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Transient free convection flow due to the arbitrary motion of a vertical plate

Published online by Cambridge University Press:  24 October 2008

P. C. Sinha  and
Punyatma Singh
P. C. Sinha
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, India
Punyatma Singh
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, India
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Extract

The paper deals with the free convection flow along a vertical plate moving arbitrarily in its own plane. The basic equations of the boundary-layer flow and heat transfer are linearized and the first two approximations are considered. The first approximation is the case of steady-state free convection flow while the second approximation is the response of the fluid velocity and temperature fields to the motion of the plate for which limiting solutions are obtained by the Laplace transform technique in two regions; namely, for large times and for small times. The particular case when the plate is given an impulsive start at t = 0 is investigated in detail. It is shown how the skin friction and the rate of heat transfer at the plate respond to the motion of the plate.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 677 - 688
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Eshghy, S., Abpaci, V. S. and Clark, J. A.J. Appl. Mech., Trans. Amer. Soc. Mech. Eng., Ser. E, 32 (1965), 183.CrossRefGoogle Scholar
(2)Fettis, H. E.Proc. Fourth Midw. Conf. Fluid Mech. (Purdue University, 1956).Google Scholar
(3)Foote, J. R.Z. Angew. Math. Phys. 9 (1958), 64.CrossRefGoogle Scholar
(4)Goldstein, R. J. and Briggs, D. G.J. Heat Transfer, Trans. Amer. Soc. Mech. Eng., Ser. C, 86 (1964), 296.Google Scholar
(5)Illingworth, C. R.Proc. Cambridge Philos. Soc. 46 (1950), 603.CrossRefGoogle Scholar
(6)Jakob, M.Heat transfer, p. 499 (John Wiley and Sons, Inc. 1949).Google Scholar
(7)Kelleher, M. D. and Yang, K. T.Z. Angew. Math. Phys. 19 (1968), 31.CrossRefGoogle Scholar
(8)Lighthill, M. J.Proc. Boy. Soc. Ser. A, 224 (1954), 1.Google Scholar
(9)Menold, E. R. and Yang, K. T.J. Appl. Mech. Trans. Amer. Soc. Mech. Eng., Ser. E, 29 (1962), 124.CrossRefGoogle Scholar
(10)Nanda, R. S. and Sharma, V. P.J. Phys. Soc. Japan, 17, 10 (1962), 1651.CrossRefGoogle Scholar
(11)Nanda, R. S. and Sharma, V. P.J. Fluid Mech. 15 (1963), 419.CrossRefGoogle Scholar
(12)Pohlhausen, E.Z. Angew. Math. Mech. 1 (1921), 115.CrossRefGoogle Scholar
(13)Rao, A. K.Appl. Sci. Res. Sec. A, 10 (1961), 141.CrossRefGoogle Scholar
(14)Siegel, R.J. Heat Transfer, Trans. Amer. Soc. Mech. Eng., Ser. C, 80 (1958), 347.Google Scholar
(15)Schetz, J. A. and Eichhorn, R.J. Heat Transfer, Trans. Amer. Soc. Mech. Eng., Ser. C, 84 (1962), 334.CrossRefGoogle Scholar
(16)Sugawara, S. and Michiyoshi, I.Proc. of First Japan Nat. Cong. Appl. Mech. (1952), 501.Google Scholar