Transformations, properties, and exact solutions of nonstationary axisymmetric boundary-layer equations

A nonstationary axisymmetric boundary-layer equation with a pressure gradient, which is written for the stream function, has been studied. It has been shown that this equation can be reduced to a twodimensional boundary-layer equation with variable viscosity that depends on a longitudinal coordinate. A series of new exact generalized and functional separable solutions that admit representation in elementary functions has been described. All of the solutions contain several (two to five) arbitrary functions. Formulas have been given that make it possible to generalize exact solutions to nonstationary axisymmetric boundarylayer equations by introducing additional arbitrary functions. The results are valid for any shape of a body of revolution (or a circular tube with a variable section) in a fluid flow.