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The Rayleigh–Stokes problem for a heated generalized second-grade fluid with fractional derivative model. (English) Zbl 1113.76016
Summary: We investigate Rayleigh-Stokes problem for a generalized second-grade fluid flowing on a heated flat plate with heated edge. For description of such a viscoelastic fluid, we use the fractional calculus approach in the constitutive model. Exact solutions of velocity and temperature fields are obtained using Fourier sine transform and fractional Laplace transform. The well-known solutions of Stokes’ first problem for viscous Newtonian fluid and for the second-grade fluid appear as limiting cases of our results.

MSC:
76A10 Viscoelastic fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
26A33 Fractional derivatives and integrals
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