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Free convection at low Prandtl numbers

Published online by Cambridge University Press:  29 March 2006

H. K. Kuiken
Affiliation:
Technological University of Delft, Department of Mathematics Present address: University of British Columbia, Department of Mechanical Engineering, Vancouver.

Abstract

In this paper it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero. The method of matched asymptotic expansions is used to integrate the equations for this extreme case. An expression is derived for the Nusselt—Grashof relation and the results are compared with those of previous investigations which attack the problem in a different way.

Type
Research Article
Copyright
© 1969 Cambridge University Press

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References

Braun, W. H. & Heighway, J. E. 1960 NASA TN-292.Google Scholar
Eckert, E. R. G. 1950 Introduction to the Transfer of Heat and Mass. New York: McGraw-Hill.Google Scholar
Finston, M. 1956 ZAMP, 7, 527.Google Scholar
Kuiken, H. K. 1967 Perturbation techniques in free convection. Doctoral Thesis, Techn. Univ. Delft.Google Scholar
Kuiken, H. K. 1968 J. Eng. Math. 2, 95.Google Scholar
Lefevre, E. J. 1956 Ninth Intern. Congr. Appl. Mech. Paper I 168.Google Scholar
Lykoudis, P. S. 1962 Int. J. Heat Mass Transf. 5, 23.Google Scholar
Moese, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.Google Scholar
Ostrach, S. 1953 NACA Rep. 1111.Google Scholar
Slater, L. J. 1960 Confluent Hypergeometric Functions. Cambridge University Press.Google Scholar
Sparrow, E. M. & Gregg, J. L. 1958a NASA Memo, 2-27-59E.Google Scholar
Sparrow, E. M. & Gregg, J. L. 1958b Trans. ASMS, 80, 379.Google Scholar
Van Dyke, M. 1962 J. Fluid Mech. 14, 161.Google Scholar
Van Dyke, M. 1964 Pertubation Techniques in Fluid Mechanics. New York: Academic.Google Scholar
Yang, K. T. 1960 J. Appl. Mech. 28, 230.Google Scholar