Masters Theses


"An analysis is made of laminar magnetohydrodynamic (MHD) flow development in the entrance region of a parallel-plate channel. The problem is formulated in general for any velocity distribution at the channel inlet by extending the linearization method of Sparrow, Lin, and Lundgren for non-MHD duct flows. This method involves linearization of the inertia terms in the equation of motion by introducing a stretched axial coordinate. A closed form solution is obtained for the velocity distributions which are continuous across the channel and along the length all the way from the entrance to the fully developed region. An expression for the pressure drop is also developed. The general solutions are then specialized for two classes of non-uniform inlet velocity profile; linear and parabolic. Numerical results are obtained for the velocity distributions, pressure drop, and entrance lengths. In general, it is found that the effect of increasing the Hartmann number is to (1) flatten the velocity profile, (2) increase the pressure drop and (3) shorten the entrance length. A comparison is made of the present results with those reported by other investigators using different methods of solution. Excellent agreement between the two is obtained. This supports the validity of the present analysis for MHD flows in the entrance region of a parallel-plate channel. In addition, owing to the novel feature of the solution, it is felt that the present method of analysis is superior to previous methods of analysis"--Abstract, pages ii-iii.


Chen, T. S.

Committee Member(s)

Crosbie, A. L. (Alfred L.)
Pagano, Sylvester J., 1924-2006


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


University of Missouri--Rolla

Publication Date



x, 67 pages

Note about bibliography

Includes bibliographical references (page 38).


© 1970 Gwok-Liang Chen, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Channels (Hydraulic engineering)
Laminar flow -- Mathematical models

Thesis Number

T 2467

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