Concentration-dependent viscosity and thermal radiation effects on MHD peristaltic motion of Synovial Nanofluid: Applications to rheumatoid arthritis treatment

https://doi.org/10.1016/j.cmpb.2019.01.001Get rights and content

Highlights

  • Pressure gradient increases by increasing Hartmann number for both models.

  • Nb and Nt have two opposite behavior on velocity in Model-(I) and Model-(II).

  • Nb has the same behavior on distributions of temperature and concentration.

  • RA patients can be treated by applying the magnetic field on an electrically conducting fluid.

Abstract

Background and Objective

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. Consequently, the present paper opts to investigate the influence of the concentration-dependent viscosity on Magnetohydrodynamic peristaltic flow of Synovial Nanofluid in an asymmetric channel in presence of thermal radiation effect.

Method

Our problem is solved for two models, in the first model which referred as Model-(I), viscosity is considered exponentially dependent on the concentration. Model-(2), Shear thinning index is considered as a function of concentration. Those models are introduced for the first time in peristaltic or Nanofluid flows literature. The governing problem is reformulated under the assumption of low Reynolds number and long wavelength. The resulting system of equations is solved numerically with the aid of Parametric ND Solve.

Results

Detailed comparisons have been made between Model-(I) and Model-(2) and found unrealistic results between them. Results for velocity, temperature and nanoparticle concentration distributions as well as pressure gradient and pressure rise are offered graphically for different values of various physical parameters.

Conclusions

Such models are applicable to rheumatoid arthritis (RA) treatment. Rheumatoid arthritis patients can be treated by applying the magnetic field on an electrically conducting fluid, due to the movement of the ions within the cell which accelerates the metabolism of fluids.

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]μ(C¯,D¯)=μ0eα¯C¯(1+γ2|D¯2|)n.

Model-(II), Shear thinning index is considered function of concentration [48]μ(C¯,D¯)=μ0(1+γ2|D¯2|)n(C¯).Where|D¯|=(2(U¯x¯)2+2(V¯x¯)2+(V¯x¯+U¯y¯))12,andn¯(C¯)=12(eαC¯1).where D¯ is the symmetric part of velocity gradient,C¯ 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 (X¯,Y¯) such that X¯ are along the central line and Y¯ transverse to it. Further the temperature along the channel are assumed to be T¯0 and T¯1 to the upper and lower walls of the channel respectively through Fig. 1.Y¯=H¯1(X,t¯)=d1+a1cos[2πλ(X¯ct¯)],UpperwallY¯=H¯2(X,t¯)=d2b1cos[2πλ(X¯ct¯)+ϕ].LowerwallWhere 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:

  • Pressure gradient growths by increasing Hartmann number for both models.

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.

References (52)

  • M. Sheikholeslami et al.

    Heat transfer behavior of Nanoparticle enhanced PCM solidification through an enclosure with V shaped fins

    Int. J. Heat Mass Transf.

    (2019)
  • M. Sheikholeslami

    New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media

    Comp. Meth. Appl. Mech. Eng.

    (2019)
  • M. Sheikholeslami

    Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method

    Comp. Meth. Appl. Mech Eng.

    (2019)
  • M. Sheikholeslami et al.

    Application of neural network for estimation of heat transfer treatment of Al2O3-H2O nanofluid through a channel

    Comp. Meth. Appl. Mech. Eng.

    (2019)
  • M. Sheikholeslami

    Influence of magnetic field on Al2O3-H2O nanofluid forced convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM

    J. Mol. Liq.

    (2018)
  • M. Sheikholeslami et al.

    Second law analysis for nanofluid turbulent flow inside a circular duct in presence of twisted tape turbulators

    J. Mol. Liq.

    (2018)
  • M. Sheikholeslami et al.

    Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law

    Int. J. Heat Mass Transf.

    (2018)
  • M. Sheikholeslami

    Application of Darcy law for nanofluid flow in a porous cavity under the impact of Lorentz forces

    J. Mol. Liq.

    (2018)
  • M. Sheikholeslami et al.

    Lorentz forces effect on NEPCM heat transfer during solidification in a porous energy storage system

    Int. J. Heat Mass Transf.

    (2018)
  • M.M. Bhatti et al.

    Simultaneous effects of coagulation and variable magnetic field on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism

    Microvascul. Res.

    (2017)
  • A.A. Khan et al.

    Mass transport on chemicalized fourth-grade fluid propagating peristaltically through a curved channel with magnetic effects

    J. Mol. Liq.

    (2018)
  • M.M. Bhatti et al.

    Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer Porous medium

    Adv. Powder Technol.

    (2018)
  • R. Ellahi et al.

    Structural impact of kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: application of cooling process

    J. Mol. Liq.

    (2018)
  • S.Z. Alamri et al.

    Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo–Christov heat flux model

    Phys. Lett. A

    (2019)
  • M.M. Bhatti et al.

    Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer Porous medium

    Advan. Powder Technol.

    (2018)
  • A.A. Khan et al.

    Mass transport on chemicalized fourth-grade fluid propagating peristaltically through a curved channel with magnetic effects

    J. Mol. Liq.

    (2018)
  • Cited by (41)

    • Dynamics of Walters’ B fluid due to periodic wave in a convectively heated channel with internal heat generation

      2022, Mathematics and Computers in Simulation
      Citation Excerpt :

      In industry, MHD found its relevance in nuclear turbines, missile satellites, purification of crude oil etc. Many researchers [4–23] discussed the peristaltic transport of non-Newtonian flow in different surface and channel configurations with magnetic field. Heat transfer occurs significantly during peristaltic pumping of many physiological fluids.

    View all citing articles on Scopus
    View full text