Effects of Heat Transfer and an Endoscope on Peristaltic Flow of a Fractional Maxwell Fluid in a Vertical Tube

We investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Maxwell model through two coaxial vertical tubes. This analysis has been carried under low Reynolds number and long wavelength approximations. Analytical solution of the problem is obtained by using a fractional calculus approach. The effects of Grashof number, heat parameter, relaxation time, fractional time derivative parameter, amplitude ratio, and the radius ratio on the pressure gradient, pressure rise, and the friction forces on the inner and outer tubes are graphically presented and discussed.