Effect of Surface Radiation on Natural Convection in Parabolic Enclosures

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Abstract
The interaction of natural convection and surface radiation in two-dimensional parabolic cavities heated from below with insulated walls and flat top and bottom walls is studied numerically. The shape of the cavities arises from the design of non-imaging optics-based compound parabolic concentrators (CPC). A numerical model based on finite differences is developed to solve the mass, momentum, and energy equations. A coordinate transformation is used to map the parabolic shape into a rectangular domain where the governing equations are solved. The results show that surface radiation significantly changes the temperature distribution and local Nusselt number inside the parabolic enclosure. Solutions are obtained for two different parabolic geometries that correspond to two different levels of concentration.

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