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The unsteady magnetohydrodynamic (MHD) thermosolutal Marangoniconvection flow with heat and mass transfer over an unsteady stretching sheet isexamined. The surface tension is assumed a linear function of the temperature andconcentration. The quasilinearization method (QLM) is applied with employing themethod of complementary function and the fourth order Runge-Kutta method to theyielding ordinary nonlinear equations. The analytical solution for the steady flow, withsome special values of the problem parameters, is compared with the present numericalresults. The results show that the decreasing of the surface tension enhances the flowmovement due to decreasing the free surface rigidity. Also, the enhancement of thetemperature provokes the free surface and reduces the surface tension. This result is inagreement with the previous experimental published results. Also, the flow velocityincreases with reducing the surface tension. Meanwhile, the concentration surface tensioncoefficient reduces the concentration profiles. Finally, the numerical solution is comparedwith the previous published results for a special choice of the parameters. The graphicaland tabulated results reveals on the high fidelity of the numerical method.

Thermosolutal Marangoni Convection Effect on the MHD Flow over an Unsteady Stretching Sheet