Rapid method for determining concentric cylinder radiation view factors

eNCENTRIC cylinders are among the more common mfigurations encountered in radiation heat transfer analyses, being descriptive of assemblies ranging from infrared telescopes to tube furnaces. In performing thermal analyses on such structures with finite-element computer programs, it is often necessary to break the shell and tube into various concentric ring elements and compute radiation view factors between these elements. Figure 1 depicts a collection of concentric cylindrical geometries. In general, the tube-shell view factors of Fig. 1 can be determined using available computer programs which numerically integrate over the areas involved. However, these programs are cumbersome; thereby limiting their casual usage. A recent paper by Reid and Tehnant * numerically analyzed configuration IV in Fig. 1 for the special case where L=Y. The more general case, along with the other configurations in Fig. 1, is not in the open literature, although the equal-length case is given in Ref. 2. The novelty of the method presented in this Note lies in the utilization of the cylinder-disk view factor Fj.2 of Figs. 2 and 3. By combining various cylinder-disk view factors, for any of the structures in Fig. 1 F';_5 can be determined in closed form where it is the diffuse view factor from the outer curved surface of the inner tube to the outer cylinder. The view factors from the ends of the inner cylinder to the outer cylinder in configurations II, III, and IV are not considered since they can be determined using disk-disk relations as can the shell-shell view factors. Of course, F3.j can be readily computed from Fj_3 using reciprocity.