An approximate solution to the Navier–Stokes equations was found for the case describing two-dimensional steady-state laminar flow over an array of porous pipes with high wall Reynolds number. The Navier–Stokes equations in cylindrical coordinates reduced to a fourth-order nonlinear differential equation, which was solved for high wall Reynolds number flows through the porous wall using a zeroth- and first-order singular perturbation method. Our analytic solution for the high wall Reynolds number case is consistent with solutions found from the low Reynolds number case and that found using finite element analysis.
Flow Within a Pipe Annulus With Injection and Suction Through a Porous Wall With High Wall Reynolds Numbers
Moussy, Y., and Snider, A. D. (January 13, 2011). "Flow Within a Pipe Annulus With Injection and Suction Through a Porous Wall With High Wall Reynolds Numbers." ASME. J. Fluids Eng. January 2011; 133(1): 014501. https://doi.org/10.1115/1.4003183
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