Inverse radiation heat transfer in diffuse-gray enclosures with hidden surfaces.

摘要

A computer program was written to solve the inverse problem of radiant exchange in diffuse-gray enclosures and used to estimate the temperature and radiosity distributions in sample enclosures in the presence of hidden surfaces. The equations of radiant exchange were formed using the net radiation method and a non-participating medium was assumed. The ill-posedness of the problem was overcome using a subdomain function specification (SFS) approach in which predetermined shape functions were used to specify the temperature (or the black emissive power) on all surfaces. A least-squares solution by constrained simulated annealing was used to determine the combination of shape function coefficients that best reproduced the known information. Two simple enclosures were studied; a two-dimensional square enclosure with infinitely long, uniform-temperature walls, and a three-dimensional right circular cylinder.;Results from the 2-D study compared well with those reported in the literature. An analytical solution was used to identify combinations of shape-function coefficients and problem constraints that produced unique mathematical solutions to the inverse problem. Results from the 3-D study showed that the inverse problem can be solved to within reasonable accuracy, provided that the problem is sufficiently constrained. In all cases, the best agreement between 'measured' and computed temperatures occurred when measurements were added at selected points on or near the hidden surfaces. The inverse model was then applied to a case where the radiosity measurements on the surfaces of a right-circular cylinder were supplied from the digital image produced by an infrared scanning radiometer. The predicted temperatures agreed well with the measurements on the cylinder base, but diverged considerably on the wall. A study of the radiometer system showed that the trouble on the wall was primarily caused by increased optical blurring due to the magnification of radiosity gradients in the line-of-sight of the detector at high polar angles. A mathematical model of geometric projection and optical blurring was introduced and applied to the simple problem of a 1-dimensional fin. The blurred radiosity distributions resembled the radiometer measurements on the cylinder wall and base at high and low polar angles, respectively.