Transient temperature distribution in a multilayer medium subject to radiative surface cooling - Yuen, W.Y.D. (Applied mathematical modelling, 1994)
In the hot processing of flat products, it is important to estimate accurately the temperature distribution in the workpieces with efficient algorithms to complement the process control system. Normally, this can be achieved by standard numerical means, such as the finite-difference method,after a model for the conduction of heat in the workpieces subject to the appropriate boundary conditions is formulated. However, when the workpieces are stacked together or when they are wound into the form of a coil, the numerical computation becomes more involved. The thermal resistance at the contact interfaces, which arises from imperfect contact due to oxidation of the workpieces or air gaps, plays an important role in restricting the heat flow in the workpieces and must be included in the formulation of the model. In this paper, the heat balance integral method is applied to solve the above problem, with special emphasis on the modelling of the thermal resistance at the contact interfaces. The resulting solution procedure is simple and the numerical scheme is efficient. Good accuracy, sufficient for general engineering applications, is obtained. This study may be applied to general heat conduction problems in a multilayer medium subject to nonlinear boundary conditions, and in particular, finds application in the hot rolling process.