The effects of inclination 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 103 to 105 in a square enclosure of infinite span lying horizontally at , then rotated about its axis for cases. It has been found that the mean Nusselt number increases with increasing values of Rayleigh number but 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 value settles to unity () as heat transfer takes place principally due to thermal conduction. The mean Nusselt number for both Newtonian and Bingham fluids decreases with increasing until reaching a local minimum at an angle before rising with increasing until . For the mean Nusselt number decreases with increasing before assuming at for all values of . The Bingham number above which becomes unity (denoted ) has been found to decrease with increasing until a local minimum is obtained at an angle before rising with increasing until . However, decreases monotonically with increasing for . A correlation has been proposed in terms of , Ra, and Bn, which has been shown to satisfactorily capture obtained from simulation data for the range of Ra and considered here.
Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 7, 2014; final manuscript received January 19, 2015; published online March 3, 2015. Assoc. Editor: Oronzio Manca.
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Yİğİt, Ş., Poole, R. J., and Chakraborty, N. (May 1, 2015). "Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures." ASME. J. Heat Transfer. May 2015; 137(5): 052504. https://doi.org/10.1115/1.4029763
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