Temperature field of the supported thin-walled constructions with one-sided heating

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

A temperature field in a reinforced by frames and stringers arbitrary-shaped shell exposed to a plane-parallel radiant heat flux from an infinitely remote heat source is investigated. A convective heat transfer exists between the shell and the environment. Geometric parameters of cross sections of reinforcing elements are small as compared with both the distances between them and the radius of curvature of the shell midsurface. With these assumptions, the normal component of radiant heat flux moves smoothly over the surface of the shell. Therefore, the gradients of temperature field will reach the extreme values in the vicinity of the reinforcing elements in the directions perpendicular to their axes.
The asymptotic dependence of the distribution of the temperature is found from the solution of the heat conduction problem: 

where is the distribution of the temperature with height ribs,  are the thickness and the height of section of ribs, are the coefficients of thermal diffusivity and thermal conductivity of material ribs, — coefficient of heat transfer from the reinforcing element in the environment, is the temperature distribution along the shell, is the shell thickness, are the coefficients of the thermal diffusivity and thermal conductivity of shell‘s material, is the coefficient of heat transfer from the shell into the environment, is the time dependence of the heat flux, is its maximum value, is the cosine of the angle of incidence of the heat flux on the shell surface, is a curvilinear coordinate extends from the lower base of the cross section of the ribs to the top on the axis of symmetry and next to the shell middle surface perpendicular to the edge.
Using Laplace transform the various asymptotic solutions are constructed. At small times the convective heat transfer between the shell and the environment has no significant effect to the temperature field, and for the practical calculation the following expressions can be used:

Keywords:

shell, temperature field, supporting elements, convective heat transfer, radiant heat flux, the Laplace transform, asymptotic solutions

References

1. Afanasev P.P., Golubev I.S., Lavochkin S.B., Novikov V.N., Parafes S.G., Pestov M.D., Turkin I.K. Bespilotnye letatel’nye apparaty. Osnovy ustroistva i functsionirovanija (Unmanned aerial vehicles. The basic structure and functioning of), Moscow, MAI, 2010, 654 p.
2. Turkin I.K. Proectirovanie toncostennych constructsij letatel’nyh apparatov, functsionirujutshikh v extremalnykh uslovijah (Design of thin-walled constructions of aircraft operating in extreme conditions), Moscow, Engineering, 1965, 567 p.
3. Besuchov N.I., Bazhenov V.L., Goldenblat N.I., Nikolaenko N.A., Sinjukov A.M. Raschety na prochnost’, ustojchivost’ I colebanija v uslovijakh temperature (Calculation of strength, stability and fluctuations in high-temperature conditions), Moscow, Engineering, 1965, 567 p.
4. Zino I.E., Tropp E.A. Asimptotichescie metody v zadachakh teorii teploprovodnosti ( asymptotic methods in the theory of thermal conductiovity), Leningrad, Leningrad State University, 1978, 224 p.
5. Gorunov A.V., Klimenko B.M., Rumjantev B.P., Samarin A.V. Temperaturnye zadachi i ustoichivost’ plastin i obolochek, Sbornik statei, Saratov, 1988, pp. 12-14
6. Gorshkov A.G., Gorunov A.V., Liberzon R.E., Mathematical methods , physical and mechanical fields, 1982, vol.16, pp. 52-55.

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