  We consider an initial boundary problem for the planar MHD system under the
general condition on the heat conductivity $\kappa$ that may depend on both the
density $\rho$ and the temperature $\theta$ satisfying
$\kappa(\rho,\theta)\geq\kappa_1 \theta^{q}$ for some constants $\kappa_1>0$
and $q>0.$ Firstly, the global existence of strong solution for large initial
data is obtained, and then the limit of the vanishing shear viscosity is
justified. In addition, the $L^2$ convergence rate is obtained together with
the estimation on the thickness of the boundary layer.
