Impact of magnetic field on the pulsatile flow through cylindrical conduit

Abstract

This work investigates the effect of magnetic field, on the stress coefficient and the vorticity of a pulsatile
flow, electrically conducting in a cylindrical conduit. The imposed magnetic field is supposed to be uniform
and constant. An exact solution of the equations governing pulsatile MHD flow in a conduit has been
obtained in the form of Bessel functions. The analytical study has been used to establish an expression
between the Hartmann number and the stress coefficient and the vorticity variation. The numerical method
is based on an implicit finite difference scheme using the Thomas algorithm and Gauss Seidel iterative
method. The velocity distributions, as well as the stress coefficient and the vorticity were obtained both with
and without a magnetic field. The results show that the amplitude of the vorticity increases as the Hartmann
number increase. The effect of the magnetic field is significant only from Hartmann number M=5.The stress
coefficient increases with the Hartmann number due to a dephasing compared to the imposed flow which
increases considerably starting from Hartmann number M=10 to reach a value around 45°C.