A mathematical model of a slab reheating furnace with radiative heat transfer and non-participating gaseous media

A mathematical model of the reheating process of steel slabs in industrial fuel-fired furnaces is developed. The transient temperature field inside the slabs is computed by means of the Galerkin method. Radiative heat transfer inside the furnace constitutes boundary conditions that couple the dynamic subsystems of the slabs. Constraining the heat fluxes to piecewise linear, discontinuous signals furnishes a discrete-time state-space system. Conditions for an exponential decrease of the open-loop control error are derived. Measurements from an instrumented slab in the real system demonstrate the accuracy of the model. The simple and computationally inexpensive model is suitable for trajectory planning, optimization, and controller design.