Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T23:30:28.908Z Has data issue: false hasContentIssue false
  • English
  • Français

An Initial Value Method for the Solution of MHD Boundary-Layer Equations

Published online by Cambridge University Press:  07 June 2016

T. Y. Na
T. Y. Na*
Affiliation:
Dearborn Campus, University of Michigan
Get access

Summary

An initial value method is introduced in this paper for the solution of the two-point non-linear ordinary differential equations resulting from an analysis of the MHD boundary-layer flow originally treated by Greenspan and Carrier. By using this method, the iteration process is eliminated. The method is seen to be applicable to the solution of similar two-point boundary value problems where certain physical parameters appear either in the differential equation or in the boundary conditions and solutions for a range of the parameter are sought.

Type
Research Article
Information
Aeronautical Quarterly , Volume 21 , Issue 1 , February 1970 , pp. 91 - 99
Copyright
Copyright © Royal Aeronautical Society. 1970

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

1. Goldstein, S. Modern developments in fluid mechanics, Vol. 1, pp. 135–136. Oxford University Press, London, 1957.Google Scholar
2. Greenspan, H. P. and Carrier, G. F. The magnetohydrodynamic flow past a flat plate. Journal of Fluid Mechanics, Vol. 6, pp. 77–96, 1959.CrossRefGoogle Scholar
3. Klamkin, M. S. On the transformation of a class of boundary value problems into initial value problems for ordinary differential equations. SIAM* Review, Vol. 4, pp. 43–47, 1962.Google Scholar
4. Na, T. Y. Transforming boundary conditions to initial conditions for ordinary differential equations. SIAM* Review, Vol. 9, No. 2, pp. 204–210, 1967.Google Scholar
5. Na, T. Y. Further extension on transforming from boundary value to initial value problems. SIAM* Review, Vol. 10, pp. 85–87, 1968.Google Scholar
6. Na, T. Y. and Tang, S. C. A method for the solution of heat conduction with non-linear heat generation. Zeitschrift für Angewändte Mathematik und Mechanik, Vol. 49–1/2. pp. 45–52, 1969.CrossRefGoogle Scholar
7. Glauert, M. B. A study of the magnetohydrodynamic boundary layer on a flat plate. Journal of Fluid Mechanics, Vol. 10, pp. 276–288, 1961.Google Scholar