Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures

The effects of inclination 180 deg >= phi >= deg on steady-state laminar natural convection of yield-stress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 10(3) to 10(5) in a square enclosure of infinite span lying horizontally at phi = 0 deg, then rotated about its axis for phi > 0 deg cases. It has been found that the mean Nusselt number (Nu) over bar increases with increasing values of Rayleigh number but (Nu) over bar values for yield-stress fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to the weakening of convective transport. For large values of Bingham number Bn (i.e., nondimensional yield stress), the mean Nusselt number (Nu) over bar value settles to unity ((Nu) over bar = 1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number (Nu) over bar for both Newtonian and Bingham fluids decreases with increasing phi until reaching a local minimum at an angle phi* before rising with increasing phi until phi = 90 deg. For phi > 90 deg the mean Nusselt number (Nu) over bar decreases with increasing phi before assuming (Nu) over bar = 1.0 at psi = 180 deg for all values of Ra. The Bingham number above which (Nu) over bar becomes unity (denoted Bn-max) has been found to decrease with increasing phi until a local minimum is obtained at an angle phi* before rising with increasing phi until phi = 90 deg. However, Bn-max decreases monotonically with increasing phi for 90 deg < phi < 180 deg. A correlation has been proposed in terms of phi, Ra, and Bn, which has been shown to satisfactorily capture (Nu) over bar obtained from simulation data for the range of Ra and phi considered here.