Mathematical Models of the Oil Fired Continuous Furnace

By one-dimensional model, the flame jets are simulated as a flat flame layer lying between upper and lower exhaust gas layers. Then (he Hottel method of uni-dimensionat system is used to calculate the radiative transfer between these layers.
On the bases of Ricou-Spalding empirical formula for the free jet entrainment the mass transfer between the flame and its surrounding gas is calculated, then the mean temperature t_f is determined according to the heat balance equation. The heat transfer in the billet described as one-dimensional heat conduction problem is solved by using the finite difference method.
A simplified heat transfer simulation model is also developed for determination of the mean charge temperature or billet center temperature per unit grad of furnace temperature increment in each furnace zone as represented by ∂θ_m/∂Ti or ∂θ_s/∂Ti. The weight factors of the minimum fuel consumption function in different zones W_i are also obtained.
An example is given to show the optimal control of furnace zone temperature according to the above mentioned linear programming system.