Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid

Abstract

The Graetz problem for fully developed laminar flow in horizontal rectangular channels with uniform wall heat flux is extended by including buoyancy effects in the analysis for the case of large Prandtl number fluid. A general formulation valid for all Prandtl numbers is presented and the limiting case of large Prandtl number is approached by a numerical method. The typical developments of temperature profile, wall temperature and secondary flow in the thermal entrance region are presented for the case of square channel γ = 1. Local Nusselt number variations are presented for the aspect ratios γ = 0.2, 0.5, 1, 2 and 5 with Rayleigh number as parameter. Due to entry and secondary flow effects, a minimum Nusselt number occurs at some distance from the entrance, depending on the magnitude of Rayleigh number. This behavior is similar to that observed in the thermal entrance region where the transition from laminar to turbulent flow occurs. The effect of Rayleigh number is seen to decrease the thermal entrance length, and the Graetz solution, neglecting buoyancy effects, is found to be applicable only when Rayleigh number is less than about 10 3. A study of the practical implications of large Prandtl number on heat transfer results for hydrodynamically and thermally fully developed case reveals that the present heat transfer results are valid for Prandtl number ranging from order 10 to infinity.