Dynamic thermoelasticity in the problem of heat shock based on the general energy equation

Аuthors

Kartashov E. M.^*, Nenakhov E. V.^**

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

*e-mail: kartashov@mitht.ru
**e-mail: newnew94@mail.ru

Abstract

The problem of heat shock was studied for the case of the solid body surface sharp cooling in terms of dynamic thermoelasticity based on the generalized energy equation, namely the equation of non-stationary heat conduction of a hyperbolic type with allowance for the finite velocity of heat propagation. Various modes of sudden cooling, such as temperature mode, thermal mode, cooling by medium, resulting in tensile stresses in the inner sections of the solid body, in contrast to the similar cases of sudden heating creating compression stresses were studied. Exact analytical solutions of a series of boundary-value problems of dynamic thermoelasticity were obtained, numerical experiments were performed, and their features were described. It is shown, that two wave fronts are formed in the solid – the elastic wave front, and the thermal wave front. Depending on the ratio of their propagation rates, the elastic wave either precedes the thermal wave, or lags behind it. A comparison with the classical case of dynamic thermoelasticity while cooling is made. It is shown, that in the latter case, the presence of finite heat transfer from the surface of a solid body leads to the absence of thermal stress ruptures. At the same time, for a generalized dynamic problem the nature of the stresses remains the same as for an infinitely large value of the heat transfer coefficient (which means the existence of a boundary condition of the first kind, i.e. temperature cooling).With this, the accounting for the thermal inertia in the hyperbolic type heat equation and in the boundary condition of the third kind leads to the dynamic temperature stresses decrease, but with heat transfer on the solid surface increasing the dynamic temperature stresses increase. This allowed determining the most dangerous cooling mode, which was the temperature cooling.

Keywords:

heatstroke, the final velocity of heat propagation, dynamic thermoelastic stresses, tensile stress

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