Usage of the heat conduction model for the experimental determination of thermal diffusivity

Abstract

The article deals with the mathematical model of a one-dimensional heat conduction, which is applied to the experimental determination of thermal diffusivity, respectively specific heat capacity. In the introduction of a contribution are analyzed the processes in a field of the processing of raw materials in which an important role is the process of heat transfer by conduction. There is listed a review of the formulation and solution of the Fourier equation of heat conduction without heat source in the form of partial differential equations of integer and fractional order is listed. The experimental methods for the measurement of thermal diffusivity are also described in the introduction. In the next section is described the mathematical model of one-dimensional heat conduction with the initial and boundary conditions. The principles of implicit and explicit numerical method of solution of partial differential equation describing one-dimensional heat conduction are described. The one-dimensional mathematical model of heat conduction for various initial and boundary conditions of the first and second kind was implemented in MATLAB environment in the form of separate m-functions for implicit and explicit method. The description of the laboratory equipment HT10XC and its module HT11C which is used to measure the thermal conductivity is also listed in the article. The experimental measurements were carried out on the laboratory facility, which is a physical model of heat conduction process. The measurement results compared with the results of simulations of mathematical model are presented in the paper. At the conclusion of the contribution is a proposal for a method of measurement of thermal diffusivity. The method results from experimental measurement of the thermal conductivity on the laboratory facility HT10XC and subsequent realization of simulations on the mathematical model in order to identify the parameter of the model that represents the thermal diffusivity of the measured samples. On the basis of the measured value of thermal diffusivity and its definition can be estimated the specific heat capacity of the measured samples.