Flow through an oscillating rectangular duct for generalized Maxwell fluid with fractional derivatives

The velocity field and the associated shear stresses corresponding to the unsteady flow of generalized Maxwell fluid on oscillating rectangular duct have been determined by means of double finite Fourier sine and Laplace transforms. These solutions are also presented as a sum of the steady-state and transient solutions. The solutions corresponding to Maxwell fluids, performing the same motion, appear as limiting cases of the solutions obtained here. In the absence of w, namely the frequency, and making α → 1, all solutions that have been determined reduce to those corresponding to the Rayleigh Stokes problem on oscillating rectangular duct for Maxwell fluids. Finally, some graphical representations confirm the above assertions.

► Velocity field and shear stresses for generalized Maxwell fluid on oscillating rectangular duct have been determined. ► Solution is obtained by double finite Fourier sine and Laplace transforms and is a sum of steady-state and transient parts. ► Solutions for Maxwell fluids, performing the same motion, appear as limiting cases of the solutions obtained here. ► Making ω→0ω→0 and α→0α→0, determined solutions →→ Rayleigh Stokes problem on oscillating rectangular duct for Maxwell fluids. ► Finally, some graphical representations confirm the above assertions.