Magnetic force effects on peristaltic transport of hybrid bio-nanofluid (AuCu nanoparticles) with moderate Reynolds number: An expanding horizon
Introduction
In 1995, Choi [1] presented a new form of fluid known as Nanofluids, which consists of tiny nanoparticles (NPs). Nanoparticles have a very small size less than 100 nm, and a higher rate of thermal conductivities. Heat transfer can be improved outstandingly by introducing the nanoparticles in the base fluid [2]. The base fluids are of various kinds, for instance, organic fluids (e.g. refrigerants, tri-ethylene-glycols, ethylene), bio-fluids, water, lubricants, polymeric solutions, oils, and other common fluids. However, NPs are made up of metals which are chemically stable (e.g. copper & gold), oxide ceramics (e.g. CuO, Al2O3), metal oxides (e.g. titania, silica, alumina, zirconia), the carbon in different forms (e.g. carbon nanotubes, graphite, diamond, fullerene), metal nitrides (e.g. SiN, AIN), functionalized NPs, and metal carbides (e.g. SiC). An extensive amount of research has been done on the nanofluid flows involving the modeling, preparation, convective, boiling heat transfer, and characterization, and their applications in different areas [[3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]].
The rudimentary problem with a mono type of nanofluid is either they have better rheological features or have a good thermal network. Mono NPs do not hold all favorable features that are important for a specific application. But, various real-time applications required trade-off betwixt various features/characteristics of nanofluids. For instance, metal oxide NPs i.e. Al2O3 reveals better stability and chemical inertness but with lower thermal conductivity, whereas metallic NPs i.e. copper, aluminum, and silver, holds a higher rate of thermal conductivities, they are unstable and chemically reactive. The hybridizing process is beneficial to improve the heat transfer features. Hybrid nanofluids are new types of nanofluids, which can be produced by the suspension of multiple kinds of nanoparticles (two or more than two) in base fluids, and hybrid nanoparticles in the base fluids. A hybrid nanomaterial is a substance that contains chemical and physical features of multiple materials together and gives these features in a homogenous phase. The synthetic hybrid nanomaterial reveals significant physiochemical features that do not present in the individual components. Noteworthy research has been conducted associated the features of these composites [15] and hybrid nanomaterials containing carbon nanotubes which have been utilized in nanocatalysts, bio- and electrochemical sensors, etc. [16] but the applications of hybrid nanomaterial have not significantly evolved and requires more attention to overcome this gap.
In contrast with other types of metallic NPs, Copper- and gold-based nanostructures reveals auspicious material because of their unique properties. Gold NPs depicts exclusive physicochemical properties along with SPR (surface plasmon resonance) and capability to connect thiol and amine groups, grant surface modification and the applications in biomedical science [17]. Gold NPs reveal alluring features that are beneficial in cancer therapy. Gold NPs are small and can pierce along the whole body, or acquiring at tumor places owing to enhanced permeability and retention (EPR) impact. Significantly, they can connect drugs and proteins which can vigorously target cancer cells. Gold NPs are biocompatible, it is known that the preparations of these NPs can be toxic in vivo and vitro systems. The atomic number of Gold NPs is high, which shows better absorption of kilo-voltage X-rays and gives greater contrast compared with standard agents. Gold NPs resonate when it is disclosed under the light of specific energies, generation heat which is beneficial in tumor-selective photo-thermal therapy [18,19].
On the other hand, Copper NPs are highly reactive and are beneficial in a wide variety of catalytic reactions including one or two electrons pathway because of the existence of the broad range of oxidation states [20]. This feature has been utilized to manufacture third-generation sensors for the physiologically associated electro-active analytes e.g. uric acid, ascorbic acid, glucose, L-cysteine, and dopamine, etc. Copper also holds intrinsic antibacterial, anti-inflammatory, and antifungal features which are beneficial in manufacturing the microbe-resistant device, bandages, and ointments. Furthermore, copper is a significant element that is necessary as a co-factor for the normal functioning of numerous metabolic enzymes [21]. This feature can be utilized to synthesize anti-tumor formations that persuade the killing of diseased/tumor cells by changing the intracellular level of copper ions. Because of their smaller size, they are effortlessly attainable to the micrometer-sized human cells and are willingly interact with the existence of biomolecules on the cell's surface [22]. Due to the distinguishing features of copper, Copper NPs gained significant importance in biomedical science.
Magnetic NPs have great significance in biomedical engineering as well as great importance for targeting drugs for the treatment of various diseases. Magnetic NPs have unique features that are applicable in MDT (magnetic drug targeting), MFH (magnetic fluid hyperthermia), and MRI (Magnetic resonance imaging) agents, etc. In particular, MFH and MDT show promising outcomes to treat a cancer patient. However, limitations are related to the strength of the extrinsic magnetic fields and the issues associated with the penetration depth of the tissues which need to be optimized further. Moreover, it is also required to develop design-to-perform magnetic NPs to enhance productivity with localized accuracy of treatment and drug delivery.
Peristaltic motion is an important mechanism in the human body that can easily be observed in smooth muscles. It occurs due to the contraction/expansion of smooth muscles. Such types of flows are helpful to transport sanitary fluids and can be found in industrial peristaltic pumping. In biomedical sciences, peristaltic flows help to propagate blood through tiny vessels. In peristaltic flow, there are two important mechanisms i.e. material reflux and fluid trapping. Material reflux is associated with the net upstream convection of fluid particles opposite to the propagation of boundary waves, while fluid trapping is associated with the generation and downstream propagation of free eddies, known as fluid boluses. These two mechanisms have significant importance in physiology because of the formation of thrombus in blood and pathological propagation of bacteria.
Therefore, in view of these applications, various authors tried to explore the peristaltic flows under the suspension of nanoparticles. Ghasemi et al. [23] presented an analytical and numerical study of peristaltic flow under the suspension of nanoparticles that are applicable in drug delivery systems. Noreen et al. [24] presented a detailed analysis of the blood moving in a vertical direction under the suspension of NPs. Changdar and De [25] studied the NPs as a drug carrier moving through a stenosed artery filled with blood. Ebaid et al. [26] used the homotopy perturbation method to examine the mathematical behavior of peristaltic motion under the suspension of gold NPs. Elnaqeeb et al. [27] examined the blood flow having variable viscosity with copper and gold NPs through a tapered stenosed artery. Abdelsalam and Bhatti [28] presented an application for cosmetics and tumor treatment using the peristaltic motion of blood under the presence of gold NPs through a uniform artery. Seikh et al. [29] studied the blood flow through small vessels filled with magnetized NPs. Ellahi et al. [30] presented a hybrid investigation on the analytical-numerical solutions of magnetized nanofluids in the presence electric field with a porous medium. Abbasi et al. [31] discussed the behavior of various kinds of nanoparticles on the peristaltic motion of nanofluid. Zhang et al. [32] contemplated Zinc Oxide NPs suspended in blood propagating through tapered arteries under magnetic effects. Aneela and Xu [33] examine the peristaltic motion of the hybrid Carreau fluid model with NPs and heterogeneous/homogenous reactions.
After the above discussion and promising applications of hybrid nanofluid, the proposed study aims to examine the induced magnetic field effects on peristaltic propulsion of hybrid bio-nanofluid under the suspension of gold and copper NPs. The base fluid is considered as blood which propagating through a uniform channel. The plasma is essentially a Newtonian fluid, and the blood plasma is a component of blood, and it is a transparent liquid substance that tends to yellow. Plasma represents the intravascular portion of the extracellular fluid, and blood plasma constitutes about 55% of the total blood volume in the human body. So, we can consider the blood as a Newtonian fluid. Blood plasma has an essential role in the transport of water, salts, and nutrients such as sugars, vitamins, hormones, etc. The impact of nonlinear thermal radiation and heat generation/absorption is also contemplated with energy equations. Adomian decomposition method is used to solve the nonlinear partial differential equations. The proposed methodology provide better results compared with other similar methods [[34], [35], [36]]. All the results are presented explicitly against velocity and temperature profile and plotted for streamlines, magnetic force, contours, axial and normal velocity, induced magnetic field, current density, temperature profile, magnetic pressure distribution, wall shear stress, and Nusselt number, respectively.
Section snippets
Description of the mathematical model
Consider the flow of an unsteady hydromagnetic viscous, in-compressible, and electrically conducting bio-fluid-based (AuCu) hybrid-nanofluid through a symmetric channel in two-dimensional having uniform cross-section with a sinusoidal wave propagating down towards its wall. The rectangular coordinates are contemplated with X− axis allocated through the center-line of the channel, and Y− axis is allocated towards its transverse direction. The system is occupied with an extrinsic magnetic field
Adomian decomposition scheme
In this portion, we will confer about the proposed scheme which is known as the Adomian decomposition scheme. This method is beneficial to solve the coupled linear/nonlinear differential equations and integral equations that arise in the field of fluid mechanics and provide better results compared with other similar methods [41]. This method was introduced by George Adomian and considerable work has been done to solve various problems [[42], [43], [44]]. The Adomian decomposition scheme
Problem solution
We will employ the Adomian decomposition solve to solve the nonlinear system of third and fourth equations in (8) and (9) with the boundary Eq. (10), we get:
Graphical results and discussion
This section is devoted to examining the graphical outcomes of multiple physical parameters involved in the proposed modeling. Specifically, we plotted the following graphs, i.e., streamlines, magnetic force, contours, axial and normal velocity, induced magnetic field, current density, temperature profile, magnetic pressure distribution, wall shear stress, and Nusselt number. To make it more significant, we considered different cases, which include Base fluid, Gold nanofluid, copper nanofluid,
Conclusions
In the present analysis, we examine the magnetic force and nonlinear thermal radiation on hybrid bio-nanofluid flow in a peristaltic channel under the influence of an applied magnetic field with high and low Reynolds number. Momentum, Maxwell, and heat with nonlinear thermal radiation and heat source think equations are considered in the dimensionless form without approximation as a system of nonlinear partial differential equations. The expressions of velocity, induced magnetic field
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
M. M. Bhatti was supported by the Cultivation Project of Young and Innovative Talents in Universities of Shandong Province [Nonlinear Sciences Research Team].
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