The temperature distribution on a spherical shell in the presence of a primary radiative source and a reflecting and radiating infinite plane
Bannerot, Richard B
Chapman, Alan J.
Master of Science
A thin-walled conducting spherical shell, rotating with a constant angular velocity about an axis of rotation oriented perpendicular to an infinite plane located at some unspecified distance from the shell, is exposed to a distant source of parallel radiation. The plane is assumed to radiate diffusely as well as reflect heat energy. Convective heat transfer as well as radial conduction in the shell is neglected. The non-linear differential equation obtained from a heat balance made on a volume element of the shell is approximated by a linearized equation. The solution to the linearized equation is found in terms of Legendre polynomials and associated Legendre functions. Then some numerical results are obtained for which selected problem parameters are varied.