Flow of a newtonian fluid in a blood vessel with permeable wall—A theoretical model

A perturbation solution of the flow of a homogeneous Newtonian fluid through a tube of finite length with a permeable wall is analysed through a theoretical model in view of its applications in hemodynamics. The flow is characterized by three important parameters: G, the characteristic Reynolds number associated with the pressure outside the tube, β the ratio of radius to length of the tube, and ε a filtration coefficient. ε is assumed to be small so that the validity of the perturbation method is ensured. Perturbation solutions obtained up to O(ε2) are discussed.