Local radiation equilibrium temperatures in semigray enclosures

Abstract

Abstract : A rigorous analytical formulation is derived for computing local radiation equilibrium temperatures in diffusely reflecting, semigray cavities. Radiosity integral equations for solar and thermal radiation are related through a heat balance to obtain a third integral equation for the temperature distribution in an enclosure. The temperature equation is solved, in principle, by postulating a resolvant in terms of Fredholm's solution. The solution is reduced to an approximate formulation suitable for engineering applications by introducing a mean value for the integral and using Hottel's script eff in place of the resolvant. The resulting solution shows that local temperature depends on the sum of local direct solar energy, weighted diffusely reflected solar energy from other cavity regions, and weighted temperature of other regions. The analysis is completed by presenting closed-form expressions suitable for hand computation of mean temperatures in a semigray enclosure of two surfaces: (1) A concave surface which 'sees' itself (shape factor F11 not = 0) and (2) a plane surface (F22 = 0). Numerical results are given for an L-shape geometry and a shallow circular cavity to compare the solutions derived in the paper to those obtained by computer nodal analyses. (Author)