Exact solutions of Rayleigh-Stokes problem for heated generalized Maxwell fluid in a porous half-space. (English) Zbl 1151.76006
Summary: We investigate the Rayleigh-Stokes problem for generalized Maxwell fluid in porous half-space with a heated flat plate. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive model is used. By using the Fourier sine transform and the fractional Laplace transform, w obtain exact solutions for velocity and temperature. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.
MSC:
| 76A10 | Viscoelastic fluids |
| 76S05 | Flows in porous media; filtration; seepage |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
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