View Factors in Radiation Between Two Parallel Oriented Cylinders of Finite Lengths

A simple double-integral expression for the diffuse radiation view factor, F₁₂, between two parallel cylinders of finite lengths is derived. No closed-form solution appears possible except for the limiting case of infinite long cylinders for which an analytical expression for the view factor F₁₂^∞ is derived by applying the crossed string method. The accuracies of the line source approximations are evaluated, and the regions for which they are accurate to one percentage or better are identified. The view factor F₁₂ between two opposing cylinders of equal length is computed by numerical integration and normalized by F₁₂^∞. The results are presented. Analytical expressions, which approximate the view factors between two opposite cylinders of finite length, are derived and their accuracy is evaluated over a useful parameter range. The range of their applications corresponds approximately to that for the line source approximation. This result is expected, because the errors are caused in part by blockage of radiation which is similar.