Graduate Thesis Or Dissertation
 

Flows of anisotropic fluids induced by rotating disks

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  • The simplest existing properly invariant theory for anisotropic fluids, proposed by Ericksen, includes equations governing the nature of a preferred direction. An analysis of simple shearing motion given by Ericksen suggested that this type of theory might be applicable to some fluids which are commonly treated as isotropic and might describe them more accurately than comparably simple theories of isotropic fluids. Many research workers have investigated various flow problems of anisotropic fluids in one or two dimensions, but none have considered fully three dimensional problems owing to the inherent non-linearity and other complexities. Von Karman considered the steady motion of an incompressible viscous fluid induced by an infinite rotating plane lamina and reduced the equations of motion and continuity to ordinary differential equations by certain transformations. Cochran improved upon von Karman's solution and Stuart considered the flow of a viscous fluid induced by an infinite rotating disk with uniform suction. It was observed that no work has been done to date on the problem of flows of an anisotropic fluid induced by an infinite rotating plane lamina. The present work has been undertaken with a view to open up the possibility of treating problems of anisotropic three dimensional non-linear flow and the like, which occur in many technological, biophysical, oceanographic, and atmospheric studies. The problem considered in this work is that of an anisotropic flow induced by an infinite rotating disk. The problem has been divided into two parts: (1) solution for large suction and (2) solution for arbitrary suction with the orientation primarily in one direction. For the large suction case, the velocity and orientation vector profiles have been found to be largely dependent upon the values of the rheological parameters, with the disk acting like a centrifugal fan for some values and a centripetal fan for others. For the arbitrary suction case with the orientation primarily in one direction, under suitable transformations we have been able to reduce the governing equations from partial to ordinary differential equations. Using the asymptotic matched expansion procedure, solutions of the transformed equations have been obtained and examined. The effect of variation in rheological parameters on the flow and orientation field has been discussed. Also, the influence of different values of the suction on the flow has been considered. The anisotropic character of the fluid influencing the flow has been contrasted with that of the corresponding classical viscous fluid.
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