Abstract
Due to the wide variation of thermal constants such as specific heat, difference equations are used mostly to predict the heating temperature of slabs in the furnace. The difference equation approach entails time sharing, and thus vast amount of recursive computation is required to perform the prediction calculation of heating temperature of slabs by means of difference equation. As a result, the difference equation approach has a defect in long computation time. This drawback becomes a great obstacle when the difference equation approach is used in the application of on-line predictive control of heating temperature of slabs in the furnace.
In this paper, a new and fast algorithm is proposed for the prediction calculation of heating temperature. The algorithm uses analytical solution but is recursive in nature. First, the prediction of temperature is calculated through analytical solution derived in this paper. Every time when the calculated tempereture goes beyond the prespecified temperature a range, the calculation interrupts to correct the thermal conductivity approriate to the next range of temperature and to reset the initial distribution of temperature, and then the prediction calculation restarts.
The heat conduction equation which describes the slab considered in this paper is assumed to be one-dimensional. The temperature distribution of slabs governed by one-dimensional heat conduction equation can be approximated by quadratic function. Hence, in this paper, the analytical solution of one-dimensional heat conduction equation with quadratic function as its initial temperature distribution is derived using Laplace transform.
The proposed algorithm for the prediction of rising temperature has a great advantage in reduction of computation time over the difference equation aproach. As the proposed algorithm takes into account the nonlinearity of thermal conductivity, the computation accuracy is expected to be nearly equal to that of the difference equation approach.
Several numerical examples show the following results:
(i) the required computation time is reduced to 1/5 as compared with that of difference equation approach,
(ii) the accuracy of prediction remains within the allowable range.
These facts assure that the proposed algorithm is an effective way to the prediction computation of heating temperature and can be employed for the on-line control of slabs in the furnace.
