A parametric study of optimal number and location of radiant heaters in enclosures with participating media

An inverse solution technique is applied to the design of radiant enclosures when design variables are discrete and radiation is the dominant mode of heat transfer. The enclosure contains an absorbing, emitting and linear anisotropic scattering medium in radiative equilibrium. The discrete ordinate method is employed to solve the radiative transfer equation. The goal of the design problem is to nd the best number and location of discrete equally powered heaters which produce the desired (specied) temperature and heat ux prole over the design surface of enclosures. The inverse problem is formulated as an optimization problem and is solved using a micro-genetic algorithm. Results show that the micro genetic algorithm is able to nd the optimal solution by just searching a few percent of feasible solutions. The ability of this methodology is demonstrated by nding the optimal number and location of heaters in an irregular enclosure. Then, the eect of some thermophysical properties, such as extinction coecient, scattering albedo, scattering phase function, and design surface emissivity, on the optimal solution is considered