A Simple Method of Calculating the Effectiveness of High Temperature Radiation Heat Shields, and Its Application in the Construction of a High Temperature Vacuum Furnace*

A method is given whereby one may graphically determine the radiation heat transfer properties of a number of closely packed radiation shields. The method uses the gray body formula, taking into account variations in total thermal emissivity of the adjacent shields as a function of temperature. Results were used in the construction of a high temperature vacuum furnace. Excellent correlation was found between graphically predicted and calorimetrically measured results. (Submitted to Rev.. Sci. .Instr.) * Work supported by the U. S. Atomic Energy Commission. INTRODUCTION With very large furnace hot zones, power losses are appreciable. At the time construction of a high temperature furnace was considered, we were advised no simple way of calculating radiation losses was known. The literature contained a smattering of empirical data, but not enough to give us complete confidence in determining losses for our particular configuration. Data were available from vendors for particular heater and heat shield configurations. However, these data included “secondary” heat losses resulting from work support structures, power-feed-through penetrations, etc. Data were insufficient to separate secondary losses from primary radiation losses through the ideal radiation shields. CUSTOMARY METHOD OF CALCULATION The total power transferred between two shielding surfaces, using notation 1 similar to Crawford, is :Xs + + j’ [(AIT;$) _ @oT$)f (1) where A, T, and E denote the area, temperature, and total thermal emissivity, o is the Stefan-Boltzmann constant, a! the probability that radiation leaving the cooler surface will strike the hotter, and p the reverse probability. Subscripts “1” and “0” identify the parameters of the hotter and cooler surfaces, respectively. At this point, the approximation is usually made that in a multishield package, with high temperature gradients, emissivities will be assumed constant from shield to shield. However, for very large hot zones, with closely spaced heater and heat shields, variations in thermal emissivity of respective shields would seem much more important than shape factors. This is due to the fact that