  We investigate the magnetohydrodynamics in the presence of an external
magnetic field following the power-law decay in proper time and having spatial
inhomogeneity characterized by a Gaussian distribution in one of transverse
coordinates under the Bjorken expansion. The leading-order solution is obtained
in the weak-field approximation, where both energy density and fluid velocity
are modified. It is found that the spatial gradient of the magnetic field
results in transverse flow, where the flow direction depends on the decay
exponents of the magnetic field. We suggest that such a magnetic-field-induced
effect might influence anisotropic flow in heavy ion collisions.
