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

摘要

The effects of inclination 180 deg ≥ φ ≥ 0 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 φ = 0 deg, then rotated about its axis for φ ＞ 0 deg cases. It has been found that the mean Nusselt number Nu increases with increasing values of Rayleigh number but Nu 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 value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number Nu for both Newtonian and Bingham fluids decreases with increasing φ until reaching a local minimum at an angle φ~* before rising with increasing φ until φ = 90 deg. For φ ＞ 90 deg the mean Nusselt number Nu decreases with increasing φ before assuming Nu = 1.0 at φ = 180 deg for all values of Ra. The Bingham number above which Nu becomes unity (denoted Bn_(max)) has been found to decrease with increasing φ until a local minimum is obtained at an angle φ~* before rising with increasing φ until φ = 90 deg. However, Bn_(max) decreases monotonically with increasing φ for 90 deg ＜ φ ＜ 180 deg. A correlation has been proposed in terms of φ, Ra, and Bn, which has been shown to satisfactorily capture Nu obtained from simulation data for the range of Ra and φ considered here.