Analytical view factor solution for radiant heat transfer between two arbitrary rectangular surfaces

View factor calculation is an element of vital importance in radiation heat transfer. In engineering practice, it is common to find a radiant exchange between more complex configurations of emitting and receiving surfaces, which simultaneously include several configurations of perpendicular and parallel plane surfaces. Currently, the available technical literature does not have an analytical expression that allows the view factor to be directly computed for these combinations of surfaces. In these cases, the use of the summation and reciprocity techniques given by the superposition rule (SR) turns out to be very laborious. Therefore, this work aims to analytically develop the view factor expression for radiative heat transfer of 11 combinations between two arbitrary perpendicular or parallel rectangular surfaces in the 3-D space. The results obtained from the proposed method were compared with those computed by the Simpson's rule on Hottel's solution and the result of the quadruple integral using multiple Simpson's 1/3 rule with five intervals. Given the inexistence of similar antecedents in the literature, the proposed analytical solutions reinforce their scientific and practical value.

Automated summary

View factor calculation is essential in radiation heat transfer, but there is a lack of analytical expressions for complex surface combinations. This study introduces an analytical method to calculate the view factor for 11 combinations of perpendicular or parallel rectangular surfaces, and compares the results with existing methods.