Apparent absorptance for diffusely and specularly reflecting spherical cavities

Abstract

The apparent absorptance of a cavity α cavity, is defined as the fraction of energy flux emitted by a black-body surface stretched across the cavity opening that is absorbed by the cavity walls. Because of multiple reflections among the cavity walls, α cavity will exceed the surface absorptance, α . Such an effect, called the cavity effect, is employed in the design of receiver/reactors for solar furnaces to capture the solar radiation. The cavity effect for partial enclosures has been analyzed for specific configurations, among them: cylindrical, conical, spherical, rectangular-groove and V-groove cavities. These problems have been solved for specularly and diffusely reflecting cavity walls. Little information is presently available which describes the particular case of specularly reflecting spherical cavities with a circular opening. Such cavities offer several intriguing advantages over the conventional heavily insulated enclosures made of ceramic materials when applied for solar furnace receivers at moderate to high (2000 K and above) temperatures. Specular spherical geometries have also significant importance in modelling radiant heat transport through the void spaces across a porous material, and the apparent surface emittance was analytically derived for a differential element of a sphere. In the present study, the apparent absorptance of a spherical cavity with a circular opening is calculated for cavity walls having both specular and diffuse reflectance components.