Natural convective heat transfer from upward facing recessed and protruding heated horizontal isothermal circular elements with isothermal vertical side surfaces

Abstract

Heat transfer by natural convection from a horizontal upward facing circular isothermal heated element that is imbedded in a horizontal, adiabatic surrounding surface has been numerically investigated. The element is either recessed into or protruding from the surroundings surface by a small amount. The circular horizontal element surface is at a temperature higher than the surrounding fluid. A previous study of this type of situation assumed that the vertical side walls formed by the protrusion or recession of the element were adiabatic. However, the thermal conditions on these side walls could potentially have a significant effect on the heat transfer rate from the horizontal circular element surface and this has been investigated here by considering the case where the side walls are isothermal and at the same temperature as the horizontal circular heated element surface. The present study considers a range of conditions such that laminar, transitional, and turbulent flows can occur. The density changes with temperature have been treated using the Boussinesq approach. The standard k-epsilon turbulence model was used. Results have been obtained only for a Prandtl number of 0.74 which is essentially the value for air. A study of the effect of the dimensionless distance that the element is recessed or protrudes from the surrounding adiabatic surface on the variation of the Nusselt number with Rayleigh number has been undertaken. The variations for the case where the side wall is isothermal and the case where it is adiabatic have been compared in order to determine the effect of side wall heating.