The Radiative Boundary Design of a Hexagonal Furnace Filled With Gray and Nongray Participating Gases

The inverse radiative boundary design problem in a hexagonal furnace is numerically investigated. The aim of this study is to find the strength of heaters in a two-dimensional (2D) enclosure to produce the desired temperature and heat flux distribution on the design surface. Conjugate gradients method is chosen to perform the iterative search procedure for obtaining the optimal solution. The medium is considered participating and both gray and nongray cases are studied. FTn finite volume method (FVM) with nonorthogonal grid is employed to solve the radiative transfer equation in the furnace. In nongray cases, the medium is filled with combustive gas products. To predict nongray behavior properly, the SLW model is used. In problems with gray medium, the effects of wall emissivity, absorption coefficient, and scattering albedo are studied. For nongray problems, the effects of gas concentration and temperature of single species and gas mixtures are analyzed. In all cases, heater power can be estimated precisely and as the results show, estimated heat flux on the design surface is very close to the desired value. For this reason, the maximum root mean square error is less than 1.6%.