Inverse boundary design of a radiant furnace with diffuse-spectral design surface

An optimization technique is applied to inverse design of radiative furnaces with diffuse-spectral surfaces. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivities and then the radiative transfer equation is solved by the net radiation method for each band. The conjugate gradient method is used for estimation of temperatures over reflector and heater surfaces. 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 the results obtained by considering a diffuse-gray design surface.