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.
Papers presented at the 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Portoroz, Slovenia on 17-19 July 2017 .