  We argue that the existence of an inhomogeneous external magnetic field can
lead to radial flow in transverse plane. Our aim is to show how the
introduction of a magnetic field generalizes the Bjorken flow. We investigate
the effect of an inhomogeneous weak external magnetic field on the transverse
expansion of in-viscid fluid created in high energy nuclear collisions. In
order to simplify our calculation and compare with Gubser model, we consider
the fluid under investigation to be produced in central collisions, at small
impact parameter; azimuthal symmetry has been considered. In our model, we
assume an inhomogeneous external magnetic field following the power-law decay
in proper time and having radial inhomogeneity perpendicular to the radial
velocity of the in-viscid fluid in the transverse plane; then the space time
evolution of the transverse expansion of the fluid is obtained. We also show
how the existence of an inhomogeneous external magnetic field modifies the
energy density. Finally we use the solutions for the transverse velocity and
energy density in the presence of a weak magnetic field, to estimate the
transverse momentum spectrum of protons and pions emerging from the
Magneto-hydrodynamic solutions.
