TEMPERATURE HISTORIES OF INTERNALLY HEATED THIN BODIES COOLED BY CONVECTION AND/OR THERMAL RADIATION

The temperature variation of a thin body (i.e., one that has high thermal conductivity and small dimensions along any heat flow direction) with time is found as dT/dt = X-YT-- ZT/sup 4/, where X, Y, and Z are constants that depend on the heat generation in the body, the convective cooling, and the radiative cooling respectively, and t and T are time and temperature respectively. Solutions are found to this equation for combined convection and radiative cooling (constant X, Y, and Z); radiative cooling only (X and Z constant and Y = 0); and several cases with convective cooling only (Z ---0, and various conditions on X and Y). The existence of a maximum temperature is studied for each of these cases, by setting dT/dt = 0. (T.F.H.)