EXACT SOLUTION FOR TWO-DIMENSIONAL FLOW THROUGH CHANNELS WITH A PLANE PERMEABLE BOUNDARY BETWEEN TWO CHAMBERS WITH UNIFORM SUCTION/INJECTION
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Abstract
A one-dimensional model to determine the laminar ow of a fluid in a porous channel with wall suction or
injection is proposed. The approach is based on the integration of the Navier–Stokes equations using the
analytical solutions for the two-dimensional local velocity and pressure fields obtained from the
asymptotic developments at low filtration Reynolds number proposed by Berman [1] and Yuan and
Finkelstein [2]. It is noticeable that the resulting one-dimensional model preserves the whole ow
properties, in particular the inertial terms which can affect the wall suction conditions. The model is
validated in the case of a single porous channel of rectangular or circular cross-section with uniform or
variable wall suction. Then the model is applied to a two-dimensional multi-channel system which
consists of a great number of adjacent entrance and exit channels connected by a filter porous medium.
All existing models aren’t analytical, and need to use complex numerous calculations. The present model
is a first an attempt to reduce the problem to a simple analytical scheme based on Berman Similarity and
perturbation series solution method that allows it to be used by general engineers not using complex
mathematical methods.
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