Mathematica simulation of peristaltic pumping with double-diffusive convection in nanofluids: a bio-nano-engineering model

A theoretical study is presented to examine the peristaltic pumping with double-diffusive (thermal and concentration diffusive) convection in nanofluids through a deformable channel. The model is motivated by the need to explore nanofluid 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. Analytical approximate solutions are obtained under the restrictions of large wavelength (a << lambda -> infinity ) and low Reynolds number (Re -> 0), for nanoparticle fraction field, concentration field, temperature field, axial velocity, volume flow rate, pressure gradient and stream function in terms of axial and transverse coordinates, transverse vibration of the wall, amplitude of the wave and averaged flow rate. The influence of the dominant hydrodynamic parameters (Brownian motion, thermophoresis, Dufour and Soret) and Grashof numbers (thermal, concentration, nanoparticle) on peristaltic flow patterns with double-diffusive convection are discussed with the help of computational results obtained with the Mathematica software. The classical Newtonian viscous model constitutes a special case (Gr(T) = 0, Gr(C) = 0, Gr(F) = 0) of the present model. Applications of the study include novel pharmacodynamic pumps and engineered gastro-intestinal motility enhancement.