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TECHNICAL NOTES

The Effect of Space-Dependent Thermal Conductivity on the Steady Central Temperature of a Cylinder

[+] Author and Article Information
Louis C. Burmeister

Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045

J. Heat Transfer 124(1), 195-197 (Jul 10, 2001) (3 pages) doi:10.1115/1.1418701 History: Received September 25, 2000; Revised July 10, 2001
Copyright © 2002 by ASME
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References

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Brebbia, C., 1984, The Boundary Element Method For Engineers, Pentech Press Ltd., Estover Road, Plymouth, Devon PL6 7PZ, Great Britain.
Haji-Sheik,  A., and Sparrow,  E., 1967, “The Solution Of Heat Transfer Problems by Probability Methods,” ASME J. Heat Transfer, 89, pp. 121–131.
Turner, J., 1978, “An Improved Monte Carlo Procedure For The Solution Of The Steady-State, Two-Dimensional Diffusion Equation With Application To Flow Through Porous Media,” M. S. thesis, University of Kansas, Lawrence, KS.
Turner, J., 1982, “Improved Monte Carlo Procedures For The Unsteady-State Diffusion Equation Applied To Water Well Fields,” Ph. D. thesis, University of Kansas, Lawrence, KS.
Bellman, R., 1952, Stability Theory Of Differential Equations, McGraw-Hill, p. 109.
Luikov,  A., 1971, “Methods Of Solving The Nonlinear Equations Of Unsteady-State Heat Conduction,” Heat Transfer-Sov. Res., 3, pp. 1–51.
Grigoriu,  M., 2000, “A Monte Carlo Solution Of Heat Conduction And Poisson Equations,” ASME J. Heat Transfer, 122, pp. 40–45.
Munoz,  A., and Burmeister,  L., 1988, “Steady Conduction With Space-Dependent Conductivity,” ASME J. Heat Transfer, 110, pp. 778–780.
Clements,  D., and Budhi,  W., 1999, “A Boundary Element Method For The Solution of a Class of Steady-State Problems for Anisotropic Media,” ASME J. Heat Transfer, 121, pp. 462–465.
Carslaw, H., and Jaeger, J., 1959, Conduction Of Heat In Solids, Oxford University Press, p. 89.
Hameed,  S., and Lebedeff,  S., 1975, “Application Of Integral Method To Heat Conduction In Nonhomogeneous Media,” ASME J. Heat Transfer, 97, pp. 304–305.
Patankar, S., 1978, “A Numerical Method For Conduction In Composite Materials, Flow in Irregular Geometries and Conjugate Heat Transfer,” Proc. Sixth Int. Heat Transfer Conf., Toronto, Canada, Vol. 3, Paper No. CO-14, pp. 297–302.
Munoz, A., 1984, “Variable Thermal Conductivity And The Monte Carlo Floating Random Walk,” Master of Science thesis, University of Kansas, Lawrence, KS.

Figures

Grahic Jump Location
Conductive heat flux q across a differential element of area rdθ on the periphery of a cylinder
Grahic Jump Location
Control volumes for determination of the central temperature of a cylinder in terms of the peripheral temperatures by a finite difference method

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