MHD convective heat transfer of nanofluids through a flexible tube with buoyancy: A study of nano-particle shape effects

Highlights

• Convective heat transfer of nanofluids synthesized for shaped particles.

• Model is applicable in biological and biomimetic exploiting.

• The fluid and cilia dynamics is of the creeping type.

• A Lorentzian magnetic body force model is employed.

• Comparative study for different nanoparticle is conducted.

Abstract

This paper presents an analytical study of magnetohydrodynamics and convective heat transfer of nanofluids synthesized by three different shaped (brick, platelet and cylinder) silver (Ag) nanoparticles in water. A two-phase nanoscale formulation is adopted which is more appropriate for biophysical systems. The flow is induced by metachronal beating of cilia and the flow geometry is considered as a cylindrical tube. The analysis is carried out under the low Reynolds number and long wavelength approximations and the fluid and cilia dynamics is of the creeping type. A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected. Solutions to the transformed boundary value problem are obtained via numerical integration. The influence of cilia length parameter, Hartmann (magnetic) number, heat absorption parameter, Grashof number (free convection), solid nanoparticle volume fraction, and cilia eccentricity parameter on the flow and heat transfer characteristics (including effective thermal conductivity of the nanofluid) are examined in detail. Furthermore a comparative study for different nanoparticle geometries (i.e. bricks, platelets and cylinders) is conducted. The computations show that pressure increases with enhancing the heat absorption, buoyancy force (i.e. Grashof number) and nanoparticle fraction however it reduces with increasing the magnetic field. The computations also reveal that pressure enhancement is a maximum for the platelet nano-particle case compared with the brick and cylinder nanoparticle cases. Furthermore the quantity of trapped streamlines for cylinder type nanoparticles exceeds substantially that computed for brick and platelet nanoparticles, whereas the bolus magnitude (trapped zone) for brick nanoparticles is demonstrably greater than that obtained for cylinder and platelet nanoparticles. The present model is applicable in biological and biomimetic transport phenomena exploiting magnetic nanofluids and ciliated inner tube surfaces.

Introduction

Magnetohydrodynamic (MHD) convective heat and mass transfer of metallic-water nanofluids induced by cilia motion has garnered some interest owing to emerging applications in biomedical engineering, biomimetic thermal design [1], etc. MHD is the study of magnetic properties of electrically-conducting fluids including salt water, plasma etc. It is simulated using the equations of fluid dynamics coupled with Maxwell’s electromagnetic field equations. Convective heat transfer is process of heat transport from one place to another place by movement of fluids which works on principle of energy conservation. Modern nanotechnology fluid systems utilize nanofluids which are synthesized by the suspension of nanoparticles of size 1–50 nm within a base fluid e.g. water. The term “nanofluids” was first proposed by Choi [2]. The study of nanofluids is a major advance in thermal engineering since heat transfer performance has been proven to be substantially better with nanofluids than pure liquids. Nanofluids exhibit superior properties compared to conventional heat transfer fluids, as well as fluids containing nano-sized metallic particles. Since the radius of nanoparticles is very small then the relative surface area of nanoparticles is much larger than conventional particles. As a result the stability of suspensions of nanoparticles is comparatively better. Good summaries of recent developments in research on the heat transfer characteristics of nanofluids include the reviews by Das et al. [3], Wen et al. [4], Trisaksri and Wongwises [5] and Wang and Majumdar [6]. These have identified numerous applications of nanofluids in areas ranging from solar collector design to anti-bacterial medical systems. These reviews have also emphasized that suspended nanoparticles remarkably increase the forced convective heat transfer performance of the base fluid and furthermore that at the same Reynolds number heat transfer in nanofluids increases with the particle volume fraction. Many studies addressing magnetohydrodynamic nanofluid flows have appeared employing a diverse range of nano-particle models and also different numerical and analytical methods to solve the conservation equations. These investigations involve models which amalgamate the physics of MHD and energy, mass, momentum conservation principles. Uddin et al. [7] used a finite element algorithm to investigate magnetic field effects on radiative conducting nanofluid transport from a stretching sheet with hydrodynamic and thermal slip effects. Sheikholeslami et al. [8] used a Lattice Boltzmann method and KKL (Koo–Kleinstreuer–Li) correlation to investigate nanofluid flow and heat transfer in an enclosure heated from below. They observed that heat transfer is elevated with greater magnetic (Hartmann) number and heat source length whereas it is reduced with greater Rayleigh number. Bég et al. [9] deployed a homotopy analysis method to compute the influence of porous media drag on nanofluid boundary layer flow from a sphere. Makinde et al. [10] used the 4th order Runge–Kutta method to analyze free convection effects on magnetized stagnation point flow of nanofluids from both shrinking and stretching sheets. Turkyilmazoglu et al. [11] obtained closed-form solutions for magnetic nanofluid boundary layer slip flow from an extending/contracting sheet, observing that a unique solution exists for the stretching sheet scenario whereas multiple solutions are observed for the shrinking sheet case. Akbar et al. [12] investigated analytically the influence of different nanoparticle geometries (brick, platelet and cylindrical) on heat transfer characteristics in magnetic peristaltic nanofluid pumping. They observed that increasing Hartmann number (magnetic body force) accelerates the flow for the case of platelet nanoparticles but induces deceleration for brick nanoparticles. They further identified that thermal conductivity is a maximum for brick-shaped nanoparticles. Bég et al. [13] employed Maple software and finite difference codes to study the influence of wall temperature variation and surface tension (Marangoni effect) on hydromagnetic nanofluid boundary layer flow. Fullstone et al. [14] used a two-phase approach to simulate agent based effects in nanoparticle transport in blood flow. Kahan and Khan [15] studied power-law index and mass boundary condition effects on hydromagnetic non-Newtonian nanofluid transport. Recent experimental work by Bao et al. [16] has further established the importance of magnetic nanofluids in medical engineering including new areas such as lithography, magnetic particle imaging, magnetic-assisted pharmacokinetics and positive contrast agents of potential benefit in magnetic resonance imaging.

Biological fluid dynamics has also continued to embrace new frontiers of emerging technologies. Medical applications provide an excellent forum for combining many areas of science and engineering simulation to develop multi-faceted solutions for complex phenomena. Mathematical models are therefore increasingly merging the concepts of engineering mechanics, biology and chemistry with a diverse array of computational methods. Surface science in medicine has exposed engineers to the mechanism of cilia movement. Cilia are hair-like (nano size) structures that can beat and generate metachronal waves in synchrony causing the movement of unicellular paramecium. There two types of cilia - motile and non-motile (or primary cilia). Non-motile or primary cilia are found in nearly every cell in all mammals and do not beat. They are found in human sensory organs such as the eye and the nose. Motile cilia are found on the surface of cells and they beat in a rhythmic manner i.e. they exhibit a continuous pattern of contraction and relaxation which is very similar to the pattern like peristaltic movement. They are found in the lining of the trachea (windpipe), where they sweep mucus and dirt out of the lungs and the beating of cilia in the fallopian tubes of female mammals moves the ovum from the ovary to the uterus. Considering this oscillating movement as being similar to a metachronal wave in living systems, various researchers have developed mathematical models to describe the fluid mechanics of this phenomenon. Sleigh [17] discussed the propulsion of cilia as metachronic wave. Sleigh and Aiello [18] further reported on the movement of water by cilia. Miller [19] investigated the movement of Newtonian fluids sustained by mechanical cilia. Blake [20] implemented a spherical envelope approach for simulating ciliary propulsion. Blake [21] further reported interesting mathematical results for cilia-induced Stokes flows in tubules. Cilia propulsion has also attracted some attention in recent years, largely motivated by biomimetic systems and new trends in nanotechnology. Khaderi et al. [22] studied the performance of magnetically-driven artificial cilia for lab-on-a-chip applications. Dauptain et al. [23] discussed the hydrodynamics of ciliary propulsion. Khaderi et al. [24] further examined metachronal motion of symmetrically beating cilia. Khaderi and Onck [25] developed a numerical model to analysis the interaction of magnetic artificial cilia with surrounding fluids in three-dimensional flow systems, motivated by pharmaco-nano-robotics. Kotsis et al. [26] reviewed developments in cilia flow sensors in treatment of polycystic kidney diseases. Brown and Bitman [27] explored the roles of cilia in human health and diseases. Akbar and Butt [28] developed a mathematical model for heat transfer in viscoelastic fluid flow induced cilia movement. Akbar and Khan [29] studied the metachronal beating of cilia in magnetized viscoplastic fluids using a modified Casson non-Newtonian model. Akbar and Khan [30] further explored heat transfer in bi-viscous fluids induced by ciliary motion. Nadeem and Sadaf [31] presented analytical solutions for copper-nano-particle-blood flow under metachronal wave of cilia motion in a curved channel.

The above studies however did not explore the influence of nano-particle geometry on transport phenomena in cilia-induced propulsion. Motivated by novel developments in magnetic-assisted gastric treatments [32] and biomimetic cilia magnetic propulsion [33], [34], and further [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45] in the present article we present a new mathematical model to study the magnetohydrodynamic flow and convective heat transfer effects on cilia movement of Ag-water nanofluids through a cylindrical vessel. A Lorentzian magnetic force model is considered in the present study and magnetic induction effects are neglected. Analytical solutions for velocity, temperature and pressure are obtained under the assumption of low Reynolds number and long wavelength approximation i.e. lubrication theory. The influence of three different nano-particle geometries, thermal buoyancy and heat source on flow and heat transfer characteristics for silver-water nanofluid are investigated. Furthermore geometric effects of the ciliary movement are also studied with the help of graphical and numerical results. The present analysis is relevant to further elucidating transport phenomena in nanofluid biomimetic cilia-actuated magnetohydrodynamic propulsion systems.