  Non-central heavy-ion collisions generate the strongest magnetic field of the
order of $10^{18}-10^{19}$ Gauss due to the electric current produced by the
positively charged spectators that travel at nearly the speed of light. Such
transient electromagnetic fields may induce various novel effects in the
hydrodynamic description of the quark gluon plasma for non-central heavy-ion
collisions. We investigate the longitudinal acceleration effects on the 1+1
dimensional relativistic magnetohydrodynamics with transverse magnetic fields.
We analyze the proper time evolution of the system energy density. We find that
the longitudinal acceleration parameter $\lambda^*$, magnetic field decay
parameter $a$, equation of state $\kappa$, and initial magnetization $\sigma_0$
have nontrivial effects on the evolutions of the system energy density and
temperature.
