| Two dimensional mathematical model was developed by zone method. Direct radiative exchange area was obtained by Gauss-Legendre integration expression, and the reflected radiative heat fluxes were solved by Gauss line element method. Then total radiative exchange areas were obtained.Energy balance equations describing heat transfer in hearth were solved by main variables correction method. Heat conduction equation of steel was simplified into one-dimensional, and it was solved by finite difference method. The above equations were coupled which provide boundary conditions for each other.Ternary model was also developed. Newton's method was adopted. Heat conduction equation of steel is same as the one in zone method.The results of ternary model were compared with ones of zone method considering high precision of the latter. Modification of some parameters was carried on such as gas emissivities, and the precision of ternary model was improved.Three-zone method was proposed to overcome the hypothesis that radiation was in the zone. It ignores far radiation and only considers radiation with adjacent two zones. The results show that three-zone method has better precision than ternary model, which can be called advanced ternary model.Ternary model can be on-line used. The presentation has advantage of improving the precision of on-line model. |
