Date of Award
Mathematics and Statistics
Chandna, O. P.
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The aim of this dissertation is the integration of the governing equations of motion for steady, two-dimensional potential gas flows. Although there has been an ongoing search for the solutions of these equations for over one hundred and fifty years, only a limited number of exact solutions in closed form exist prior to this thesis. The methods or processes that were employed in the past inevitably required dealing with a non-linear partial differential equation in the potential function with unmanageable boundary conditions or pre-deciding the type of gas that flows along a flow pattern. By adopting and pursuing a new approach, exact solutions in closed form are obtained in this thesis. This approach specifies a priori the form of the streamline pattern or a specific geometric pattern and determines the exact solution and the permissible gas for each chosen pattern. This approach also obtains exact solutions of the non-linear partial differential equation in the potential function even though it does not deal directly with this equation. This dissertation contains two parts. The first part treats and develops investigations when the forms for the flow patterns are considered. Following the classification of all permissible flows for the chosen forms, exact solutions for these permissible flows are determined. The second part of this thesis is concerned with specified streamline patterns defined by Re$\lbrack f(z)\rbrack$ = constant or a linear combination of Re$\lbrack f(z)\rbrack$ and Im$\lbrack f(z)\rbrack$ equal to any constant when f(z) is a known analytic function of z. This new approach involves transformations of independent variables only so that systems of ordinary differential equations and linear partial differential are dealt with. New and existing exact solutions in closed form of these equations are obtained. However, in some cases, the transformation employed yielded nonlinear ordinary differential equations for which only particular solutions were obtained. In addition, equations of state corresponding to these solutions are also determined and analyzed. The exact solutions for incompressible, inviscid and irrotational flows can also be easily obtained by this new approach.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1994 .H875. Source: Dissertation Abstracts International, Volume: 56-11, Section: B, page: 6154. Adviser: O. P. Chandna. Thesis (Ph.D.)--University of Windsor (Canada), 1994.
Husain, Iqbal., "Exact solutions of steady plane potential compressible flows: A new approach." (1994). Electronic Theses and Dissertations. 1999.