DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media: A Digestive Transport Model

Abstract

A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive (intestinal) transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the digestive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is employed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method (DTM), a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional (rheological material) parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.