Asymptotic analysis of solutions of a nonlinear problem of unsteady heat conduction of layered anisotropic inhomogeneous shells under boundary conditions of the first kind on the front surfaces

Abstract

The heat conduction problem is formulated for the layered shells consisting of heatsensitive anisotropic inhomogeneous layers, with boundary conditions of general form. The heat sensitivity of the material layers is described by the linear dependence of their thermophysical characteristics on temperature. The equation of heat conduction, boundary conditions and conditions of thermal conjugations on the boundaries of the contact between the layers are written in the dimensionless form. Two small parameters in dimensionless ratios are defined: thermophysical parameter characterizing the degree of thermal sensitivity of the material layers and geometrical parameter characterizing the relative shell thickness. Sequential recursion of dimensionless ratios is carry out, first on thermophysical small parameter, and then on the geometrical parameter. The first type of recursion allowed to linearize the problem of heat conduction. On the basis of the second type of recursion the exterior asymptotic expansion of the solution is built for the problem of nonstationary heat conduction of layered anisotropic heterogeneous shells with boundary conditions of the first kind on the facial surfaces. The obtained two-dimensional governing equation is analyzed. The asymptotic properties of solutions of the problem of heat conductivity are investigated.

Keywords

• thermal conductivity
• thermal sensitivity
• asymptotic analysis
• sandwich shells
• anisotropy and heterogeneity