Flow and Heat Transfer of Non-Newtonian Maxwell Fluid over a Stretchable Rotating Disk

Abstract

The rheology of complex fluids involving diverse non-Newtonian fluids has motivated investigations in this area. This is due to the fact that in industrial applications, complex fluids have become more and more important. On the other hand, swirling and/or rotating flows have fascinated researchers for centuries owing to their great technical and scientific importance. The research presented in this thesis is concerned with the swirling flows of a complex fluid. Particularly, in this work the governing equations of Maxwell fluid have been developed and explored numerically for a specific number of configurations. The aim of this thesis is to develop and investigate the swirling flows for convective heat transport involving Maxwell fluids. The swirling and/or rotating systems are extensively used to model the flow and heat transfer associated with the internal-air systems of gas turbines, where disks rotate close to a rotating or a stationary surface. Further, these systems are used in chemical reactors, rotating-disk cleaners, transport engineering (automobile brakes), electro-chemistry (rotating-disk electrodes), etc. In view of such practical importance of these flows, in this thesis, we have focused on studying the numerical solutions of such flow problems arising in three different configurations of the rotating disk systems, viz. (i) flow over single stretchable rotating disk (under the influence of partial slip), (ii) thin film flow over a stretchable rotating disk, and (iii) flow between two stretchable rotating disks. These mentioned configurations have been investigated numerically for both steady and unsteady swirling flows along with heat transport phenomenon for Maxwell fluid model characterizing the relaxation time features. As the governing equations corresponding to these flows are highly nonlinear, and fully coupled which offer a significant level of complexity to get closed form analytic solutions. Thus, the popular and promising numerical techniques namely, Runge-Kutta Fehlberg (RK45), midrich scheme, and collation method bvp4c are adopted to acquire the numerical solutions of the considered problems. xv In our study the behavior of the several influential parameters is studied by examining the velocity, temperature and concentration fields for a number of swirling flows of Maxwell fluid. Our study demonstrates that the impact of centrifugal force is perceived strongly in the vicinity of disk. It is noted that with boosting the disk rotation which in turn increase the radial and azimuthal velocity components result in a decrease in the axial velocity component. Moreover, the momentum boundary layer develops thinner by amplifying the Deborah number. Further, the rotation parameter plays a significant role in enhancing the fluid film thickness.