Hybrid method to calculate direct exchamge areas using the finite volume and method and midpoint intergration

This paper presents a hybrid method to calculate direct exchange areas for an infinitely long black-walled rectangular enclosure. The hybrid method combines the finite volume method (FVM) with the midpoint integration scheme. Direct numerical integration of direct exchange areas for adjacent and overlapping zones is difficult because of singularities in the integrand. Therefore, direct exchange areas of adjacent and overlapping zones are calculated using the FVM. Direct exchange areas of nonadjacent zones are calculated by the efficient midpoint integration scheme. Thus, direct exchange areas in an infinitely long enclosure can be obtained with both efficiency and accuracy. Volume-volume direct exchange areas of zones with various aspect ratios and optical thickness have been calculated and compared to exact solutions, and satisfactory results are found.