Peristaltically induced motion of a MHD third grade fluid in a deformable tube

We consider incompressible, magnetohydrodynamic (MHD) third grade fluid confined in a circular cylindrical tube. The tube surfaces are electrically non-conducting. Travelling sinusoidal wave is imposed on the tube which induces peristaltic motion in the fluid. The stream function, axial velocity and pressure gradient are determined analytically for small Deborah number (Γ). The analysis consists of a perturbation expansion in terms of the Deborah number up to O(Γ). Solutions for pressure rise and frictional force per wavelength are given through the use of numerical integration. The general solution of highly non-linear equation for the hydrodynamic third grade fluid is developed. The results are finally compared with the third grade hydrodynamic and Newtonian fluid cases. It is found that the axial velocity increases by increasing Deborah number but decreases for large values of Hartmann number.