Peristaltic transport of biological graphene-blood nanofluid considering inclined magnetic field and thermal radiation in a porous media
Graphical abstract
Introduction
Graphene and graphene-based nanomaterials, because of their numerous outstanding chemical and physical properties, are utilized in various fields ranging from energy storage, electronic sensors, and photocatalysis to biomedical and nanomedicine applications such as drug/gene delivery, sensitive biosensors, bio-imaging, and different types of cancer therapies [1,2]. In the field of nanomedicine, graphene and its derivatives demonstrate several unique benefits in comparison to other drug delivery systems, including ultra-large surface area, high drug-loading efficiency, excellent stability, controlled release property, facile modification surface characteristics, great conductivity, strong near-infrared (NIR) absorbance, size control, excellent biocompatibility, and low toxicity [3,4]. The above great features make graphene as a potent candidate for diverse biomedical applications, involved gene delivery, physico-chemical control of drugs release, organized drug delivery, intended drug delivery, external field incited drug delivery, anti-cancer drug delivery, photothermal anti-cancer therapy, and multifunctional nanocarriers for combined therapy [5,6]. Nanocarriers, which are involved the anti-cancer drugs, should first contact with a living body and reach to desired tumors through the penetration of obstacles in the blood circulation with minimal damage of volume or activity to treat cancer cells effectively. Thus, nanographene as the delivery carrier is injected into the blood circulatory system to travel throughout the bloodstream to reach tumor sites [7,8].
Peristalsis phenomenon is the transport of fluid, induced by the propagation of sinusoidal and progressive waves along the flexible walls of channel/tube, which takes place from a section of lower pressure to higher pressure [9]. This mechanism is an inherent property of muscular structures to transport the content in several physiological systems like the flow of blood through arteries, the movement of food particles in the digestive tract, transportation of urine from the kidney to the bladder, embryo movement through the uterus, the transport of male and female reproductive cells through their reproductive tracks, etc. [[10], [11], [12]]. Since the fluid transported through this mechanism avoids contamination due to the lack of direct contact with the external environment, researchers apply the peristaltic process for many biomedical devices such as heart-lung machines to pump the blood, dialysis machines, and novel pharmacological delivery systems, etc. Moreover, Peristaltic transport of nanofluids is useful for biomedical engineering, particularly in modern drug delivery systems and cancer therapy [13,14].
Magnetohydrodynamics (MHD) is the study that deals with the transport of a conducting fluid in the existence of a magnetic field [15]. Consideration the MHD flow of nanofluids in the peristaltic channel plays a key role in the area of bioengineering and nanomedicine. For instance, magnetic nanoparticles are transferred into a human body directly to treat cancer cells, using an intravenous injection method. Blood as a bio-magnetic fluid with a non-invasive nature in the presence of an external magnetic field can guide the nanoparticles to the tumor site [3,6]. There are several benefits for magnetic nanoparticles under the exogenous magnetic field in biomedicine the decline of cancer drug side consequences, the decrease in the frequency of the drug contents used by the patient, and the decrease fluctuation in circulating drug levels [16,17]. Therefore, this strategy is appropriate for smart drug delivery and anticancer application due to its non-invasive, controllable, safe, and high-efficiency features [18,19].
The radiative heat transfer (radiation therapy) has so many applications in biomedical and cancer therapy [20]. Different external forces such as magnetic field, infrared (IR) radiation, X-rays used for the creation of heat treatment in different parts of the human body. Heat is transferred bellow the skin surface into tissues and muscles, thus, the temperature raises at the cellular level makes variations in tissue protein synthesis, elasticity, cell inactivation, protein synthesis, and flow rate of blood [21,22]. The purpose of thermal treatment using nanoscaled materials is the ablation of the tumor and killing of cancer cells [23,24].
There is an interaction between blood and solid walls when blood flows through the vessels, significantly affected hydrodynamics [25]. Therefore, taking porosity into account to find out the fluid dynamic principles involved in the blood flow through tapered arterial stenosis is vital [26]. The transport models through porous media are widely appropriate for the simulation of blood flow through the cancer tumor [27].
Based on the aforementioned points, the vast applications of nanofluids with peristaltic pumping in biomedical science and engineering, the understanding of the behavior of peristaltic flow with various nanoparticles in the different condition is intensively important. Afterward, many investigations have been carried out by research groups. Table 1 summarizes a few recent studies that have discussed the peristalsis phenomenon through various aspects by employing diverse analytical and numerical approaches.
In this study, taking into account that the magnetic field and radiotherapy can effectively treat a lot of different types of cancer, an inclined magnetic field together with thermal radiation is applied to a peristaltic porous vessel. In some medicine systems like arteries of the human body, to analyze the blood flow, porosity should be taken into account by porous-medium model. Moreover, due to the anti-cancer properties of graphene, nanoparticles of graphene are added to the blood. The mathematical model of the problem is presented and the Optimal Collocation Method as a semi-analytical method is constructed to achieve the velocity profile, temperature distribution, streamlines, and isotherm lines of blood flow.
Section snippets
Formulation of the problem
Let us consider the radiative and magnetohydrodynamic peristaltic motion of a nanofluid comprising graphene nanoparticle induced by sinusoidal traveling waves through an asymmetric wavy channel filled with a porous medium. Here, an inclined magnetic field is applied in which angle of inclination is varied in the range 0 ° < α < 90° with respect to the y-axis. Porous media are modeled as a source term in the Navier–Stokes equations by Darcy's Law [38,39]. Impacts of Joule heating
The solution of the problem
In this part, we will employ the Optimal Collocation Method (OCM) to solve Eqs. (22), (23). This procedure is suggested via Khazayinejad et al. [45,46] for the solution of boundary layer problems as an upgrade of the Collocation Method [[47], [48], [49]]. To attain an approximate solution in the domainh1 < y < h2, it is essential to suppose a trial function. The suitable approximations include unknown coefficients “c” are chosen as follows:
Validation
The purpose of this subsection is to check the accuracy of our solutions. For this aim, Fig. 2 compares present code results using the Optimal Collocation Method with those available from the literature for the limiting case M = 0, Da = ∞ and R = 0 (in the absence of Magnetic field, porous media, and thermal radiation) for the velocity and temperature profile. It can be seen a great match between the previously published results with the present one that shows the accuracy and reliability of
Results and discussion
In this section, the influence of pertinent parameters on the behavior of velocity and temperature have been analyzed and explained physically with the assistance of graphical results. The Graphical illustrations are indicated through Figs. 3 to 11 for controlling parameters like magnetic field, magnetic inclination angle, Phase difference, Grashof number, Flow rate, geometry parameter, Darcy parameter, Brinkman number, and nanoparticles volume fraction. Moreover, the effect of the magnetic
Conclusion
This study explains the usage of graphene nanoparticles on peristaltic motion in an asymmetric blood vessel with the wave-shaped walls under the influence of thermal radiation and an inclined magnetic field, especially in the area of biomedicine sciences. Injection of nanoparticles into blood vessels has illustrated promising indications as the treatment for some fatal diseases like diverse cancers due to their useful ability to efficiently transmit heat along with the injected drug or medicine
Nomenclature
- Qs
Heat sink/source parameter
- Re
Reynolds number
- Gr
Grashof number
- FL
Lorentz force
- B
Magnetic field
- M
Hartmann number
- Ec
Eckert number
- qr
radiative heat flux
- k∗
mean absorption coefficient
- k0
permeability parameter
- Br
Brinkman number
- Da
Darcy resistance parameter
- Pr
Prandtl number
- R
radiation parameter
- W
weighting function
velocity components
cartesian coordinates
- F
dimensionless flow rate in wave frame
flow rates in fixed frame
- a1, a2
amplitude of the left and right waves
- d1,d2,a
geometry parameters of channel
- qr
CRediT authorship contribution statement
Mehdi Khazayinejad: Conceptualization, Software, Validation, Investigation, Writing - original draft. Mohammad Hafezi: Conceptualization, Software, Validation, Investigation, Writing - original draft. Bahram Dabir: Conceptualization, Methodology, Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that there is no conflict of interest.
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