THERMAL SCIENCE

International Scientific Journal

Dariusz M. Perkowski

,

Piotr Sebestianiuk

,

Jakub Augustyniak

AXISYMMETRIC STATIONARY HEAT CONDUCTION PROBLEM FOR HALF-SPACE WITH TEMPERATURE-DEPENDENT PROPERTIES

ABSTRACT
The study examines problems of heat conduction in a half-space with a thermal conductivity coefficient that is dependent on temperature. A boundary plane is heated locally in a circle zone at a given temperature as a function of radius. A solution is obtained for any function that describes temperature in the heating zone. Two special cases are investigated in detail, namely Case 1 with given constant temperature in the circle zone and Case 2 with temperature given as a function of radius, r. The temperature of the boundary on the exterior of the heating zone is assumed as zero. The Hankel transform method is applied to obtain a solution for the formulated problem. The effect of thermal properties on temperature distributions in the considered body is investigated. The obtained results were compared with finite element method model.
KEYWORDS
temperature, heat flux, temperature-dependent conductivity, Kirchhoff transform, Hankel transform
PAPER SUBMITTED: 2018-12-06
PAPER REVISED: 2019-03-12
PAPER ACCEPTED: 2019-03-20
PUBLISHED ONLINE: 2019-04-07
DOI REFERENCE: https://doi.org/10.2298/TSCI181206109P
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 3, PAGES [2137 - 2150]
REFERENCES
  1. Nowiński, J.L., Thermoelastic problem for an isotropic sphere with temperature dependent properties, ZAMP, 10, 565-575, 1959.
  2. Nowiński, J.L., A Betti-Rayleigh theorem for elastic bodies exhibiting temperature dependent properties, Applied Scientific Research, Section A, 9, 429-436, 1960.
  3. Nowiński, J.L., Theory of thermoelasticity with applications, Sijthoff and Noordhoff Int. Publ., Alphen aan den Rijn, 1978Hahn, D.W. and Ozisik Necati, M., Heat conduction, John Wiley & Sons, Inc, 2012.
  4. Hata, T., Thermoelastic problem for a Griffith crack in a plate with temperature-dependent properties under a linear temperature distribution, Journal of Thermal Stresses 2, 3-4, 353- 366, 1979.
  5. Hata, T., Thermoelastic problem for a Griffith crack in a plate whose shear modulus is an exponential function of the temperature, ZAMM, 61, 2, 81-87, 1981.
  6. He, J.H., Non-perturbative method for strongly nonlinear problems, Berlin: Dissertation De Verlage in Internt GmbH, 2006.
  7. Lyapunov, A.M., General Problem on Stability of Motion (English translation), London: Taylor and Francis, (Original work published 1892), 1992.
  8. Matysiak, S.J., Wave fronts in elastic media with temperature dependent properties, Applied Scientific Research 45, 97-106, 1988.
  9. Yevtushenko A.A., Grzes P., Axisymmetric finite element model for the calculation of temperature at braking for thermosensitive materials of a pad and a disc, Numerical Heat Transfer, Section A Applications 62 (3), 211-230, 2012.
  10. Adamowicz, A. and Grzes, P., Three-dimensional FE model for calculation of temperature of a thermosensitive disc, Applied Thermal Engineering, 50, 572-581, 2013.
  11. Thuresson D., Influence of material properties on sliding contact braking applications, Wear 257 (5-6), 451-460, 2004.
  12. Noda, N., Thermal Stresses in Materials with Temperature-Dependent Properties, Appl. Mech. Rev 44(9), 383-397, 2009.
  13. Zhu, X.K. and Chao, Y.J., Effects of temperature-dependent material properties on welding simulation, Computers and Structures 80, 967-976, 2002.
  14. Cole, J.D., Perturbation Methods in Applied Mathematics, Waltham Massachusetts: Blaisdell Publishing Company, 1968.
  15. Nayfeh, A.H., Perturbation Methods, New York: John Wiley and Sons, 2000.
  16. Lyapunov, A.M., General Problem on Stability of Motion (English translation), London: Taylor and Francis, (Original work published 1892), 1992.
  17. He, J.H., Non-perturbative method for strongly nonlinear problems, Berlin: Dissertation De Verlage in Internt GmbH, 2006.
  18. Mosayebidorcheh, S., Ganji, D.D. and Farzinpoor, M., Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient, Propulsion and Power Research, Volume 3, Issue 1, March 2014, Pages 41-47, 2014.
  19. Weigand, B., Analytical Methods for Heat Transfer and Fluid Flow Problems, Berlin: Springer-Verlag Berlin Heidelberg, 2010.
  20. Chichinadze A.V., Calculation and Investigation of External Friction During Braking, Nauka, Moscow, 1967. (in Russian).
  21. Gradshteyn, I.S. and Ryzhik, I.M., Tables of integrals, series and products. New York: Academic Press, 1965.
  22. Kulchytsky-Zhyhailo R., Spatial issues of thermoelasticity, Publishing house of Bialystok University of Technology, 2002. (in Polish).
  23. Barber J. R., Ciavarella M., Contact mechanics, Int. J. Solids Structures, Vol.37, 29-43.
  24. Tillman A.R., Borges V.L., Guinmares G., de Lima e Silva A.L.F., Identification of temperature dependent thermal properties of solid materials, J. Braz. Soc. Mech. Sci. Eng. 4:269-278, 2008.
  25. Schreiber E., Saravanos D.A., Soga N., Elastic constatnts and their measurement, McGraw-Hill, New York, p 196, 1973.
PDF VERSION [DOWNLOAD]
Axisymmetric stationary heat conduction problem for half-space with temperature-dependent properties

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence