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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics
Review of Turbulence and Turbulence Modeling

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ME 637 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Exact Solutions to the Navier-Stokes Equation

Transform Method

An alternative is to use the transform method. Taking the Laplace transform of Equation (1), it follows that

(19)

or

(20)

The solution to (20) is
(21)

Boundary conditions (2) and (3) imply that
(22)

Thus, the solution in the transform domain is given by
(23)

Inverse Laplace transform of (23) gives
(24)



Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu