The Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative model

Abstract

The Rayleigh–Stokes problem for a generalized second grade fluid subject to a flow on a heated flat plate and within a heated edge was investigated. For description of such a viscoelastic fluid, fractional calculus approach in the constitutive relationship model was used. Exact solutions of the velocity and temperature fields were obtained using the Fourier sine transform and the fractional Laplace transform. The well-known solutions of the Stokes’ first problem for a viscous Newtonian fluid, as well as those corresponding to a second grade fluid, appear in limiting cases of our results.