Evaluation of the geometric mean transmittance and total absorptance for twodimensional systems
Abstract
It has been found that the evaluation of the geometric mean transmittance and total absorptance between an infinitesimal area and an arbitrary finite area with an intervening absorbing and emitting medium is greatly simplified by making use of a mathematical identity which has never been recognized before. Solutions for three specific geometries were generated and identified as 'fundamental solutions'. While the obtained solutions are of great value for threedimensional applications, they are difficult to use for systems with twodimensional geometry. The present investigation has the objective to develop the corresponding twodimensional fundamental solutions for the considered problem in radiative heat transfer. The application of the derived relations is illustrated with the aid of an example, involving the evaluation of the geometric mean beam length in the three limits for a circular cylinder of infinite length.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 July 1982
 DOI:
 10.1016/00179310(82)900837
 Bibcode:
 1982IJHMT..25.1069Y
 Keywords:

 Absorptance;
 Mean;
 Radiative Heat Transfer;
 Thermal Absorption;
 Transmittance;
 Two Dimensional Bodies;
 Circular Cylinders;
 Integral Equations;
 Numerical Integration;
 Superposition (Mathematics);
 Fluid Mechanics and Heat Transfer