START-UP FLOWS OF 2ND GRADE FLUIDS IN DOMAINS WITH ONE FINITE DIMENSION

A number of unidirectional transient flows of a second grade fluid in a domain with one finite dimension are studied. The method of integral transforms (Fourier, Hankel or Laplace) is applied to obtain exact so lutions. A general theorem on start-up flows for second grade fluids i s presented that allows us to determine unidirectional flows of second grade fluids once the corresponding solution is known within the cont ext of the Navier-Stokes theory. In the process of obtaining solutions for the fluid of second grade, we find several new exact solutions wi thin the context of the classical Navier-Stokes theory.