A General Correlation for Laminar Natural Convection Heat Transfer From Single Horizontal Cylinders in Liquids and Gases With All Possible Prandtl Numbers

Abstract

Abstract The natural convection heat transfer coefficients on single horizontal cylinders with uniform surface heat fluxes were derived numerically from the fundamental equations for laminar natural convection heat transfer by finite difference method without the boundary layer approximation for a wide range of Rayleigh numbers for the Prandtl numbers ranging from 0.005 to 3000. Based on the numerical solutions for the Prandtl numbers, a correlation which describes the numerical solutions of the average Nusselt numbers for the investigated Prandtl numbers within ± 5 percent is presented. The average Nusselt numbers calculated from the correlation are compared with the experimental results for various fluids with the Prandtl numbers ranging from 0.005 to about 18000 obtained by the authors and by other workers: the authors’ experimental results for various liquids such as water, ethanol, glycerin, liquid sodium, liquid nitrogen and liquid helium obtained under a wide range of bulk liquid temperatures and system pressures with a variety of cylinder diameters, as well as the data by other researchers obtained for air, He, Ar, H2, O2, N2, CO2 gases, silicone oils and some liquid metals such as sodium, mercury and tin, agree with the correlation within ±20 percent differences when the fluid properties are evaluated at the reference temperature defined by Tf = Tw – 0.7(Tw – T∞) where Tw and T∞ denote the cylinder surface temperature and the bulk fluid temperature respectively. It was found that the conventional correlations are not in agreement with the authors’ correlation or experimental results for extremely high or low Prandtl numbers.