Radiation heating through transparent and opaque walls

Abstract

A transparent material has been used through which radiation flux passes to heat the fluid. The fluid is placed in a container in which it is in contact with a transparent wall. The fluid is so well stirred that its temperature can be taken to be the same throughout. The temperature of the fluid is a function of time. A wall of thickness 0 < x < L is considered. The temperature of the wall is a function of time and position. It is assumed that all the radiation flux entering the wall at the outside wall ( x = 0) is reaching the inside wall ( x = L). In an actual case some of the radiation flux is absorbed in the transparent wall. At the outside wall, convective heat transfer takes place to the surroundings. At the inside wall, there is convective heat transfer taking place to the fluid. The solution to this boundary value problem is obtained by the use of the “inversion theorem” for the Laplace transformation. Similarly, a solution to the fluid heated through an opaque wall is obtained. In this case, it is assumed that no radiation flux is passing through the outside wall, or in other words, a perfectly opaque wall is assumed. The two solutions are compared for identical heat-transfer parameters for transparent (glass) and opaque (copper) walls. The results indicate that the glass wall heats up faster and reaches a higher steady-state temperature than the copper wall. The steady-state temperature of the glass wall increases with an increase in the wall thickness. The steady-state temperature of the copper wall is independent of the wall thickness. This effect gives glass an advantage over copper as wall material.