Volume 46 (2003) Issue 4 Pages 470-478
Design methods for thermal systems with predominant radiation are given, followed by applications of these methods to idealized but practical engineering systems. It is argued that such designs in general present inverse mathematical problems, in that an outcome (the desired output of the systems) is prescribed, and the necessary inputs (geometry, heater placement, heater power distribution) are to be found that will achieve the desired output. Such inverse problems require some methods for handling their ill-conditioned nature. Two general techniques are discussed: Regularization methods, which remove or ameliorate the ill-conditioned portion of the problem at the expense of some degree of accuracy; and optimization methods, which replace the ill-conditioned problem with a well-posed problem that must be solved repetitively through a systematic approach to a useful solution. Applications of both methods to a variety of radiative transfer problems are discussed and demonstrated, including problems in which heater power is determined, problems in which the geometry of the enclosure must be determined, and problems with a prescribed transient power distribution on the processed material that must be provided by the heaters. Problems with conduction and/or convection in addition to radiation are also discussed, as are problems with specularly reflecting surfaces, participating media between the heaters and the processed materials, and enclosures with complex geometries.