Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T13:37:35.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Transpiration and natural convection: the vertical-flat-plate problem

Published online by Cambridge University Press:  29 March 2006

J. F. Clarke
J. F. Clarke
Affiliation:
Department of Aerodynamics, Cranfield Institute of Technology, Bedford.
Get access Rights & Permissions [Opens in a new window]

Abstract

A study is made of the natural convective flow which is induced in an infinite expanse of gas by the presence of a vertical hot flat plate from which hot gas of the same chemical type is being blown. The transpiration rate is assumed to be such that a self-similar boundary-layer type of solution is available. It differs from previous analyses in the following respects. Most important, the density is not assumed to be constant a t any stage in the description of the flow field. Also the form of the induced flow in the outer domain is calculated and proves to be substantially independent of the blowing rate in this case; the induced outer flow is found to be of large lateral extent. Finally, the variable-gas-property problem is carried to second order and solutions are obtained by using an ‘exact’ form of Howarth-Dorodnitsyn variable. The opportunity is taken t o make some comments about the comparison between theory and experiment for finite flat plates without transpiration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 1 , 23 January 1973 , pp. 45 - 61
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ede, A. J. 1967 Advances in free convection. In Advames in Heat Transfer, vol. 4 (ed. J. P. Hartnett & T. F. Irvine). Academic.
Eichhorn, R. 1960 Trans. A.S.M.E. 82, 260–263.
Merkin, J. H. 1972 Int. J. Heat Mass Transfer, 15, 989–999.
Nachtsheim, P. R. & Swigert, P. 1965 N.A.S.A. Tech Note, D-3004.
Ostrach, S. 1964 Laminar flows with body forces. In High Speed Aerodynamics and Jet Propulsion (ed. F. K. Moore), vol. 4, Theory of Laminar Plows, §F. Oxford University Press. (See also 1953 N.A.C.A. Rep. no. 1111)
Ruppert, P. E. & Landahl, M. T. 1967 Phys. Fluids, 10, 831–835.
Schmidt, E. & Beckman, W. 1930 Tech. Mech. u. Thermodynamik, 1, 341–349, 391–406.
Sparrow, E. M. & Cess, R. D. 1961 Trans. A.S.M.E. 83, 387–389.
Sparrow, E. M. & Gregg, J. L. 1958 Trans. A.S.M.E. 80, 879–886.
Yang, K.-T. & Jerger, E. W. 1964 J. Heat Transfer, 86, 107–115.