The unsteady magnetohydrodynamic (MHD) thermosolutal Marangoni
convection flow with heat and mass transfer over an unsteady stretching sheet is
examined. The surface tension is assumed a linear function of the temperature and
concentration. The quasilinearization method (QLM) is applied with employing the
method of complementary function and the fourth order Runge-Kutta method to the
yielding ordinary nonlinear equations. The analytical solution for the steady flow, with
some special values of the problem parameters, is compared with the present numerical
results. The results show that the decreasing of the surface tension enhances the flow
movement due to decreasing the free surface rigidity. Also, the enhancement of the
temperature provokes the free surface and reduces the surface tension. This result is in
agreement with the previous experimental published results. Also, the flow velocity
increases with reducing the surface tension. Meanwhile, the concentration surface tension
coefficient reduces the concentration profiles. Finally, the numerical solution is compared
with the previous published results for a special choice of the parameters. The graphical
and tabulated results reveals on the high fidelity of the numerical method.