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In order to the great importance of thermal instability in nature, industrial applications, chemical processes as well as in geophysical and astrophysical engineering, the numerical solution for unsteady heat transfer of viscous compressible boundary layer fluid flow, along a porous plate with the induced magnetic field, has been studied when the system rotation being zero. The governing non-linear coupled partial differential equations have been transformed by using usual transformations. The obtained non-linear dimensionless coupled partial differential equations have been solved numerically. The explicit finite difference method is used, as solution technique and MATLAB R2015 software is used for simulation. The obtained results for the density, velocity, induced magnetic field as well as temperature distributions are shown graphically.