Further boundary conditions in heat conduction problems in multilayer structures

Abstract

This paper presents an approximate analytical solution of the heat conduction problem for a two-layer plate under symmetric boundary conditions of the first kind. The solution was determined on the basis of the property of the parabolic heat transfer equation associated with an infinite velocity of heat propagation, by determining the accessory unknown function and accessory boundary conditions in the integral heat balance method. Local coordinate systems are given in order to obtain the simplest possible coordinate system satisfying the matching conditions and boundary conditions for each separate layer. An accessory unknown function is the temperature change over time in the center of symmetry. The use of this function in the heat balance integral method allows for reduction in the solution of the initial partial differential equation to the integration of an ordinary differential equation with respect to the additional unknown function. Further boundary conditions are defined in such a way that their satisfaction by an unknown solution is equivalent to the satisfaction of the equations at the boundary points. Studies have shown that the equation fulfillment at the boundaries leads to their fulfillment within the regions.