An unsteady, two-dimensional, hydromagnetic, laminar mixed convective boundary layer flow of an incompressible and electrically-conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer are discussed. The results show that increased cooling (Gr>0) of the plate and the Eckert number leads to a rise in the velocity profile. Also, an increase in Eckert number leads to an increase in the temperature. Effects of S c on velocity and concentration are discussed and shown graphically.