Abstract
In this paper, we solve the Brinkman equation for unidirectional, steady, incompressible and Newtonian flow through a duct of uniform cross-section in the shape of a regular N-gon under no-slip boundary condition on the surface of the duct in the absence of applied forces. We calculate solutions for small values of N and by analysing them we devise a recursive scheme of generating solutions for all . We obtain approximate expressions for the vortex lines for all values of N by applying a trigonometric perturbation on circular vortex lines and graphically compare them with exact vortex lines. We also graphically compare both exact and approximate vortex lines with Schwarz-Christoffel transformation.
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