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A mathematical model of time-dependent thin-film flow of Carreau liquid over a stretching surface is studied in this investigation in the presence of couple stress and uniform magnetic field. To explain the properties of heat and mass transport phenomena, the influence of both thermophoresis and Brownian motion variables is used. For the conversion of the model framework (momentum, heat, and concentration expression with boundary conditions) into a set of ordinary differential equations, the appropriate transformation technique is followed. By using analytical tool, HomotopyAnalysis Method (HAM), the transformed model expressions are solved. For different estimations of the affected physical factors, the numerical results involving skin-friction coefficient, Nusselt number, Sherwood number, fluid velocity profile, thermal profile, and concentration profile are displayed graphically. Besides, the findings for skin-friction coefficient,  Nu x , and  ϕ η are given in the table format. In raising the fluid temperature, the effect of thermophoresis and magnetic parameters is beneficial. With the Brownian motion and Schmidt number, the solute concentration is found to reduce.

Magnetohydrodynamic Impact on Carreau Thin Film Couple Stress Nanofluid Flow over an Unsteady Stretching Sheet