Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium

This article deals with the combined effects of heat and mass transfer on the peristaltic propulsion of two-phase fluid flow through a Darcy-Brinkman-Forchheimer porous medium with compliant walls. The Sisko fluid model together with small particles is considered in the presence of extrinsic magnetic field and chemical reaction. It is well-known that different biological fluids behave like a Newtonian or non-Newtonian fluid depending upon the shear rates. The non-Newtonian fluid models are more complicated than Newtonian fluid and difficult to express using the single constitutive relationship between stress and strain rate. These constitutive equations provide a complex mathematical formulation and become numerous challenges to find numerical and analytical solutions. Small magnetic particles are helpful to manipulate and control the two-phase flow by magnetic force. Moreover, it is also beneficial in drug targeting for the treatment of different diseases. Further, two-phase flow plays an important role to examine the muscular expansion and contraction during the propagation of various biological fluids. An appropriate approximation is considered such as long wavelength and creeping flow regime to model the governing equations. Analytical solutions are obtained using the perturbation method. Moreover, numerical computations are performed to determine the features of peristaltic pumping. The results of different rheological properties for particle and fluid phase are discussed mathematically as well as graphically for different sundry parameters. The current analysis has an extensive amount of applications in medical engineering and also significant importance of smart fluid pumping systems in various engineering processes.