Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

[+] Author and Article Information
B. S. Berger

Department of Mechanical Engineering, University of Maryland, College Park, Md. 20742

B. Alabi

Department of Mechanical Engineering, Imperial College, London, England

J. Appl. Mech 45(4), 812-816 (Dec 01, 1978) (5 pages) doi:10.1115/1.3424424 History: Received November 01, 1977; Revised April 01, 1978; Online July 12, 2010


A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3 , is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

Copyright © 1978 by ASME
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