Transient Radiation Heat Transfer of Thermally Compact, Lumped Bodies: An Explicit Solution

Abstract

An explicit, analytical solution is offered to the problem of transient radiation heat transfer of thermally lumped bodies. This solution is readily implemented as a calculator on a simple spreadsheet software, allowing prediction of transient radiation that can aid didactics, design, test, and operations. It is shown that transient radiation heat transfer has a few similarities, and many differences, in comparison to linear forms of transient heat transfer such as conduction and convection. Both linear and radiation forms of transient heat transfer asymptotically approach their steady-state conditions. Differences of note are that transient radiation heat transfer is nonself-similar, it depends upon two nondimensional variables, transient radiative heating is generally faster than transient radiative cooling, and externally applied heat sources substantially delay transient radiation heat transfer relative to internally applied heat sources.