This examniation is interested with the study of time-dependent magnetized free convection flowing via an infinite vertical permeable surface in the existence of viscous dissipative fluxing. The fundamental flow regulating formulas for this investigation are resolved computationally by applying the finite element methodology. The speed, temperature in addition to concentricity are determined systematically and numerically analyzed for several governing parameters through graphically. Also, Nu , Sh , and C f by the combinations of different flow pertinent parameters are demonstrated in tabular forms, as well as physical features of the problem are examined. The obtained results are compared with earlier work with some limitations. The outcomes are in good concurrence with the existing ones. The outcomes of the research may be valuable in various industrial applications.