Free surface dynamics of thin second-grade fluid over a heated stretching sheet with variable fluid properties: long-wave modeling and simulation

In this paper, we extend the long-wave theory for the free surface dynamics of the thin non-Newtonian second-grade fluid (ANZIAM J 60(2): 249–268, 2018) over the stretching sheet by the inclusion of thermo-capillarity and the variable fluid properties effect in the systematic long-wave theory framework. The two-dimensional flow of non-Newtonian fluid over a non-porous heated stretching sheet is described by the conservation of mass, momentum, and energy equations with free surface and no-slip boundary conditions. From standard long-wave theory expansion technique in terms of the small aspect ratio of the fluid layer, we derive the transient equation systematically to describe the free surface dynamics of the thin-liquid film. We apply the finite volume method with implicit flux discretization for numerical investigation of the effects of thermocapillary forces, non-Newtonian parameter, and variable fluid properties. The investigation reveals that the Newtonian fluid with variable viscosity property exhibits faster thinning in comparison to the second-grade non-Newtonian fluid concerning the prescribed temperature at the sheet and the stretching rate. Furthermore, under constant fluid properties assumptions, the derived non-Newtonian thin-film model decouples from the thermal problem and reduces to the isothermal viscous model of Santra and Dandapat (Z Angew Math Phys 60(4): 688–700, 2009).