Analytical and Numerical Study of Magnetohydrodynamics Flow of an Elastic–Viscous Fluid in an Annulus With Porous Boundaries Having Fixed and Moving Wall Configurations

ABSTRACT The current investigation covers the flow of elastic‐viscous liquids through a cylindrical annular region in an electrically conducting, incompressible laminar flow when cross‐flow is present. The flow is subjected to a constant external magnetic field and moves through a saturated porous medium with a constant permeability. The equality of cross‐flow conditions at the two inner surfaces is crucial for flow continuity. It is simple to implement the condition by applying a remotely controlled magnetic field to equalize the impinging surface velocities. The solution illustrates the compatibility of two methodologies: the analytical methodology, that is, perturbation method, and the numerical methodology based on BVP4C. The values , , , and of the governing parameters, which could be variable based on the model chosen, are taken into consideration in the discussion. One of the important observations that came out of the study is that an increase in suction causes a reduction in the axial velocity, while an increase in injection could cause reverse flow. The results are in agreement with the previous models that have not taken magnetic effects into account. In the present model, however, due to the presence of the magnetic field, the flow does not become unstable, and there are no inflection points seen, unlike the case where the magnetic field was absent. Another important observation is that the pressure in the annular region reduces with an increase in the magnetic field.