Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface

Abstract The effect of Marangoni convection on the flow and heat transfer within a power-law liquid film on an unsteady stretching sheet is examined. The governing equations are non-dimensionalized using suitable transformation variables and the resulting transformed PDEs are then solved numerically by an implicit finite-difference scheme. Results for the velocity and temperature distributions, the free-surface temperature, and the wall temperature gradient are presented for various values of the unsteadiness parameter S , the power-law index n , the thermo-capillarity number M , and the modified Prandtl number Pr . The velocity and temperature distributions in the film are affected significantly by the thermally-induced Marangoni convection adjacent to the free surface. A fluid with a smaller Pr is more sensitive to the Marangoni effect. For Pr less than a moderate value (e.g., at selected values of n and ξ , Pr ⩽ 1 for S = 0.8 and Pr ⩽ 10 for S = 1.2 ), the Marangoni effect tends to increase the heat transfer rate; whereas this impact diminishes in the high Pr regime.

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