The Problem of Non-Stationary Thermal Conductivity: Formulation in Derivatives and Solution by the Boundary Element Method

The formulation of the transient heat conduction problem with respect to the heat flux vector and its solution using the boundary element method is described. The primary advantage is the direct determination of the heat flux without the need for numerical differentiation of the temperature field. A boundary integral equation is derived for the problem formulated in terms of the heat flux vector. The procedure for solving the problem using the boundary element method is detailed, and a system of governing equations is established. A solution to a test problem concerning the transient temperature distribution in a bounded domain is presented. Comparison of the computational results with an analytical solution illustrates the reliability and acceptable engineering accuracy of the obtained solutions.