For incompressible Newtonian flow, the Navier–Stokes equations apply in the bulk:
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Within the porous sheath, Darcy–Brinkman formulation is used: For incompressible Newtonian flow
The objectives of this paper are:
[ \beginaligned \nabla \cdot \mathbfu &= 0,\ \rho \left( \frac\partial \mathbfu\partial t + \mathbfu\cdot\nabla\mathbfu \right) &= -\nabla p + \mu \nabla^2\mathbfu. \endaligned ] are of legal age