A novel formulation and analysis for heat transfer in von Kármán flow involving viscoelastic fluid: OHAM solutions

Abstract

This research concentrates on the von Karman flow of viscoelastic fluid obeying second grade model over a heated permeable disk. Our interest is to explore how fluid motion triggered around the disk is affected by the existence of both elasticity and viscous dissipation effects. It is found that the problem exhibits self-similar solution only when a prescribed wall temperature distribution is considered. Series solutions are worked out by using an easy to implement yet reliable routine BVPh 2.0 of MATHEMATICA based on the homotopy analysis method. The total squared residual of the system is evaluated which illustrates that the approximate solution accurately matches the exact solution at sufficiently higher order of approximation. The influence of parameters on the disk pumping efficiency and resisting torque is also deliberated. Graphical results reveal a marked formation of momentum/thermal boundary layer provided that the viscoelastic fluid parameter is sufficiently large. An important outcome is that the elastic effects of fluid tend to reduce the torque required to main disk rotation. Moreover, flow behavior near the disk is substantially altered by wall suction effect. Entrained flow is predicted to accelerate whenever elastic effects are present.