Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine,Lviv, Ukraine. Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Rzeszow, Poland.
Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved numerically by the method of lines. Directing it to the Cauchy’s problem for systems of ordinary differential equations studied feature which takes place on the cylinder axis. Taken into account the dependence on the temperature coefficient of heat transfer that the different interpretation of its physical content makes it possible to consider both convective and convective-ray or heat ray. Using the perturbation method, the corresponding thermoelasticity problem taking into account the temperature dependence of mechanical properties of the material is construed. The influence of the temperature dependence of the material on the distribution of temperature field and thermoelastic state of infinite circular cylinder made of titanium alloy Ti-6Al-4V by radiant heat transfer through the outer surface has been analyzed.
H. Harmatij, M. Król and V. Popovycz, "Quasi-Static Problem of Thermoelasticity for Thermosensitive Infinite Circular Cylinder of Complex Heat Exchange," Advances in Pure Mathematics, Vol. 3 No. 4, 2013, pp. 430-437. doi: 10.4236/apm.2013.34061.
[1] J. J. Burak and R. M. Kushnir, “Modeling and Optimization in Termomehanitsi Electrically Inhomogeneous Bodies,” In: J. J. Burak and R. M. Kushnir, Eds., Thermoelasticity Thermosensitive Bodies, Vol. 3, Lviv, 2009, p. 412. [2] V. A. Lomakin, “The Theory of Elasticity of Inhomogeneous Bodies,” Moscow State University Press, Moscow, 1976, p. 367. [3] N. H. Moiseev, “The Asymptotic Methods of Nonlinear Mechanics,” Nauka, Moscow, 1981, p. 400. [4] R. M. Kushnir and V. Popovycz, “Stressed State Thermosensitive Body Rotation in the Plane Axialsymmetric Temperature Field,” Visnuk Dnipropetrovskoho University, Median Mechanics, No. 2, 2006, pp. 91-96. [5] Y. Tanigawa, T. Akai, R. Kawamura and N. Oka, “Transient Heat Conduction and Thermal Stress Problems of a Nonhomogeneous Plate with Temperature-Dependent Material Properties,” Journal of Thermal Stresses, Vol. 19, No. 1, 1996, pp. 77-102. doi:10.1080/01495739608946161 [6] N. Noda, “Thermal Stresses in Materials with Temperature-Dependent Properties,” Thermal Stresses Journal, 1986, pp. 391-483. [7] V. S. Popovych and H. Yu Harmatiy, “Analytical and Numerical Methods of Solutions of Heat Conduction Problems with Temperature-Sensitive Body Convective Heat Transfer,” Problems of Mechanics and Mathematics, Pidstryhach, No. 13-93, Lviv, 1993, p. 67. [8] H. Yu. Harmatiy, M. B. Kutniv and V. S. Popovich, “Numerical Solution of Unsteady Heat Conduction Problems with Temperature-Sensitive Body Convective Heat Transfer,” Engineering, No. 1, 2002, pp. 21-25. [9] A. Samarskiy, “The Theory of Difference Schemes,” Nauka, Moscow, 1977, p. 656.