Nonlinear heat conduction problem for a thin shell

Аuthors

Gorunov A. V.^*, Molodoznikova R. N., Prokofev A. I.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: msgor@mail.ru

Abstract

The problem of heat conductivity for an arbitrary thin-walled shell exposed to a plane-parallel radiant heat flux from the infinitely remote source of radiation is considered. A convective heat transfer between the shell and the environment is described by the Newton law. Thermophysical parameters of the shell depend on the temperature.
Nonlinear heat conduction problem is described by the following differential equation of heat conductivity:

with the initial condition

and the boundary one:

is the function of temperature distribution along the shell; is the ambient temperature; and are the curvilinear coordinates on the shell midsurface; n is the normal unit to the boundary of the shell; is the time; is the angle of incidence of the radiant heat flow on the surface of the shell; is the shell thickness; are the function radiant heat flux and its maximum value; is the coefficient of heat transfer from the shell into the environment; — are the heat capacity, the mass density, the thermal conductivity, and the thermal diffusivity coefficients for the shell material; are the coefficients at the initial temperature; A, B are the coefficients of the first quadratic form of the shell midsurface; R is the least radius of curvature of the shell midsurface.
At the initial moment the temperature of the shell is equal to zero. Excluding the process of thermal conductivity in the shell midsurface various asymptotic solutions are constructed.
The formula for the temperature field in the shell in the case of a linear dependence where are constants is obtained in the following form:

The obtained asymptotic solutions provide the accuracy sufficient for practical use for various aircrafts structures.

Keywords:

nonlintar heat conduction problem, aircrafts, radiant heat flux, convective heat transfer, asymptotic solutions

References

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