A simulation code for batch heat treatments

The paper describes a numerical model that uses a finite-difference technique to simulate 2D-thermal transients of solid and hollow cylinders in convective and radiant cavities with participating media and time-dependent wall cavity temperatures. The model takes into account all the thermo-physical property variations with temperature of both gases and materials under treatment. These last (usually named "load") are subject to strong nonlinear thermal boundary conditions and must undergo given thermodynamic transitions. The proposed model is validated with respect to the solutions obtained by other calculation techniques for some simplified problems. Simple thermal transients (cooling) are considered for constant-property cylinders in a convective environment, the analytical solution being taken as a reference. Simplified radiation cases are also examined and the solutions yielded by the model are compared with those given by a finite element commercial code (ANSYS®). Stability and accuracy characteristics of the calculation algorithm are identified as a function of operating conditions and discretization criteria (discretized Biot and Fourier numbers).