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Start-up flows of second grade fluids in domains with one finite dimension. (English) Zbl 0866.76004
Summary: 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 solutions. A general theorem on start-up flows for second grade fluids is presented that allows us to determine unidirectional flows of second grade fluids once the corresponding solution is known within the context of the Navier-Stokes theory. In the process of obtaining solutions for the fluid of second grade, we find several new exact solutions within the context of the classical Navier-Stokes theory.
MSC:
76A05Non-Newtonian fluids
35Q35PDEs in connection with fluid mechanics