Rotationally symmetric flow of Reiner-Rivlin fluid over a heated porous wall using numerical approach

Abstract

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter $\alpha$ that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of $\alpha$ . Flow pattern for different choices of $\alpha$ is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with $\alpha >1$ , entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter $\alpha$ in the range $\alpha >1$ , whereas opposite trend is apparent in the case $0\le \alpha <1$ . Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.