MULTI-STEP DTM SIMULATION OF MAGNETO-PERISTALTIC FLOW OF A CONDUCTING WILLIAMSON VISCOELASTIC FLUID

Modern peristaltic MHD pumps and endoscopes frequently exploit the use of a radial magnetic field. The working fluids may be Newtonian or non-Newtonian depending on the physiological application. In this study we examine the effects of radial variable magnetic field on peristaltic transport of an electrically-conducting viscoelastic Williamson fluid in an axisymmetric channel, as a simulation of rheological biomagnetic flow in an endoscope. The multi-step differential transform method (MDTM), a powerful semi-numerical technique, is used to compute approximate solutions to the system of transformed nonlinear ordinary differential equations governing the flow. The reliability and effective performance of the MDTM is demonstrated via benchmarking of the solutions with a purely numerical method (fourth-order Runge–Kutta shooting quadrature) and also the semi-analytical differential transform method (DTM). DTM solutions diverge for some differential equations which have extremely nonlinear behaviors or boundary-conditions at infinity. This problem is circumvented with MDTM. The main advantages of MDTM are that it can be used directly for solving equations without any requiring linearization, discretization or perturbation. MDTM formulates Taylor series in a very different manner from other techniques. The MDTM computations show that a magnetic field accelerates the axial flow in the presence of a hydrodynamic pressure gradient for low Weissenberg numbers (weakly elastic biofluids). Furthermore the velocity is increased with increasing rheological effects as simulated via the Weissenberg number, for the constant magnetic field scenario, whereas the flow is accelerated for the variable magnetic field scenario. Excellent agreement is demonstrated between MDTM and numerical quadrature.

Peristaltic flow, Williamson fluid, visco-elasticity, magnetic endoscopes, Radial variable magnetic field, Multi-step differential transform method (MDTM), peristaltic magnetic pumps, Weissenberg number, gastric magneto-fluid dynamic control