that the mean Nusselt number Nu‾ increases with increasing Rayleigh number Ra due to the strengthening of advective transport. An increase in the sidewall inclination angle φ leads to a decrease in the mean Nusselt number Nu‾ due to an increase in the area for heat loss from the trapezoidal enclosure. The value of the mean Nusselt number Nu‾ was found to decrease with increasing Bingham number Bn. At high values of Bingham number Bn, the fluid flow essentially stops within the enclosure and the heat transfer takes place primarily due to conduction and, accordingly, the mean Nusselt number Nu‾ settles to a constant value, for a given value of sidewall inclination angle φ, irrespective of the value of nominal Rayleigh number Ra. Furthermore, a correlation for the mean Nusselt number Nu‾ in trapezoidal enclosures with a heated bottom wall, an adiabatic top wall, and cooled inclined sidewalls accounting for the range of Rayleigh numbers Ra, Bingham numbers Bn and inclined wall angles φ considered which provides adequate approximation of the corresponding values obtained from the numerical simulations has been identified.