Computational analysis of gravity driven flow of a variable viscosity viscoelastic fluid down an inclined plane

• We investigate gravity driven flow of a viscoelastic liquid down an inclined plane.
• We assume unsteady, non-isothermal flow with convective cooling at the free surface.
• Semi-implicit finite difference schemes are implemented for the solution process.
• Parameters influence on the flow quantities is demonstrates in detail.
• Non-Newtonian effects on the flow quantities are also demonstrated and discussed.

We investigate the unsteady non-isothermal gravity driven flow of a variable viscosity viscoelastic liquid along an inclined plane with convective cooling at the free surface. It is assumed that the convective heat exchange with the ambient at the free surface follows Newton’s law of cooling and that the viscoelastic fluid behaves according to the generalized Oldroyd-B model with the necessary adjustments for thermodynamics. The unsteady and coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed quantitatively and qualitatively with respect to various parameters embedded in the problem. In particular, the effects of shear-rate dependent viscosity and viscoelasticity are explored in depth as they represent the main findings of our investigation and indeed represent the novel contributions of our investigation under the non-isothermal framework.