This study describes a numerical solution of an unsteady magnetohydrodynamic flow of a Maxwell fluid on an elongating surface in the existence of radiation, higher-order chemical, Dufour and Soret effects. The heat source/sink is also taken into consideration. The governing boundary layer equations are transformed into a system of non-linear ordinary differential equations by means of similarity transformation. The consequential equations are cracked numerically by R-K-based shooting technique. The effects of various important parameters on the flow quantities are studied through graphs. A numerical study of the skin friction, rate of heat transfer, and rate of mass transfer is also a part of this investigation. We observe that the effect of the magnetic field and the permeability parameter is to decrease the velocity field, skin friction coefficient, heat transfer rate, and mass transfer rate. However, the temperature and concentration fields increase with growing values of the space-dependent heat source/sink parameter and the Soret number. © 2020 by Begell House,.