Application of Transparent Enclosure Theory to Solar Energy Absorption by Cylindrical Tubes in Sunspaces

Abstract

A general matrix formulation for beam and diffuse radiative solar transfer is presented for an enclosure containing partially transparent walls. The general theory is used to study the absorption of radiant solar energy in a building sunspace having a south-facing window and a row of opaque vertical cylindrical-tube solar absorbers. A two-dimensional model is formulated for the sunspace in which a typical cylindrical absorber tube is subdivided into a number of uniform elements and the window and sunspace surfaces are each represented as single elements. The matrix expressions are evaluated for incident solar flux conditions typical for a south vertical window on a clear winter day. The results are presented as dimensionless ratios of absorbed-to-incident solar flux as a function of the tube spacing to radius ratio. The spatial distribution of absorbed solar flux is presented at discrete time interals for the cylindrical tube. Space and time-averaged values of absorbed solar flux are also presented for the cylinder, the window, and the room. The potential application of these results for thermal modeling in passive solar applications is discussed.