International Scientific Journal

Authors of this Paper

External Links


Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface ( x = 0 ) at t = 0 . The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions.
PAPER REVISED: 2012-01-16
PAPER ACCEPTED: 2012-01-16
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 2, PAGES [625 - 629]
  1. Carslaw, H.S., Jaeger, J.C., Conduction of Heat in Solids. Oxford University Press, London, 1959.
  2. Breaux , H.J., Schlegel, P.T. , Transient heating of thin plates, Int. J Heat Mass Transfer, 13(1970),1,pp. 18-211.
  3. Muzychka, Y. S., Yovanovich , M. M., Culham, J. R. , Thermal Spreading Resistance in Compound and rthotropic Systems, J. Thermophysics and Heat Transfer, 18 (2004),2, pp. 45-51.
  4. Schneider, G. E. , Strong, A. B. , Yovanovich , M. M., Transient thermal response of two bodies, ommunicating through a small circular contact area , Int. J. Heat Mass Transfer 20 (1977), 4, pp. 301- 08.
  5. Aderghal, N. , Loulou, T. , Bouchoucha, A., Rogeon , Ph. , Analytical and numerical calculation of urface temperature and thermal constriction resistance in transient dynamic strip contact , Appl. herm. Eng., 31 (2011),8-9, pp. 1527-1535 .
  6. Gabano, J.-D. , Poinot , T., Fractional modelling and identification of thermal systems , Signal rocessing, 91 (2011),3, pp. 531-541.
  7. Chaudhry, M.A., Zubair, S.M., Some analytical solutions of time-dependent, continuously perating heat sources. Heat Mass Transfer, 28(1993),4, 217-223.
  8. Hou, Z.B. , Komanduri, R. , General solutions for stationary/moving plane heat source problems in anufacturing and tribology, Int. J. Heat Mass Transfer. 43 (2000),10, pp.1679-1698.
  9. Agrawal , O. P. , Application of Fractional Derivatives in Thermal Analysis of Disk Brakes , onlinear Dynamics , 38( 2004),1-4, pp. 191-206.
  10. Oldham , K.B., Spanier , J. , The Fractional calculus , Academic Press, New York, 1974.
  11. Siddique, I. , Vieru,D. , Stokes flows of a Newtonian fluid with fractional derivatives and slip at the wall, nt. Rev. Chem. Eng., 3 (2011), 6, pp. 822- 826.
  12. Qi , H., Xu, M. , Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional erivative, Appl. Math. Model., 33 (2009),11,pp.4184-4191. doi:10.1016/j.apm.2009.03.002.
  13. dos Santos, M. C. , Lenzi, E. , Gomes, E. M. , Lenzi,, M. K. , Lenzi, E. K. , Development of Heavy Metal rption Isotherm Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 814-817.
  14. Hristov J., Starting radial subdiffusion from a central point through a diverging medium (a sphere): Heatbalance ntegral Method, Thermal Science, 15 (2011), Supl. 1, pp.S5-S20 . doi: 10.2298/TSCI1101S5H
  15. Pfaffenzeller, R. A. , Lenzi, M. K. , Lenzi, E. K. , Modeling of Granular Material Mixing Using Fractional alculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 818-821.
  16. Meilanov, R.P., Shabanova, M.R. , Akhmedov, E.N. , A Research Note on a Solution of Stefan Problem ith Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 810-813.
  17. Voller, V.R. An exact solution of a limit case Stefan problem governed by a fractional diffusion equation, nt. J. Heat Mass Transfer, 53 (2010), 23-24, pp. 5622-5625.
  18. Liu, J., Xu, M., Some exact solutions to Stefan problems with fractional differential equations, J. Math. nal. Appl., 351(2010), 2, pp. 536-542
  19. Yu.I. Babenko, Heat-Mass Transfer: Methods for calculation of thermal and diffusional fluxes, Khimia ubl., Moscow, 1984 (in Russian).
  20. Sazonov, V. S. , Exact Solution of the Problem of Nonstationary Heat Conduction for two Semi-spaces in on-ideal Contact, J. Eng. Phys. Thermophys., 79 (2006), 5, pp. 86-87.

© 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