Concentration-dependent viscosity and thermal radiation effects on MHD peristaltic motion of Synovial Nanofluid: Applications to rheumatoid arthritis treatment
Introduction
In early time, the study of Nanofluids has gained more scientific interest of the physician, modelers and physiologists due to its vital applications in medicine, industry and physiology. Such applications contain surgery, drug delivery and cancer diagnosis, neuro electronic interfaces and protein engineering, shedding new light on cells and kinesis, etc. Recently, a physician uses nanotechnology as a good alternative to be considered when envisioning precise medication for treating rheumatoid arthritis (RA). It is possible to increase bioavailability and bioactivity of therapeutics through uses of nanoparticles, and enable selective targeting to damaged joints [1]. Prasad et al. [2] introduced the nanomedicine delivers promising treatments for rheumatoid arthritis. Generally, Nanofluids have many applications in most of scientific fields as the researchers' interest in recent time. For instance, Kothandapani and Prakash [3] have investigated the effect of magnetic field on Williamson Nanofluids in a non-Uniform channel. Hayat et al. [4] discussed the influences of Dofour and Soret in MHD peristalsis of Pseudoplastic Nanofluid with chemical reaction. Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Padé Method was discussed by Ganji and Hatami [5]. Hasona et al. [6] delineated the combined effects of magnetohydrodynamic and temperature dependent viscosity on peristaltic flow of nanofluid through a porous medium.
Furthermore, the magnetic field is considered as an essential statement in studying of magnetic therapy of many illnesses. Especially, with the contact of this present paper, it has noticed that the flow attribute of fluid in an electrically conducting can be amended when the MHD is insecure to it. Physicianally, RA patients can treat as the magnetic field is utilized on a Synovial.fluid, due to the activity of the ions during the cell that quicken the fluids metabolism. In peristaltic, the influence of magnetic field on Synovial.fluid was discussed by Balli and Sharma [7]. Sucharitha et al. [8] have investigated the influences of Joule heating on peristaltic motion of Nanofluid. They found that the enhancement in magnetic field causes to growth in the concentration. Hatamia et al. [9] studied the Analytical investigation of MHD nanofluid flow in non-parallel walls, Ziabakhsh and Domairry [10] discussed the solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method. Hatami et al. [11] studied the forced convection analysis for MHD Al2 O3 – water nanofluid flow over horizontal plate. Different considerations of MHD Nanofluid flow can be seen in researches [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40].
Thermal radiation (radiation therapy) was used as one of the treatments appointed by physician to patients [41], [42], [43], [44], [45], that portrays the execution that embrace heat transfer, into tissues or muscles. In addition, the Heat with electromagnetic force, as in shortwaves, which can transmit a heat into muscle and tissues to reach heat above 2 inches to treatment the hurt in tendons and joints. In peristaltic flow, Kothandapani and Prakash [46] scrutinized the thermal radiation effects on dusty fluid; they found that by enhancing the thermal radiation, increases in permeability are noticed to suppress temperatures in the channel.
The biomedical fluid which fills the Synovial joint cavity is called Synovial fluid which behaves as in the fluid classifications to Non-Newtonian fluids. Also it's described as a several micrometers thick layer among the interstitial cartilages with very low friction coefficient. In addition, it supports the joint by high effective cartilage lubrication and it acts as a transport medium of metabolic/nutrients. Blood cells, ultrafiltration of the blood plasma devoid of high-molecular proteins and aggressors are the essential components of Synovial fluid [47]. Puestejovska [48] has discussed two models of Synovial fluid. Synovial fluid properties was evaluated by Morris et al. [49], they noticed that the Synovial fluid properties are relying on the fluid concentration. In early time, Khan et al. [47] discussed the influence of induced magnetic field on peristaltic motion of Synovial fluid. Moreover, Synovial fluid consists of mixtures that reveal a viscoelastic fashion. When a Synovial fluid is proliferating with versatile conditions where there is no instantaneous input, then it proceeds as a Stokesian fluid. When it is only subject to immediate input, then its viscoelastic characteristics manifests itself. Riaz et al. [50] discussed the mass transport with asymmetric peristaltic propulsion coated with Synovial fluid.
In this investigation, it is aimed to discuss the combined effects of concentration dependent viscosity and thermal radiation on peristaltic flow of Synovial.Nanofluid in an asymmetric channel. Two models of Synovial fluids are solved numerically with aid of Parametric ND Solve in Mathematica 11. The influences of penitent parameters in system of equations on the distributions of velocity, temperature and concentration are discussed.
Section snippets
Synovial models
Two models of Synovial fluid which behaves as a non-Newtonian fluid in two dimensional flows are considered.
Model-(I), Viscosity is considered exponentially dependent on the concentration [47]
Model-(II), Shear thinning index is considered function of concentration [48]Whereandwhere is the symmetric part of velocity gradient, is the concentration of hyaluronan in
Problem modeling
We consider a two dimensional Synovial Nanofluid in an asymmetric channel. Width of the channel is d1 + d2 with constant speed c in axial direction. We choose rectangular coordinates such that are along the central line and transverse to it. Further the temperature along the channel are assumed to be and to the upper and lower walls of the channel respectively through Fig. 1.Where a1
Method of solution
The Mathematica function Parametric ND Solve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some partial differential equations (PDEs). In a system of ordinary differential equations there can be any number of unknown functions xi, but all of these functions must depend on a single “independent variable” t, which is the same for each function. Partial differential equations involve two or more independent
Solution procedure and discussion
The solution of two nonlinear Models (I) and (II) is obtained numerically by built-in command Parametric ND Solve in Mathematica 11. Model-(I) represented by Eqs. (19)–(21) with boundary condition (27) and (28). Model-(II) represented by Eqs. (24)–(26) with boundary condition (27) and (28). Behaviors of different parameters on velocity, temperature and concentration as well as pressure gradient and pressure rise.
Conclusion
We have offered a theoretical approach to deliberate the peristaltic transport of Synovial.Nanofluid with concentration-dependent viscosity and thermal radiation effects. Two models of viscosity are debated. Formulated models are calculated with aid of Mathematica 11 using Parametric ND Solve, and then a detailed comparison have been made between those two models. The main noteworthy consequence is attentive as follows:
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Pressure gradient growths by increasing Hartmann number for both models.
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Conflict of interest
The authors do not have financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
Acknowledgments
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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