Magnetic-induced effects on the fluid flow through a porous tube

In this paper, we will study the steady-state laminar flow of an electrically conducting fluid under the influence of a magnetic field through a tube with permeable walls. The fluid flow is described by a nonlinear system given by the Navier–Stokes equations taking into account magnetic-induced effects. The main goal is to investigate the effects of the porosity of the tube and the magnetic field on the fluid flow. Using asymptotic analysis with respect to the small parameter representing the ratio between the tube’s thickness and its length, we construct an explicit first-order approximation for the axial and radial velocity of the fluid. The first-order asymptotic approximation takes into account the porosity of the tube as well as the effects of the magnetic field on the fluid flow through the presence of the corresponding nondimensional parameters, and we illustrate this by providing numerical examples.