The theoretical approach is daunting. The most recent , theoretical modeling was done by W. Fiveland ( B+W) using a Galerkin method , but the inaccuracies are tied into the lack of knowledge of the radiation physical properties of the entrained flyash.
A more practical approach to obtain the average furnace heat absorption and funace exit gas temperature is what I call the "Russian Normative Method". A simplified summary of this is presented in the text by S. Kakac "Boilers, Evaporators, and Condensers", in the chapter written by the chinese engineer.
After obtaining the average exit gas temperature and furnace heat absorption rate, it is neccesary to estimate the variation as a function of height, and also to impose limits on the expected variation between average and peak values of absorption rate ( such as when the slag falls of a section of furnace wall).