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Thermostressed state of a cylinder with thin near-surface layer having time-dependent thermophysical properties

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We develop a method for the solution of boundary-value problems of the thermostressed state of cylindrical bodies with thin near-surface layers having time-dependent thermophysical properties. The presence of a thin near-surface layer in a long solid cylinder is taken into account in the formulated boundary-value problem by means of a nonclassical nonstationary boundary condition with variable coefficients. The replacement of this condition by the classical first-kind condition enables one to reduce the original problem to finding the solution of an integro-differential equation with variable coefficients. This equation has a Volterra-type integral operator and is solved by using spline approximations. The efficiency of this method has been partially verified on the well-known problem of heating of a thin homogeneous plate with variable Biot number by environment. We investigate the thermostressed state of a cylinder for both linear and exponential normalized surface parameters of heat transfer and heat capacity over time. For different stages of heating, we analyze at what constant values of parameters the thermal regime of the cylinder is closest to the mode with variable parameters. The obtained solutions and data on their properties can be used in solving the problems of boundary parametric identification.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    O. I. Yatskiv, R. M. Shvets’ & B. Ya. Bobyk

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  1. O. I. Yatskiv
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  2. R. M. Shvets’
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  3. B. Ya. Bobyk
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 4, pp. 90–105, October–December, 2011.

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Yatskiv, O.I., Shvets’, R.M. & Bobyk, B.Y. Thermostressed state of a cylinder with thin near-surface layer having time-dependent thermophysical properties. J Math Sci 187, 647–666 (2012). https://doi.org/10.1007/s10958-012-1090-y

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