Inverse Solution of Radiative Heat Transfer in Two-Dimensional Irregularly Shaped Enclosures

An inverse solution technique is used to predict the necessary temperature and heat flux distributions of the heater section of a two-dimensional enclosure so the heater satisfies the specified heat flux and temperature distributions of design surfaces, while satisfying one thermal boundary condition for the other walls. Radiation is the dominant mode of heat transfer in systems where high temperatures are present; therefore, it is considered as the only mode of heat transfer in this study. The two-dimensional enclosures considered in this study are made up of straight segments, positioned so that they form irregularly shaped enclosures approximating situations for many of the real cases in industrial applications. The enclosure walls are gray, emitting diffusely and reflecting either diffusely or specularly. The medium inside the enclosure may be transparent, absorbing-emitting or absorbing-emitting and isotropically scattering. For the participating medium cases, the gray medium is considered as isothermal, homogeneous and isotropically scattering. The Monte Carlo method is used for formulation of radiative heat transfer. The method is preferred for its accuracy and ease of handling complex geometries and various surface and medium properties. The main contribution of this study is to solve inverse design problems for complex geometries that contain blockage and shading effects, as could be the case in many real industrial applications. The resulting system of equations, which includes Fredholm equations of the first kind, is known to be highly ill-conditioned in nature. The solution for this ill-conditioned system is handled by the conjugate gradient method, an iterative solution method, which obtains smooth and very accurate solutions in a few steps for linear systems.