Peristaltic flow of a fractional second grade fluid through a cylindrical tube

Abstract

The investigation is to explore the transportation of a viscoelastic fluid with fractional second grade model by peristalsis through a cylindrical tube under the assumptions of long wavelength and low Reynolds number. Analytical solution of problem is obtained by using Caputo's definition. It is assumed that the cross-section of the tube varies sinusoidally along the length of tube. The effects of fractional parameter, material constant and amplitude on the pressure and friction forceacross one wavelength are discussed numerically with the help of illustrations. It is found that pressure decreases with increase in fractional parameter whereas increases with increase in magnitude of material constant or time. The pressure for the flow of second grade fluid is more than that for the flow of Newtonian fluid.