Three-Dimensional Darcy-Brinkman Flow in Sinusoidal Bumpy Tubes

The verified Darcy-Brinkman model and boundary perturbation method are used to study the Brinkman flow in a tube with a bumpy surface, assuming the amplitude of the bumps is small compared to the mean tube radius. This study is important to understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels. The mean rate flow is found, up to second-order correction, as a function of circumferential and longitudinal wave numbers and the permeability parameter of the porous medium. Numerical results displaying the velocity components and bumpiness functions are obtained for various values of the physical parameters of the problem. The results are tabulated and represented graphically for various physical parameters. It is found that, for every permeability parameter and for given bump area, there exists a circumferential wave number, for which the flow resistance is minimized. The limiting cases of Stokes and Darcy's flows of the bumpiness function are discussed and compared with the available results in the literature.