Contour integration for the exchange of radiant energy between diffuse rectangular geometries

View factor calculation is a key point in radiation heat transfer between surfaces. In thermal engineering it is required to compute the view factor between complex geometries, which include several parallel and inclined surfaces. Currently, no analytical expressions are available for this purpose, so the use of Summation Rules (SR) is required, however, when analyzing complex geometries, the handling of SR is extremely laborious. Therefore, this work aims to develop an equation for the calculation of the view factor in the radiative heat transfer of two arbitrary rectangular inclined or parallel surfaces, using the advantages provided by vector calculus. The exact solutions obtained with contour integration were compared with the values calculated via the Algebra Factor (AF) using the Hottel and Hamilton-Morgan Solution and with the results computed from numerical integration of the quadruple integral using Simpson's rule 1/3 with five intervals. The lack of similar precedents in the technical literature reinforces the practical and scientific nature of the proposed method of analysis.

Automated summary

View factor calculation is crucial for radiation heat transfer between surfaces, especially for complex geometries. Currently, there are no analytical expressions available, so the use of Summation Rules is necessary. This study utilizes vector calculus to develop an equation for calculating the view factor between two arbitrary rectangular inclined or parallel surfaces. By comparing with other methods, the practical and scientific nature of this proposed analysis method is reinforced.