zbMATH — the first resource for mathematics

A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. (English) Zbl 1346.76009
Summary: The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. A generalized Maxwell model with the fractional calculus was considered. Exact solutions of some unsteady flows of a viscoelastic fluid between two parallel plates are obtained by using the theory of Laplace transform and Fourier transform for fractional calculus. The flows generated by impulsively started motions of one of the plates are examined. The flows generated by periodic oscillations of one of the plates are also studied.

76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
35R11 Fractional partial differential equations
Full Text: DOI