A NUMERICAL STUDY OF NATURAL CONVECTIVE HEAT TRANSFER FROM AN UPWARD FACING CIRCULAR HEATED HORIZONTAL ISOTHERMAL ELEMENT WITH A NON-FLAT SURFACE
The use of a non-flat surface to increase the natural convective heat transfer rate from an isothermal circular
horizontal element has been numerically investigated. The case where the height of the element surface rises
linearly from its outer edge to a maximum at the center of the element, the case where the height of the
surface increases in two linear steps from its outer edge to its center, and the case of a curved surface have
been considered. Conditions under which laminar flow, transitional flow, and turbulent flow exist have been
considered. The flow was assumed to be axisymmetric and steady and the Boussinesq approach was adopted.
The standard k-epsilon turbulence model was used. The mean heat transfer rate from the element surface was
expressed in terms of a Nusselt number based on the diameter of the element. For each of the three surface
shapes considered this Nusselt number is a function of the Rayleigh number, of the dimensionless height of
the surface, and of the Prandtl number. Results were only obtained for a Prandtl number of 0.7, i.e.,
effectively the value for air at standard ambient conditions. A range of the other governing parameter values
has been considered. The results indicate that the use of non-flat element surfaces of the types considered can
produce an enhancement of the heat transfer rate compared to that from a plane horizontal surface but the
results show that the heat transfer enhancement is relatively small under many of the conditions considered.