Inverse Optimal Design of Radiant Enclosures With Participating Media: A Parametric Study

Abstract

An inverse analysis is employed to estimate the required input on the heater surface (i.e., heater power distribution) that produces the desired temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the square of the difference between estimated and desired heat fluxes distribution over the design surface. The optimization problem is solved using the conjugate gradient method through an iterative procedure. The modified discrete ordinates method is used to solve the radiative transfer equation in an absorbing, emitting, and isotropic/anisotropic scattering medium. Enclosures with diffuse and gray walls are considered. Radiation is assumed to be the dominant mode of heat transfer. First, the performance and accuracy of the present method for solving direct and inverse problems are checked. Then, the effect of some thermophysical properties, such as extinction coefficient, scattering albedo, scattering phase function, and design surface emissivity, on the optimal solution is considered. And finally, effects of measurement errors in radiative properties on the optimal solution are investigated.