A semi-analytical method for natural convection in a two dimensional rectangular enclosure, with uniform volumetric heat generation, having insulated horizontal boundaries, and isothermal vertical boundaries, has been studied here. In this method, the governing equations for natural convection, have been solved under the assumption that for a cavity with small aspect ratio, the flow in the central region of the cavity is only in the vertical direction. It is found that for the cavities with small aspect ratio, the temperature in central region of the cavity is nearly constant along the horizontal direction. However, there is a uniform temperature gradient in the vertical direction, which can be related to the maximum temperature in conduction. The velocity profiles and temperature profiles obtained in the present work, are compared with the numerical simulations by Fluent and a fair agreement is found between these results.
Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation
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Joshi, MV, Gaitonde, UN, & Mitra, SK. "Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 1. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 303-309. ASME. https://doi.org/10.1115/HT-FED2004-56302
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