Exploring slip flow of viscoelastic fluid with frictional heating effects: Uncertainty analysis using response surface methodology (RSM)

Viscoelastic fluid flow along a slippery plate finds applications in different fields such as examining friction and wear characteristics of bearing surfaces using viscoelastic lubricants, extrusion, coating and moulding processes, thin film deposition among others. The present article explores boundary layer flow generated by a slippery stretching plate in a viscoelastic fluid and conducts uncertainty analysis of the governing model via response surface methodology. In addition, the analysis includes viscous dissipation mechanism that represents the conversion of mechanical energy into heat induced by viscosity. The inclusion of the wall slip condition results in a non-linear Robin-type condition for the velocity field. A dependable and user-friendly built-in package "bvp4c" of MATLAB is used to provide the computational results. The solution is used to illustrate the implication wall slip phenomenon on the resisting wall shear. One noteworthy finding is that the inclusion of either the frictional heating effect or the elasticity results in a significant decrease in the surface cooling rate. As the contribution of the heat source term grows, the rate of surface cooling decreases. Strengthening the heat sink effect reverses this result. Contour plots for stream function and isotherms are generated and compared in Newtonian and second grade fluid cases.