Effect of fluid Prandtl number on heat transfer characteristics in internally heated liquid pools with Rayleigh numbers up to 10 12

Abstract

This paper presents an analysis of effects of the fluid Prandtl number (Pr) on natural convection heat transfer in volumetrically heated liquid pools. Experimental and computational studies performed in the past are reviewed, with particular emphasis on the analysis of Pr number effects. As a practical exercise, numerical analysis is performed for two-dimensional square, semicircular and elliptical enclosures, and for three-dimensional semicircular and hemispherical cavities, to investigate the physics of the effect of the Pr number on heat transfer in internally heated liquid pools with Rayleigh numbers up to 10 12. It was found that the fluid Prandtl number has a small effect on heat transfer in the convection-dominated regions (near the top surface and side walls) of the enclosures. The decrease of the Pr number leads to the decrease of the top and side wall Nusselt (Nu) numbers. The effects of the Pr number on the Nu number at the bottom surface of the enclosures are found to be significant and they become larger with increasing Rayleigh numbers. Two physical mechanisms, i.e. thermal diffusivity and kinematic viscosity phenomena, have been proposed to explain the fluid Prandtl number effects. Calculational results have been used to quantify the significance and the area of influence for each mechanism. Also, strong dependence on the geometry (curvilinearity) of the downward cooled pool surface has been found.