# Asymptotic analysis of solution to the nonlinear problem of non-stationary heat conductivity of layered anisotropic non-uniform shells at low Biot numbers on the front surfaces

Asymptotic analysis of solution to the nonlinear problem of non-stationary heat conductivity of... Abstract 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 temperature. 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 thickness 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 thermalphysical small parameter, then, small Biot numbers and, finally, geometrical 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thermophysics and Aeromechanics Springer Journals

# Asymptotic analysis of solution to the nonlinear problem of non-stationary heat conductivity of layered anisotropic non-uniform shells at low Biot numbers on the front surfaces

, Volume 24 (2): 18 – Mar 1, 2017
18 pages

/lp/springer-journals/asymptotic-analysis-of-solution-to-the-nonlinear-problem-of-non-NQf55g2pl2
Publisher
Springer Journals
ISSN
0869-8643
eISSN
1531-8699
DOI
10.1134/S0869864317020123
Publisher site
See Article on Publisher Site

### Abstract

Abstract 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 temperature. 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 thickness 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 thermalphysical small parameter, then, small Biot numbers and, finally, geometrical 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.

### Journal

Thermophysics and AeromechanicsSpringer Journals

Published: Mar 1, 2017

### References

Access the full text.