Numerical study of natural convective heat transfer from horizontal heated elements of relatively complex shape having a uniform surface heat flux

Abstract

With natural convective heat transfer from horizontal elements of relatively complex shape that have a uniform surface temperature it has been found that if a length scale based on the ratio of the element surface area to its perimeter is used in defining the Nusselt and Rayleigh numbers then, for a given Prandtl number, the variation of Nusselt number with Raleigh number is effectively the same for all element shapes. However, in a number of practical situations the element surface is not isothermal but there is effectively a uniform heat flux over the surface. Few studies have been undertaken to determine whether natural convective heat transfer rates from horizontal heated elements having a uniform surface heat flux and relatively complex shapes can be correlated using the same procedure that applies when there is an isothermal surface. A fuller investigation of whether the results for surfaces with a uniform heat flux can be correlated in this way has been undertaken. Attention has been given to an element having a circular shape with an inner circular adiabatic section, to an Ishaped element, and to a plus (+)-shaped element. Results for a square and a circular element are also presented for comparison purposes. The elements considered are imbedded in a larger surrounding flat adiabatic surface, attention being restricted to the case where the heated elements are facing upwards. The heat transfer from the element has been assumed to be to air. The results have been obtained numerically using the commercial CFD code ANSYS FLUENT©. The possibility that turbulent flow can occur in the system has been allowed for by using the basic k-epsilon turbulence model. The results have been used to investigate whether the heat transfer rates in the laminar, transitional and turbulent flow regions for the element shapes considered here can be correlated for each of the separate flow regions by using the same length scale that has been found to apply for elements with a uniform surface temperature.