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RESEARCH PAPERS

# Geometric Factors for Radiative Heat Transfer Through an Absorbing Medium in Cartesian Co-ordinates

[+] Author and Article Information
A. K. Oppenheim, J. T. Bevans

Shell Development Company, Emeryville, Calif.

J. Heat Transfer 82(4), 360-368 (Nov 01, 1960) (9 pages) doi:10.1115/1.3679953 History: Received September 11, 1959

## Abstract

Heat flux conveyed by diffuse radiation from surface A1 and A2 through an absorbing medium is expressed by the relation

Q1−2 = J1 ∫A1×A2 f(l12)
(cos θ1 cos θ2/πl122)dA1dA2
where J1 is the radiosity of A1 (sum of the emitted, reflected, and transmitted flux per unit area), l12 is the radiation beam (the distance between surface elements dA1 and dA2 ), θ1 and θ2 are the angles between the radiation beam and the normals to the surface elements, and f(l12 ) is the function describing the absorption law. The foregoing four-dimensional integral is transformed into a sum of one-dimensional integrals for the cases of opposite-parallel and adjoining-perpendicular rectangles. The results are suitable for numerical integration with any total absorption law obtained from the actual distribution of monochromatic absorptivities over the whole spectrum.

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