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

Abstract

The effects of inclination 180deg≥د†â‰¥0deg on steadystate laminar natural convection of yieldstress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 103 to 105 in a square enclosure of infinite span lying horizontally at د†=0deg, then rotated about its axis for د†>0deg cases. It has been found that the mean Nusselt number Nuآ¯ increases with increasing values of Rayleigh number but Nuآ¯ values for yieldstress 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 Nuآ¯ value settles to unity (Nuآ¯=1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number Nuآ¯ for both Newtonian and Bingham fluids decreases with increasing د† until reaching a local minimum at an angle د†* before rising with increasing د† until د†=90deg. For د†>90deg the mean Nusselt number Nuآ¯ decreases with increasing د† before assuming Nuآ¯=1.0 at د†=180deg for all values of Ra. The Bingham number above which Nuآ¯ becomes unity (denoted Bnmax) has been found to decrease with increasing د† until a local minimum is obtained at an angle د†* before rising with increasing د† until د†=90deg. However, Bnmax decreases monotonically with increasing د† for 90deg<د†<180deg. A correlation has been proposed in terms of د†, Ra, and Bn, which has been shown to satisfactorily capture Nuآ¯ obtained from simulation data for the range of Ra and د† considered here.