MHD peristaltic flow of non-Newtonian power-law nanofluid through a non-Darcy porous medium inside a non-uniform incline
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O R I G I NA L
Nabil T. M. El-Dabe · Mohamed Y. Abou-Zeid · Mona A. A. Mohamed · Mohamed M. Abd-Elmoneim
MHD peristaltic flow of non-Newtonian power-law nanofluid through a non-Darcy porous medium inside a non-uniform inclined channel Received: 28 May 2020 / Accepted: 2 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we studied the peristaltic motion of steady non-Newtonian nanofluid flow with heat transfer through a non-uniform inclined channel. The flow in this discussion obeys the power law model through a non-Darcy porous medium. Moreover, the effects of thermal radiation, heat generation, Ohmic dissipation and a uniform external magnetic field are taken in consideration. The governing equations that describe the velocity, temperature and nanoparticles concentration are simplified under the assumptions of long wave length and low-Reynolds number. These equations have been solved numerically by using Runge–Kutta–Merson method with the help of shooting and matching technique. The solutions are obtained as functions of the physical parameters entering the problem. The effects of these parameters on the obtained solutions are discussed and illustrated graphically through a set of figures. It is found that as Brownian motion parameter increases, the axial velocity decreases, whereas the nanoparticles concentration increases and it has a dual effect on the temperature distribution. Moreover, the axial velocity and temperature increase as Prandtl number increases, while the nanoparticles decrease. Keywords Peristaltic flow · Non-Newtonian fluid · Nanofluid · Non-Darcy porous medium · Magnetohydrodynamic
1 Introduction In 1995, Choi [1] coined nanofluids in his research; it is a suspension of nanoparticles (in the size range 1-100 nm) within the base fluid that may be water, oil or ethylene glycol. The most common nanoparticles are made up of metals such as Cu, Al and Ag or nonmetals such as Al2 O3 , CuO and Fe2 O3 [2]. These fluids possess enhanced thermo-physical properties such as thermal conductivity, thermal diffusivity, viscosity and convective heat transfer coefficients compared to those of micro-fluids. Moreover, the stability of the suspension is enhanced [3]. Thereby these fluids have gained researchers’ attention due to their numerous benefits in industrial and biomedical fields such as vehicle cooling, solar water heating, domestic refrigerator, advanced nuclear systems, cancer therapeutics, magnetic resonance imaging (MRI) and biological sensors [4]. Eldabe et al. [5] used a numerical method to solve the flow of MHD peristaltic flow of Jeffry nanofluid through a porous medium with heat source and viscous dissipation. Abou-zeid [6] used HPM to solve peristaltic flow of micropolar biviscosity nanofluid under the effects of thermal radiation and viscous dissipation. Abou-zeid and Mohamed [7] studied the creeping flow of power-law nanofluid in a non-uniform inclined channel with peristalsis and slip boundary conditions. They used HPM to solve the governing e
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