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We consider an initial boundary problem for the planar MHD system under thegeneral condition on the heat conductivity $\kappa$ that may depend on both thedensity $\rho$ 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 initialdata is obtained, and then the limit of the vanishing shear viscosity isjustified. In addition, the $L^2$ convergence rate is obtained together withthe estimation on the thickness of the boundary layer.

Vanishing Shear Viscosity Limit and Boundary Layer Study on the Planar MHD system