Thermoelastic interaction of bodies with allowance for thermal resistance and pressure of an ideal gas in an intercontact gap

Abstract

The thermoelastic contact of two semi-infinite bodies of heterogeneous materials in the presence
of gas in a gap, which is caused by a groove of a small height on the surface of one of the bodies,
is investigated. The gas exerts a pressure on the gap surfaces and causes an additional thermal
resistance dependent on the gap height. As a mathematical model of the gas, the ideal gas is chosen,
which state is described by the Clapeyron-Mendeleev equation. The effect of the gas pressure,
the mechanical and thermal load on the gap deforming is taken into account. The contact problem
formulated is reduced to a system of two nonlinear singular integrodifferential equations for the
gap height and the temperature jump between the gap surfaces. Its solution is constructed using
the method of successive approximations. To find the gas pressure, the Clapeyron-Mendeleev
equation, in which the dependence of the gas temperature on the temperatures of the gap surfaces
is taken into account, is used. Numerical calculations are carried out for the pair of materials of
stainless AISI 304 steel — A380 aluminum alloy in the presence of air, argon, krypton or helium in
the gap. The influence of the gas mass, the heat flow density, and the external pressure intensity on
the gap width, the gas temperature, the thermal contact resistance between the bodies as well as
the level of thermal rectification is analyzed.