This study addresses the transient heat and mass transfer problem by laminar flow of a Newtonian, viscous electrically conducting, and heat generating/absorbing fluid on a continuously moving permeable surface. It was carried out with the well-known network simulation method. The effect of the parameters involved in the process were analyzed, so the influence of the parameters is represented graphically for several cases. The dimensionless parameters used in this study are: chemical reaction parameter, Prandtl number, Grashof number, absorption coefficient or heat generation, Schmidt number, and Hartmann number. The results presented are important because of the relevance of the conclusions for the steady and transient cases. In the study, the flow was considered laminar and two-dimensional. In addition, the transverse magnetic field is uniform and viscous dissipation effects, Hall effect, and Joule heating are omitted.