Thermoelastic State of a Semiinfinite Thermally Sensitive Three-Component Rod Under Convective-Radiative Heat Exchange
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THERMOELASTIC STATE OF A SEMIINFINITE THERMALLY SENSITIVE THREE-COMPONENT ROD UNDER CONVECTIVE-RADIATIVE HEAT EXCHANGE B. V. Protsyuk1 and О. P. Horun1,2
UDC 539.3
We propose a numerical-analytic approach to the determination of the thermoelastic state of a semiinfinite thermally sensitive three-component rod interacting with the ambient medium by convectiveradiative heat exchange. The proposed approach is based on the use of the Kirchhoff transformation, generalized functions, Green functions of the linear nonstationary problem of heat conduction for a three-component space, and linear splines. We investigate the influence of thermal sensitivity and heat-exchange parameters on the distributions of temperature, stresses, and displacements. Keywords: heat conduction, thermal sensitivity, thermoelasticity, layered bodies, convective-radiative heat exchange.
Layered structural elements are extensively used in various branches of industry. Under the conditions of high-temperature action, in order to give a more exact description of their thermoelastic state, it is necessary to use models taking into account the dependence of the physicomechanical characteristics on temperature and the conditions of convective-radiative heat exchange. The numerical and numerical-analytic approaches to the solution of problems of heat conduction and thermoelasticity for one-layer and multilayer thermally sensitive bodies for various methods of heating, including the case of convective-radiative heating, were considered in [1–6]. In what follows, we propose an approach to the solution of quasistatic problems of thermoelasticity for semiinfinite three-component thermally sensitive bodies heated by convective-radiative heat exchange. In this case, we use the Kirchhoff approach, generalized functions, and the Green functions of the linear nonstationary problem of heat conduction for a three-component space represented in the form of functional series and linear splines. Statement of the Problem Consider a semiinfinite three-component rod referred to a cylindrical coordinate system r , ϕ , z (Fig. 1). We assume that the conditions of perfect thermomechanical contact are satisfied on the interfaces z = z1 = 0 and z = z2 = h and that the surface r = R is thermally insulated and smoothly fixed (radial displacements and tangential stresses are absent). The convective-radiative heat exchange with a medium of temperature t c occurs through the bounding surface z = z 3 and the normal and tangential stresses are absent on this surface. The initial temperatures of the components are equal to zero. In this body, we determine the nonstationary temperature field and the stresses and displacements induced by this field with regard for the temperature dependences of the physicomechanical characteristics. 1 2
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 52, No. 3,
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