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The unsteady free convection and mass transfer boundary layer flow past an accelerated infinite vertical porous plate with suction by taking into account the viscous dissipation is considered when the plate accelerates in its own plane. The dimensionless momentum, energy and concentration equation are solved numerically by using explicit finite difference method with the help of a computer programming language Compaq visual FORTRAN 6.6. The obtained results of this study have been discussed for different values of well-known parameters with different time steps.