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Jordan Y. Hristov

A NOTE ON THE INTEGRAL APPROACH TO NON-LINEAR HEAT CONDUCTION WITH JEFFREY’S FADING MEMORY

ABSTRACT
Integral approach by using approximate profile is successfully applied to heat conduction equation with fading memory expressed by a Jeffrey’s kernel. The solution is straightforward and the final form of the approximate temperature profile clearly delineates the “viscous effects” corresponding to the classical Fourier law and the relaxation (fading memory). The optimal exponent of the approximate solution is discussed in case of Dirichlet boundary condition.
KEYWORDS
non-linear diffusion, fading memory, Jeffrey kernel, integral balance approach, approximate solution
PAPER SUBMITTED: 2012-08-26
PAPER REVISED: 2013-05-31
PAPER ACCEPTED: 2013-05-31
PUBLISHED ONLINE: 2013-06-16
DOI REFERENCE: https://doi.org/10.2298/TSCI120826076H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE Issue 3, PAGES [733 - 737]
REFERENCES
  1. Ferreira, J.A., de Oliveira, P., Qualitative analysis of a delayed non-Fickian model, Applicable Analysis, 87(2008), 8, pp. 873-886.
  2. Cattaneo, C, Sulla conduzione del calore, Atti Sem. Mat. Fis. Universit´a Modena, 3 (1948),1, pp. 83-101.
  3. Carillo, S., Some Remarks on Materials with Memory: Heat Conduction and Viscoelasticity, J. Nonlinear Math. Phys., 12 (2005), Suppl. 1, pp. 163-178.
  4. Curtin, M. E, Pipkin, A.C., A general theory of heat conduction with finite wave speeds, Archives of Rational Mathematical Analysis, 31 (1968), 2, pp. 313-332.
  5. Joseph, D.D., Preciozi, Heat waves, Rev.Mod. Phys., 61 (1989), 1, pp. 41-73
  6. Goodman, T.R., The heat balance integral and its application to problems involving a change of phase, Transactions of ASME, 80 (1958), 1-2, pp. 335-342.
  7. Goodman T.R., Application of Integral Methods to Transient Nonlinear Heat Transfer, Advances in Heat Transfer, T. F. Irvine and J. P. Hartnett, eds., 1 (1964), Academic Press, San Diego, CA, pp. 51-122.
  8. Hristov, J., The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and benchmark exercises, Thermal Science, 13 (2009), 2, pp.22-48.
  9. Myers, T.G., Optimal exponent heat balance and refined integral methods applied to Stefan problem, Int. J. Heat Mass Transfer, 53 (2010), 5-6, 1119-1127.
  10. Hristov, J. The Heat-Balance Integral: 1. How to Calibrate the Parabolic Profile?, Comptes Rendues Mechanique, 340 (2012b),7,485-492.
  11. Braga,W., Mantelli,M., A new approach for the heat balance integral method applied to heat conduction Problems, 38th AIAA Thermophysics Conference, Toronto, Ontario, June 6-9, 2005, Paper AIAA-2005-4686.
  12. Goodwin, J.W., Hughes, R.W., Rheology for chemists: An Introduction, 2nd ed, RSC Publishing, Cambridge, UK., 2008.
  13. Tzou, D.Y., Chiu, K.K.S, Depth of thermal penetration: Effect of relaxation and thermalization, J. Thermophysics and Heat Transfer, 13 (1999), 2, 266-269.
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A note on the integral approach to non-linear heat conduction with Jeffrey’s fading memory

© 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