International Journal of Heat and Mass Transfer, Vol.42, No.17, 3279-3290, 1999
Prandtl number effect on bifurcation and dual solutions in natural convection in a horizontal annulus
Bifurcation phenomena and existence of dual solutions in natural convection in a horizontal annulus are numerically investigated for the fluids of 0.3 less than or equal to Pr less than or equal to 1. When the Rayleigh number exceeds a critical value, two kinds of how patterns are realized: the first is the crescent-shaped eddy pattern in which the fluid in the top of the annulus ascends, and the second is the flow in which the fluid descends by forming two counter-rotating eddies in a half annulus. For the fluids of 0.3 less than or equal to Pr less than or equal to 0.5, the second flow pattern can be obtained by the impulsive heating of the inner cylinder, but it is not obtained from the zero initial condition for 0.6 less than or equal to Pr less than or equal to 1. The bifurcation points are determined, as a function of the Prandtl number. Hysteresis phenomenon occurs for the fluids of 0.3 less than or equal to Pr less than or equal to 0.4, but it is not observed for 0.5 less than or equal to Pr less than or equal to 1.
Keywords:CONCENTRIC CYLINDERS;HEAT-TRANSFER