Laminar flow over pipes with injection and suction through the porous wall at low Reynolds number

Analytic expressions describing two-dimensional steady-state laminar flow over an array of porous pipes were developed from the solution of the Navier-Stokes equations for the case of low wall Reynolds number. For flow in the shell (the space separating the porous pipes), the stream function formulation was used to find the radial and axial velocity profiles and pressure distribution. The Navier-Stokes equations in cylindrical co-ordinates reduced to a fourth-order nonlinear differential equation, which was solved for flows through the porous wall using a zeroth- and first-order perturbation method.