Effect of Prandtl Number and Diameter Ratio on Laminar Natural Convection from Isothermal Horizontal Cylindrical Annuli

Abstract

A numerical investigation of transient, two-dimensional natural convection in horizontal isothermal cylindrical annuli is performed to investigate the Prandtl number and diameter ratio effect on flow and heat transfer characteristics. The finite difference method is used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation. Both vorticity and energy equations are solved using alternating direction implicit (ADI) method and stream function equation by successive over relaxation (SOR) method. Solutions for laminar case are obtained up to Grashof number of 105 as well as three different diameter ratios, namely 1.2, 1.5, and 2.0 and the Prandtl number varies from 0.7 to 10 are considered. The computed flow patterns and temperature fields are shown by means of streamlines and isotherms, respectively, and the average heat transfer coefficients are also presented. The numerical results are summarized by Nusselt number vs. Grashof number correlations with the Prandtl number and diameter ratio as a parameter. The results of the parametric study show that the diameter ratio and Grashof number have a profound influence on the temperature and flow field and they are almost independent of a low Prandtl number fluid. The average Nusselt number increases by 25% at large of diameter ratio and Prandtl number. Good agreement with earlier available data is obtained.