We consider steady free convective heat transfer boundary layer  flow over a vertical plate embedded in a fluid insulated magnetic  field medium assuming variable thermal conductivity for the case  of variable surface temperature. The governing non-linear partial differential equations have been reduced to the coupled non-linear ordinary differential equations by suitable similarity transformations. The resulting system of equations is solved numerically by using sixth order Runge-Kutta shooting method as well as Mathematica. The solutions are found to be dependent on the governing parameters including the magnetic field parameter  the Prandtl number  Pr and the thermal conductivity parameter  Effects of these parameters on the flow fields such as velocity and temperature fields are examined. Expressions for the dimensionless heat flux parameters are taken into account and analyzed for different values of the governing parameters such as M, Pr and  and the results are presented graphically. All the solutions are valid only for insulated case  It is observed that the velocity profile increases with the increasing values of Mand  whereas it decreases with the increasing values of Pr. However, the temperature profile shows a significant decrease with the increasing values of  and Pr.

boundary layer, heat transfer, magnetic natural convection, variable thermal conductivity.