Date of Award


Degree Type


Degree Name



Mathematics and Statistics






This dissertation deals with various flow problems in graded (ordered) Non-Newtonian fluids. (1) Solutions for the equations of motion of an incompressible second-grade fluid are obtained by hodograph-transformation method. By introducing a suitable-Legendre-transform function the basic equations are recast in terms of this function, and the conditions which this function should satisfy are stated. Several illustrations of the method are considered and the results for streamlines, velocities and pressure distribution are compared with the corresponding results for viscous fluid. (2) Inverse solutions of the equations of motion of an incompressible second grade fluid are obtained by assuming certain forms for the stream functions a priori. The equations considered are in plane polar coordinates, axisymmetric polar coordinates and in axisymmetric spherical polar coordinates. Expressions for streamlines, velocity components and pressure distributions are given explicitly, in each case, and compared with the corresponding results of the viscous fluid. (3) A method for studying plane steady flows of a thermodynamically compatible third grade fluid is discussed. Using differential geometry, the equations are recast into a new curvilinear coordinate system and the partial differential equations for the coefficients E, F, and G of the first fundamental form of the metric are derived. By placing restrictions on the coefficients, a priori, flows are determined which have such a property. Some further illustrations are given in detail which reflect the use of the method.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1986 .S533. Source: Dissertation Abstracts International, Volume: 47-09, Section: B, page: 3805. Thesis (Ph.D.)--University of Windsor (Canada), 1986.