Additional functions and additional boundary conditions in heat conduction problems for multilayer bodies

Abstract

Objective. The purpose of the study is to develop a technique for obtaining an analytical solution to the thermal conductivity problem for a 2-layer plate under boundary conditions of the 1st kind.Method. The research method is based on the integral method. In this case, an additional function (DF), additional boundary conditions (ABC) and local coordinate systems are introduced. The DF describes the temperature over time at one of the points of the twolayer system. Its use reduces the partial differential equation to an ordinary equation. DKUs allow you to perform equations on boundaries.Result. It is shown that satisfying the equations on the boundaries leads to their fulfillment inside the domain. Note that additional boundary conditions are satisfied for any other method of obtaining analytical solutions. The only difference is that they are not accepted as conditions subject to separate consideration. An additional function is also a quantity that is determined by any other method of obtaining a solution. The only difference is that it is not singled out for separate consideration.Conclusion. It can be stated that the introduction of an additional function and additional boundary conditions does not distort the original formulation of the problem and is only a means to significantly simplify the process of obtaining an approximate analytical solution and the final expression for it.

Keywords

• multilayer structures
• additional function
• dku
• integral method
• local coordinates
• approximate solution