MHD Peristaltic Pumping of a Jeffrey Fluid Between Two Deformable Coaxial Tubes with Different Wavelengths

Abstract

The study of MHD peristaltic transport of a Jeffrey fluid through the gap between two deformable tubes has been investigated in this paper. The outer and the inner tubes have both sinusoidal waves travelling down their walls when the amplitudes and the wavelengths are different. The equations of motion are simplified under the assumption of long wavelengths and low Reynolds number approximations. Analytical solutions for the pressure rise and axial velocity has been obtained in the closed form. Effects of pertinent parameters on pressure gradient, pressure rise, axial velocity and mechanical efficiency have been discussed through graphs. The results show that we have two cases, the first one is [Formula: see text], i.e., the wavelength of the inner tube is smaller than that of the outer tube and the second case is the opposite one [Formula: see text]. It is found that an increase of [Formula: see text] causes a decrease of the pumping and the mechanical efficiency when [Formula: see text] while an opposite behavior for [Formula: see text] is observed. In addition and for the two cases, the pumping and the mechanical efficiency increase with increasing the amplitude ration of the outer tube or the radius ratio while they decrease with the increase in the Hartmann number, amplitude ration of the inner tube or in the ratio of relaxation to retardation times.