Exact solutions of Stokes’ first problem for heated generalized Burgers’ fluid in a porous half-space

This work is concerned with applying the fractional calculus approach to the fundamental Stokes’ first problem of a heated Burgers’ fluid in a porous half-space. Modified Darcy's law for a Burgers’ fluid with fractional model is introduced first time. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and temperature field are obtained. The solutions for a Navier–Stokes, second grade, Maxwell, Oldroyd-B or Burgers’ fluid appear as the limiting cases of the present analysis.