This paper presents the numerical results of natural convective flows between two vertical, parallel plates within a large enclosure. A parametric study has been conducted for various Prandtl numbers and channel aspect ratios. The results are in good agreement with the reported results in the literature for air for large aspect ratios. However, for small aspect ratios, the present numerical results do not agree with the correlations given in the literature. The discrepancy is due to the fact that the published results were obtained for channels where the diffusion of thermal energy in the vertical direction is negligible. The results obtained in this paper indicate that vertical conduction should be considered for channel aspect ratios less than 10 for Pr = 0.7. Correlations are presented to predict the maximum temperature and the average Nusselt number on the plate as explicit functions of the channel Rayleigh number and the channel aspect ratio for air. The plate temperature is a weak function of Prandtl number for Prandtl numbers greater than 0.7, if the channel Rayleigh number is chosen as the correlating parameter. For Prandtl numbers less than 0.1, the plate temperature is a function of the channel Rayleigh number and the Prandtl number. A correlation for maximum temperature on the plate is presented to include the Prandtl number effect for large aspect ratio channels.

No abstract

No abstract

A model for uniform parallel flow over the surface of a rectangular source of heat on a conducting plate is used to demonstrate the use of analytic Green’s functions to formulate the conjugate problem. The Green’s functions are solutions to the temperature field that arises from a point source of heat on the surface. They provide a relationship between the local heat flux and surface temperature on the plate, effectively serving the same role as the heat transfer coefficient. By coupling the pointwise Green’s function to a finite element discretization of the thin plate, the surface temperature and convective heat flux distributions on the heat source and its substrate are found by a non-iterative procedure. A parametric study shows that at high Peclet numbers, the heat transfer from the source approaches the behavior of an infinite two-dimensional source of heat. The average Nusselt numbers for rectangular sources of different aspect ratios are found to be insensitive to source aspect ratio at high Peclet numbers. Board conduction reduces the average Nusselt numbers over the source when it is defined in terms of the freestream temperature. New correlations for the source Nusselt number as a function of flow Peclet number and board conductivity are presented.

No abstract