Variational Method for Solving the Time-Fractal Heat Conduction Problem in Claydite-Block Construction

Abstract

Mathematical models of the heat conduction problem in the claydite-block construction with taking into account the fractal structure of the material is constructed. Integro-differentiation apparatus of fractional order to take into account the fractal structure of the material was used. The variational formulation of the problem was constructed. The variational method for obtaining an approximate solution of the considered problem was proposed. The results of the numerical experiments of studying the thermal conductivity of claydite-block construction depending on the time, wall thickness and materials of different fractions were obtained. Analyzing the founded distributions of temperature fields allows us to more accurately reflect the real speed of the process.