A Prediction Algorithm of Temperature in Slab in Reheating Furnace by Use of Analytical Solution

Abstract

An analytical solution of one dimensional heat conduction equation is derived under the following conditions.
(1) Constant heating energy E' is applied at the top surface of the slabs.
(2) There is no flow of heat at the bottom surface.
(3) The initial temperature distribution is approximately equal to the quadratic function determined by the both surface temperature.
Further, a practical and fast algorithm is proposed for the prediction calculation of heating temperature. The algorithm uses the analytical solution. First, the slab temperature is predicted by the analytical solution. Every time the calculated temperature goes beyond the predicted temperature range, the calculation is interrupted. The thermal constants used are corrected to become appropriate to the next range of temperature and to rest the initial distribution of temperature and energy E' decided by radiant heating energy calculation, and then the prediction calculation is started again. The proposed algorithm has a great advantage in reduction of computation time over the difference equation method. As the proposed algorithm takes into account the nonlinearity of thermal constants, the computation accuracy is expected to be nearly equal to that of the difference equation method.