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Rapid calculations for boundary-layer transfer using wedge solutions and asymptotic expansions

Published online by Cambridge University Press:  28 March 2006

H. J. Merk
H. J. Merk
Affiliation:
Koninklijke/Shell-Laboratorium, Amsterdam, Holland
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Abstract

Exact transfer calculations for boundary layers with longitudinal pressure gradients are very complicated, but in the literature several approximate methods are known for the rapid calculation of both the wall friction and the heat transfer. A ‘wedge method’ propounded by Meksyn turns out to be one of the most rapid methods, being no less accurate than other approximate methods. A way of refining this method is proposed.

This paper also shows that asymptotic expansions provide convenient relations which are capable of expressing the Nusselt number explicitly in terms of the Prandtl number.

It is shown that, together with the asymptotic expansions, Meksyn's method permits rapid calculation of local heat transfer numbers. Some examples of application are given for elliptical cylinders and spheres for several values of the Prandtl number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 3 , April 1959 , pp. 460 - 480
Copyright
© 1959 Cambridge University Press

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References

Blasius, H. 1908 Z. Math. Phys. 56, 1; also Nat. Adv. Comm. Aero., Wash., Tech. Mem. no. 1256.
Boussinesq, J. 1903 Théorie Analytique de la Chaleur, vol. ii. Paris: Gauthier-Villars.
Boussinesq, J. 1905 J. Math. Pures Appl. 1, 285.
Brown, W. B. & Donoughe, P. L. 1951 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 2479.
Cohen, C. B. & Reshotko, E. 1955 Nat. Adv. Comm. Aero., Wash., Tech. Note, no. 3326.
Davies, D. B. & Bourne, D. E. 1956 Quart. J. Mech. Appl. Math. 9, 457.
Doetsch, G. 1943 Theorie und Anwendung der Laplace-Transformation. New York: Dover.
Drew, T. B. 1931 Trans. Amer. Inst. Chem. Engrs, 26, 6.
Eckert, E. 1942 V.D.I.-Forschungsheft 416.
Eckert, E. & Livingood, J. N. B. 1953 Nat. Adv. Comm. Aero., Wash., Rep. no. 1118.
Falkner, V. M. & Skan, S. W. 1930 Aero. Res. Coun. Lond., Rep. & Mem. no. 1314: also Phil. Mag. (7), 12, 865 (1931).
Frössling, N. 1938 Beitr. Geophys. 52, 170.
Frössling, N. 1940 Lunds Univ. Arsskr., N. F. Avd. 2, 36, no. 4.
Görtler, H. 1939 Z. angew. Math. Mech. 19, 129.
Görtler, H. 1957 J. Math. Mech. 6, 1.
Hartree, D. R. 1937 Proc. Camb. Phil. Soc. 33, 223.
Hiemenz, K. 1911 Dissertation, Göttingen; also Dinglers Polytech. J. 326, 32 (1911).
Kármán, Th. von 1921 Z. angew. Math. Mech. 1, 233; also Nat. Adv. Comm. Aero., Wash., Tech. Mem. no. 1092.
Kotschin, N. J., Kiebel, I. A. & Rose, N. W. 1955 Theoretische Hydromechanik II, Akad. Verlag, Berlin, p. 399.
Lighthill, M. J. 1950 Proc. Roy. Soc. A, 202, 359.
Mangler, W. 1948 Z. angew. Math. Mech. 28, 97.
Meksyn, D. 1947 Proc. Roy. Soc. A, 192, 545, 567.
Meksyn, D. 1948 Proc. Roy. Soc. A, 194, 218.
Meksyn, D. 1950 Proc. Roy. Soc. A, 201, 268, 279.
Meksyn, D. 1955 Proc. Roy. Soc. A, 231, 274.
Meksyn, D. 1956 Proc. Roy. Soc. A, 237, 543.
Morgan, G. W. & Warner, W. H. 1956 J. Aero. Sci. 23, 937.
Piercy, N. A. V. & Preston, J. H. 1936 Phil. Mag. 21, 995.
Pohlhausen, E. 1921 Z. angew. Math. Mech. 1, 115.
Pohlhausen, K. 1921 Z. angew. Math. Mech. 1, 252.
Prandtl, L. 1904 Proc. 3rd Int. Math. Congr., Heidelberg, p. 484.
Prandtl, L. 1938 Z. angew. Math. Mech. 18, 77; also Nat. Adv. Comm. Aero., Wash., Tech. Mem. no. 959.
Schmidt, E. & Wenner, K. 1941 Forsch. Ing.-Wes. 12, 65.
Schuh, H. 1949 Temperaturgrenzschichten. Göttinger Monographien, B, 6.Google Scholar
Schuh, H. 1954 Forsch. Ing.-Wes. 20, 37.
Smith, A. M. O. 1956 J. Aero. Sci. 23, 901.
Sparrow, E. M. & Gregg, J. L. 1957 J. Aero. Sci. 24, 852.
Stewartson, K. 1950 Proc. Roy. Soc. A, 200, 84.
Tifford, A. N. 1951 J. Aero. Sci. 18, 283.
Töpfer, C. 1912 Z. Math. Phys. 60, 397.