An inverse radiation boundary design problem for an enclosure filled with an emitting, absorbing, and scattering media

This work is an inverse radiative design problem in which the objective is to determine the spatial distribution of heat source strengths which produces a desired temperature and heat flux distribution on the design surface. The furnace whose walls are diffuse-grey is assumed to be filled with an absorbing, emitting, and scattering medium. The function to be minimized is the sum of squares of the differences between the desired and calculated radiative heat fluxes at the design surface. Radiative heat flux calculations are accomplished by means of the Modified Discrete Transfer Method MDTM using the correction factors suggested by Coelho and Carvalho [P.J. Coelho, M.G. Carvalho, Conservative formulation of the discrete transfer method, ASME J. Heat Transfer, 119 (1997) 118–128.] and Cumber [P.S. Cumber, Improvements to the discrete transfer method of calculating radiative heat transfer, Int. J. Heat Mass Transfer, 38 (12) (1995) 2251–2258.]. For inverse design calculations the Conjugate Gradient Method CGM is employed, in which the sensitivity coefficients are defined and used as needed by the algorithm. Our investigation shows that the presented algorithm is able to estimate heater strengths accurately.