Free convective heat transfer in a liquid-filled vertical annulus

An experimental study of convective heat transfer in liquid-filled vertical annulus of radius ratio k =.5,338 has been conducted for the height-to-gap width ratio A = 0.5, 1, and 1.5. By using water, heptane, and ethylene glycol as the test fluids, a Rayleigh number range of 8 × 10⁶ < Ra < 3 × 10^w, and a Prandtl number range of 4 < Pr < 196 have been covered. Curvature effects on the temperature field are significant and result in a lower effective sink temperature for the boundary layer on the isothermally heated inner wall. The Nusselt number Nu thus increases with radius ratio k. However, the slope of In (Nu) versus In (k) curve is not a constant, and decreases with an increase in k. The effect of Prandtl number is weak. In the laminar flow regime, the Nusselt number is weakly dependent on the aspect ratio when Nu and Ra are considered in terms of the annulus height L. The start of laminar flow regime is delayed with an increase in radius ratio. For A = 0.5, k = 5.338, the critical Grashof number is Gr_L = 7 × 10⁴, which decreases with an increase in A. Turbulence is initiated when the local Grashof number Gr_X = 4 × 10⁹.