A numerical study of natural convective heat transfer from a horizontal pair of adjacent horizontal isothermal square elements embedded in an adiabatic surface-effect of element spacing on heat transfer rate

Abstract

Papers presented to the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 20-23 July 2015.

In natural convective heat transfer from two horizontal heated surfaces, if the surfaces are mounted relatively close together the flows over the adjacent surfaces can interact and this interaction can affect the heat transfer from the surfaces. In the present numerical study this has been investigated by considering two adjacent square horizontal isothermal surfaces or elements. The purpose of the study was to determine whether the flow interaction does have a significant effect on the heat transfer rate and, if it does, at what distance between the element does the flow interaction start to affect the heat transfer rate to a significant extent. Two adjacent square plane horizontal isothermal elements of the same size embedded in a horizontal plane adiabatic surface have been considered. It is assumed that the surfaces of the square heated elements are in the same plane as the surrounding adiabatic surface. Attention has been restricted to the case where the heated elements are facing upward. The heat transfer from the elements has been assumed to be to air because of the applications being considered. Steady flow has been assumed. Constant fluid properties have been assumed except for the density change with temperature which gives rise to the buoyancy forces. This was treated using the Boussinesq approach. For the range of conditions considered here laminar, transitional, and turbulent flows over the elements can occur. The solution has been obtained by using the commercial CFD solver ANSYS FLUENT© to numerically solve the governing equations subject to the boundary conditions. The k-epsilon turbulence model has been used. The sides of the square heated elements are assumed to be parallel to each other. The Nusselt number based on the side length of the square elements will depend on Rayleigh number, on the dimensionless distance between the adjacent sides of the elements and on the Prandtl number. Since heat transfer to air is considered results have been obtained only for a Prandtl number of 0.74. The effect on the variation of the Nusselt number with Rayleigh number of the dimensionless distance between the sides of the element has been explored and the conditions under which the effect of the interaction between the flows over the adjacent elements can be ignored have been examined.