Heat transfer characteristics of internally heated liquid pools at high Rayleigh numbers

Abstract

Detailed numerical analysis is presented for buoyancy driven flow of a Newtonian fluid contained in a square enclosure for high Rayleigh (Ra) numbers. Natural convection is due to internal heating sources, which are assumed to be uniformly distributed within the enclosure. All walls of the cavity are maintained at constant temperature. Flow and heat transfer characteristics are investigated for a Ra number range of 10⁷ to 10¹² while Prandtl (Pr) number is taken to be 7.0. Governing equations (in primitive variables) are discretised using control volume technique based on staggered grid formulation. These equations are solved using SIMPLER algorithm of Patankar. Flow and heat transfer characteristics, streamlines, isotherms and average wall Nusselt (Nu) number, are presented for whole range of Ra number considered. Finally, present results for average wall Nu numbers are compared with experimental observations obtained from open literature. It is concluded that both results are in very good agreement, which confirmed the accuracy of the scaling used for present investigation.