Inverse Design of Radiant Enclosures with Internal Source Distribution and Diffuse-nongray Design Surface

In this paper, inverse design to determine unknown heat source distribution in a radiant enclosure using an optimization method is investigated to produce desired emissive power and heat flux profiles on a diffuse-nongray design surface of a two-dimensional radiant enclosure. The medium of enclosure is emitting-absorbing, and the design surface's emissivity is assumed to be varied with respect to wavelength. Regarding diffuse-nongray design surface, the variation of emissivity with respect to the wavelength is approximated by considering a set of nongray bands with constant emissivity and then the radiative transfer equation is solved by the discrete ordinates method for each band. The total heat flux on each surface element of the design surface is approximated by a summation over the contribution of nongray bands. The conjugate gradient method is used to minimize an objective function, expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. The sensitivity problem is approximated by differentiation of the radiative transfer equation with respect to the unknown variables. The performance of the present method is evaluated by comparing the results with those obtained by considering a diffuse-gray design surface. The results show that the heat source distribution is well recovered over the heat flux specified design surface in an appropriate range of accuracy.