Plane steady flows of a third grade fluid

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 of the method in certain simple flows show that the results in the third grade fluid are different from the corresponding results in the linearly viscous Newtonian fluid.