Mathematical modelling, determination and analysis of the thermostressed state in a thermosensitive three-layer hollow cylinder subjected to the convective-radiative heating

2015;
: pp. 160-175
https://doi.org/10.23939/mmc2015.02.160
Received: December 01, 2015

Math. Model. Comput. Vol. 2, No. 2, pp. 160-175 (2015)

1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine
3
Lviv Polytechnic National University

The stationary temperature distribution in a three-layer infinitely-long hollow cylinder is modeled and determined under the condition that the internal heat sources are distributed within the second layer in accordance to the parabolic law and the convective-radiative and convective heat exchange with the environment occurs on the inner and outer surfaces, respectively. The components of the thermostressed state were found and the effect, caused by the dependence of thermophysical and mechanical material properties on the temperature, along with the intensity of radiative heat exchange, in the distribution of the temperature and stress-strain state is analyzed.

  1. Popovych V., Kalyniak B. The mathematical modelling and method of determination of static thermostressed state of the multilayer thermosensitive cylinders (in Ukrainian). The mathematical metods and physical and machanical fields. 57, 2 (2014).
  2. Carslaw H., Jaeger J. Conduction of heat in solids, 2nd ed. Oxford, Clarendon Press (1959).
  3. Kushnir R., Popovych V. Thermoelasticity of Thermosensitive Solids. Lviv, SPOLOM (2009) (in Ukrainian).
  4. Kushnir R., Popovych V. S. Heat conduction problem of the thermosensitive solids onder complex heat exchange. Heat conduction – Basic research, In Tech (2011).
  5. Noda N. Thermal stresses in materials with temperature-dependent properties. Thermal stresses I. (1986).
  6. Tanigava Y., Akai T. Transient heat conduction and thermal stress problems of a nonhomogegenous plate with temperature dependent material properties. Journal of thermal stresses. 19, 1 (1996).