COUPLED FLOW IN POROUS-MATERIAL LINED PIPES

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Abstract
The slow motion of a fluid is studied in a duct of circular constant cross-section, whose internal wall is covered by a porous material permeable to the fluid, with an eye to the inlet phenomenon produced by arbitrary initial conditions at a given station. The coupled problem concerning the simultaneous Stokes flow in the central free region and Darcy flow in the porous layer is given an analytical solution based on a suitable eigenfunction expansion. The method is based on Van Kampen’s technique, which yields the coefficients of the expansion of arbitrary initial conditions in the eigenfunctions of a general, non-self-adjoint ordinary differential equation problem one at a time, with no need to invert systems of linear equations numerically. We have applied this approach to some examples, for this purpose developing suitable numerical procedures to evaluate the special functions we needed.

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