Mathematical Modelling of Peristaltic Pumping of Nano-Fluids

Abstract

A theoretical study is presented to examine the peristaltic pumping with double-diffusive (thermal and concentration diffusion) convection in nano-fluids through a deformable channel. The model is motivated by the need to explore nano-fluid dynamic effects on peristaltic transport in biological vessels, as typified by transport of oxygen and carbon dioxide, food molecules, ions, wastes, hormones, and heat in blood flow. Approximate solutions are obtained under the restrictions of large wavelength and low Reynolds number, for nanoparticle fraction field, concentration field, temperature field, axial velocity, volume flow rate, pressure gradient, stream function, and wave amplitude. The influence of the dominant hydrodynamic parameters (Brownian motion, thermophoresis, Dufour and Soret) and Grashof numbers (thermal, concentration, and nanoparticle) on peristaltic flow patterns are discussed with the help of computational results obtained with the Mathematica software. The classical Newtonian viscous model, presented by Shapiro and others, constitutes a special case of the present model. Applications of the study include novel pharmaco-dynamic pumps, and engineered gastro-intestinal mechanisms.KeywordsBrownian motionThermophoresisDufour and Soret diffusiveGrashof numbersTrapping