A numerical study of natural convective heat transfer from a horizontal isothermal square element with an unheated adiabatic inner section

Abstract

Papers presented to the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 20-23 July 2015.A numerical study of natural convective heat transfer from a horizontal isothermal square heated element with a square inner unheated adiabatic section imbedded in a large flat adiabatic surface has been undertaken. The element is at a higher temperature than the surrounding fluid and the cases where it is facing upward and where it is facing downward have been considered. Steady flow has been assumed and fluid properties have been assumed constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations subject to the boundary conditions using the commercial CFD solver ANSYS FLUENT©. The k-epsilon turbulence model was used with full account being taken of buoyancy force effects. The heat transfer rate from the heated element expressed in terms of a Nusselt number is dependent on the Rayleigh number, the size of the inner adiabatic element section relative to the overall size of the element, and the Prandtl number. Results have been obtained only for a Prandtl number of 0.74, i.e., effectively the value for air. Conditions under which laminar, transitional, and turbulent flow exist have been considered. The variation of the Nusselt number with Rayleigh number has been explored in detail for various inner- to-overall element size ratios. The results have been used to determine whether correlation equations that apply for all inner- to-overall element size ratios can be derived.