Natural Convective Heat Transfer From an Array of Square Vertical Plates Mounted on a Large Plane Vertical Adiabatic Surface and With One High Heat Flux Element

An array of nine square heated elements mounted in a square three-by-three pattern with no gap between the elements on a large vertical adiabatic surface with natural convective flow over the elements has been considered. Each of the elements has a uniform heat flux over its surface, the heat fluxes over eight of the elements being the same and the heat flux over the ninth element being higher than that over the other eight elements. The basic aim of the study was to determine the effect the position of the higher heat flux element on the mean temperatures of the other eight elements. The situation considered is an approximate model of situations that can arise in electronic cooling. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in terms of dimensionless variables using the commercial cfd code FLUENT. The solution has the heat flux Rayleigh number, the Prandtl number, the ratio of the heat flux over the high heat flux element to the heat flux over the other eight elements, and the position of the high heat flux element as parameters. Because of the application that motivated this work results have only been obtained for Pr = 0.7. Results have been obtained for a wide range of values of the other input parameters and the effect of these parameter values on the mean surface temperatures of each of the elements has been studied.

Concluding Remarks

Recent interest in the subject of this discussion gained momentum by an observation which did not concern magnetic fields directly. The filigree which Dr. Richard Dunn on Sacramento Peak found 2 Angstrom off the center of Hαis a bright and crisp structure in the photosphere with a width o: 1/5 arcsec. It was described in proper detail by Dunn and Zirker (1973). Even in the printed pictures in their paper one clearly sees one step beyond the solar granulation. The filigree is certainly related to the small scale structure of the photospheric magnetic field, but it is not yet clear whether the flux elements are exactly cospatial and have the same small dimensions. Simon and Zirker (1974) concluded froi spectra that the field structure is wider than the filigree. On the other hand Harvey (1976) in his excellent review of the observations has also presented the arguments of several authors who conclude that the sizes of the flux elements are as small as those of the filigree. This discrepancy certainly needs further study before such even more delicate questions as the spatial extent of the downdraft inside and around the flux elements can be reliably answered from observations. The theoretical interpretation of the downdraft depends on this answer as different sources of the mass flow are involved: the overlying atmosphere and the convergent mass flow of the surrounding convection. The latter stays partly outside the flux element, partly diffuses into it with an efficiency that might be enhanced by convection of still smaller scale.