Starting Darcy–Brinkman Flow in a Sector Duct Using the Method of Eigenfuction Superposition |
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Authors: | Wang C Y |
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Institution: | 1.Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA ; |
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Abstract: | The powerful method of eigenfunction superposition is applied to the starting flow in a sector duct filled with a porous medium. Using analytic eigenfunctions and eigenvalues of the Helmholtz equation, the solution can be expressed in a simple series. The properties of the velocity and the transient flow rate are found to depend on the sector geometry and a porous medium factor. The starting solution is then used to construct the solution to arbitrary unsteady flows. |
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