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THERMAL IMPEDANCE AT THE INTERFACE OF CONTACTING BODIES: 1-D EXAMPLES SOLVED BY SEMI-DERIVATIVES

ABSTRACT
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.
KEYWORDS
PAPER SUBMITTED: 2011-11-25
PAPER REVISED: 2012-01-16
PAPER ACCEPTED: 2012-01-16
DOI REFERENCE: https://doi.org/10.2298/TSCI111125017H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 2, PAGES [625 - 629]
REFERENCES
  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.

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