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TECHNICAL NOTES

Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux

[+] Author and Article Information
V. V. Kulish

School of Mechanical and Production Engineering, Nanyang Technological University, Singapore 639798

J. L. Lage

Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337e-mail: jll@seas.smu.edu

J. Heat Transfer 122(2), 372-376 (Dec 09, 1999) (5 pages) doi:10.1115/1.521474 History: Received August 27, 1999; Revised December 09, 1999
Copyright © 2000 by ASME
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References

Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd ed., Oxford University Press, Oxford.
Arpaci, V. S., 1966, Conduction Heat Transfer, Addison-Wesley, Reading, PA.
Özisik, M. N., 1980, Heat Conduction, Wiley, New York.
Kakaç, S., and Yener, Y., 1985, Heat Conduction, Hemisphere, Washington, DC.
Poulikakos, D., 1994, Conduction Heat Transfer, Prentice-Hall, Englewood Cliffs, New Jersey.
Oldham,  K. B., and Spanier,  J., 1972, “A General Solution of the Diffusion Equation for Semiinfinite Geometries,” J. Math. Anal. Appl., 39, pp. 655–669.
Cohen, H., 1992, Mathematics for Scientists and Engineers, Prentice-Hall, Englewood Cliffs, NJ.
Bejan, A., 1993, Heat Transfer, Wiley New York.
Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
Riesz,  M., 1949, “L’intégral de Riemann-Liuoville et le Problème de Cauchy,” Acta Math., 81, p. 1.
Abramowitz, M., and Stegun, I. A., 1964, Handbook of Mathematical Functions, Dover, New York.

Figures

Grahic Jump Location
Time evolution of surface heat flux, Eq. (20), and the imposed boundary condition (dashed line): [Tb(t)−T0]/TA=sin(ωt)
Grahic Jump Location
Time evolution of surface temperature, Eq. (23), and the imposed boundary condition (dashed line): q(t)/q0=sin(ωt)

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