Home – Home – Jornals – Thermophysics and Aeromechanics 2017 number 2

The nonlinear problem of non-stationary heat conductivity of the layered anisotropic heat-sensitive shells was formulated taking into account the linear dependence of thermal-physical characteristics of the materials of phase compositions on the tem-perature. The initial-boundary-value problem is formulated in the dimensionless form, and four small parameters are identified: thermal-physical, characterizing the degree of heat sensitivity of the layer material; geometric, characterizing the relative thick-ness of the thin-walled structure, and two small Biot numbers on the front surfaces of shells. A sequential recursion of dimensionless equations is carried out, at first, using the thermal-physical small parameter, then, small Biot numbers and, finally, geome-trical small parameter. The first type of recursion allowed us to linearize the problem of heat conductivity, and on the basis of two latter types of recursion, the outer asymptotic expansion of solution to the problem of non-stationary heat conductivity of the layered anisotropic non-uniform shells and plates under boundary conditions of the II and III kind and small Biot numbers on the facial surfaces was built, taking into account heat sensitivity of the layer materials. The resulting two-dimensional boundary problems were analyzed, and asymptotic properties of solutions to the heat conductivity problem were studied. The physical explanation was given to some aspects of asymptotic temperature decomposition.