Modeling of Non-Stationary Temperature Fields in Multilayer Shells With Film Heat Sources
Natalia Smetankina, Oleksii Postnyi, Alyona Merkulova, Dmytro Merkulov
Abstract
A method for calculating non-stationary temperature fields in a non-closed cylindrical multilayer shell with a complex shape when exposed to film heat sources is offered. The shell with constant thickness isotropic layers and various physical properties is considered. The number of layers and their layout is arbitrary. Convective heat exchange occurs on the shell surfaces. The shell is affected by interlayer heat sources. The non-stationary heat conduction equation and the boundary conditions for the multilayer shell are derived from the heat balance variational equation. The temperature fields are determined while solving the nonstationary heat conduction problem for multilayer shells when the latter are heated with interlayer film heat sources. Distribution of temperature along each layer is presented by means of the Legendre polynomials. The problem is reduced to integration of a system of differential equations by modified Taylor's method. As an example, the problem of non-stationary thermal conductivity for a five-layer glazing element of an aircraft when heated with a film heat source has been solved.