Extension of the zonal method to inhomogeneous non-grey semi-transparent medium

A radiation model is proposed to extend the zonal method of Hottel to semi-transparent inhomogeneous real combusting gas–soot mixture in a 2-D black-walled rectangular enclosure. The direct exchange areas are carried out by direct numerical integration and then adjusted to meet the conservation constraints using two smoothing processes namely the Larsen and Howell's least squares and generalized Lawson's improved smoothing methods, which has not been previously done to the best knowledge of the authors. The predicted net radiative heat flux distributions compare favorably with benchmark solutions for two test cases dealing with isothermal and non-isothermal homogeneous mediums. It is concluded from this investigation that there is no significant effect of the smoothing method on the computed wall heat fluxes for the homogeneous and inhomogeneous test cases using different grey gases number. The grid dependence study depicts that the numerical solutions fully achieve grid independence. It is worth noting that it can be proceeded with the present extended zonal method and computer code to more complex cases. The results based on the generalized Lawson's smoothing method compare favorably with those yielded by the popular least squares method and, consequently, can be considered as a benchmark solution for other investigations.