The modeling of heat conduction using integer-and fractional-order derivatives

摘要

This contribution deals with the mathematical modeling of one-dimensional heat conduction using integer- and fractional-order derivatives. In the introduction of contribution the processes in a field of the raw materials processing in which an important role is the process of heat transfer by conduction, are analyzed. An overview of the description of heat conduction without a heat source in the form of partial differential equations of integer- and fractional-order is listed. In the next section the mathematical model of one-dimensional heat conduction in the form of the first and half-order derivative of temperature with respect to time with the initial and boundary conditions is described. The principles of numerical and analytical methods of solution are described. Based on the implementation of the methods in MATLAB, simulations are executed and their results described in this article, in which the possibilities of using the first and half-order derivative of temperature with respect to time are suggested for determining the selected parameter of the model - thermal diffusivity. In the conclusion of the article, the experimental measurements achieved on the device HT10XC and its module HT11C are listed. The results of experimental measurements are compared with the simulations from the view of determining the thermal diffusivity.