A transformation is presented that enables the center temperature of a cylinder to be expressed in terms of an integral of the peripheral temperature distribution for heat conduction with space-dependent thermal conductivity. Its predictions agree with exact answers and with numerical solutions obtained with finite difference methods for four test cases. The new result can be applied to a two-dimensional floating random-walk Monte Carlo procedure which previously was restricted to the case of constant thermal conductivity.
Issue Section:
Technical Notes
1.
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2.
Brebbia, C., 1984, The Boundary Element Method For Engineers, Pentech Press Ltd., Estover Road, Plymouth, Devon PL6 7PZ, Great Britain.
3.
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, and Sparrow
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, 1967
, “The Solution Of Heat Transfer Problems by Probability Methods
,” ASME J. Heat Transfer
, 89
, pp. 121
–131
.4.
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.
5.
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.
6.
Bellman, R., 1952, Stability Theory Of Differential Equations, McGraw-Hill, p. 109.
7.
Luikov
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,” Heat Transfer-Sov. Res.
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.8.
Grigoriu
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, 2000
, “A Monte Carlo Solution Of Heat Conduction And Poisson Equations
,” ASME J. Heat Transfer
, 122
, pp. 40
–45
.9.
Munoz
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, and Burmeister
, L.
, 1988
, “Steady Conduction With Space-Dependent Conductivity
,” ASME J. Heat Transfer
, 110
, pp. 778
–780
.10.
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
.11.
Carslaw, H., and Jaeger, J., 1959, Conduction Of Heat In Solids, Oxford University Press, p. 89.
12.
Hameed
, S.
, and Lebedeff
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, 1975
, “Application Of Integral Method To Heat Conduction In Nonhomogeneous Media
,” ASME J. Heat Transfer
, 97
, pp. 304
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.13.
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.
14.
Munoz, A., 1984, “Variable Thermal Conductivity And The Monte Carlo Floating Random Walk,” Master of Science thesis, University of Kansas, Lawrence, KS.
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by ASME
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