Magnetohydrodynamic transient flow in a circular cylinder

A transient flow problem of unidirectional electrically conducting fluid flow in a circular cylinder in the presence of the normal magnetic field has examined. The governing equation of fluid flow has presented by using Brinkman model and solved by separation of variables technique. The analytical solution of modelled equation is found in the form of Bessel and modified Bessel functions. Moreover, the influence of relevant parameters on the velocity of fluid is also analyzed by the graphical and tabular illustrations. The inertial and pressure forces enhance the velocity, while viscosity reduces it. In strong Magnetic field, the solution reduces to steady for shorter time scale and the steady solution can be obtained as limiting case of the solution, but the reverse nature of velocity has been obtained with Reynolds number. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.