TECHNICAL PAPERS: Conduction Heat Transfer

Nonlinear Transient Heat Conduction Using Similarity Groups

[+] Author and Article Information
M. Becker

Oregon Graduate Institute, P.O. Box 1000, Portland, OR 97291e-mail: mbecker@nycap.rr.com

J. Heat Transfer 122(1), 33-39 (Jun 29, 1999) (7 pages) doi:10.1115/1.521434 History: Received July 15, 1998; Revised June 29, 1999
Copyright © 2000 by ASME
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Kasuya,  D., and Yurioka,  N., 1993, “Prediction of Welding Thermal History by a Comprehensive Solution,” Weld. J. (Miami), 72, No. 3, pp. 107s–115s.
Moore, J. E., Bibby, M. J., Goldak, J. A., and Santyr, S., 1986, “A Comparison of the Point Source and Finite Element Schemes for Computing Weld Cooling,” Welding Research: The State of the Art, E. F. Nippes and D. J. Ball eds., ASM, Miami, pp. 1–9.
Carslaw, H. C., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd Ed., Oxford University Press, London.
Grosh,  R. J., and Trabant,  E. A., 1956, “Arc Welding Temperatures,” Weld. J. (Miami), 35, No. 8, pp. 396–401.
Myers, P. T., Uyehara, O. A., and Borman, G. L., 1967, “Fundamentals of Heat Flow in Welding,” Welding Research Council Bulletin, No. 123, pp. 1–46.
Ames, W. F., 1968, Nonlinear Ordinary Differential Equations in Transport Processes, Academic Press, New York.
Logan, J. D., 1994, An Introduction to Nonlinear Partial Differential Equations, John Wiley and Sons, New York.
Ozisik, M. N., 1980, Conduction Heat Transfer, John Wiley and Sons, New York.
Zeldovich, Ya., and Kompaneets, A. S., 1950, “On the Theory of Propagation of Heat With Temperature-Dependent Thermal Conductivity,” Izdat. Akad. Nauk SSSR, pp. 61–71.
Ames,  W. F., 1964, “Similarity for the Nonlinear Diffusion Equation,” Ind. Eng. Chem. Fundam., 4, pp. 72–76.
Boyer,  R. H., 1961, “On Some Solutions of a Nonlinear Diffusion Equation,” J. Math. Phys., 40, No. 1, pp. 41–45.
Heaslet,  M. A., and Alksne,  A., 1961, “Diffusion From a Fixed Surface With a Concentration Dependent Coefficient,” J. SIAM, 9, No. 4, pp. 584–596.
Pattle,  R. E., 1959, “Diffusion From an Instantaneous Point Source With a Concentration Dependent Coefficient,” Q. J. Mech. Appl. Math., 12, No. 4, pp. 407–409.
Radaj, D., 1992, Heat Effects of Welding, Springer-Verlag, New York.
Ion,  J. C., Easterling,  K. E., and Ashby,  M. F., 1984, “A Second Report on Diagrams of Microstructure and Hardness for Heat-Affected Zones in Welds,” Acta Metall., 32, pp. 1949–1962.
Svensson, L., 1994, Control of Microstructures and Properties in Steel Arc Welds, CRC Press, Boca Raton, FL.
Rosenthal,  D., 1941, “Mathematical Theory of Heat Distribution During Welding and Cutting,” Weld. J. (Miami), 20, No. 5, pp. 220s–234s.
Rosenthal,  D., 1946, “The Theory of Moving Sources of Heat and Its Application to Metal Treatments,” Trans. ASME, 68, pp. 849–866.
Harvey, P., 1982, Engineering Properties of Steel, ASTM, Metals Park, OH.
Goldak,  J., Chakravarti,  A., and Bibby,  M., 1984, “A New Finite Element Model for Welding Heat Sources,” Metall. Trans., 15B, No. 6, pp. 299–305.


Grahic Jump Location
Thermal conductivity of carbon steel
Grahic Jump Location
Specific heat of carbon steel




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