MHD peristaltic motion of Johnson–Segalman fluid in an inclined channel subject to radiative flux and convective boundary conditions

https://doi.org/10.1016/j.cmpb.2019.104999Get rights and content

Highlights

  • Johnson–Segalman fluid is taken.

  • Thermal radiation is outlined.

  • Inclined magnetic field is adopted.

  • Inclined channel is considered.

  • Convective conditions are utilized.

Abstract

Background: In abundant of a digestive tract like smooth muscle tissue, human gastrointestinal tract contracts in sequence to generate a peristaltic wave, which pushes a food along the tract. The peristaltic motion contains circular relaxation smooth muscles, then their shrinkage (contraction) behind the chewed material to keep it from moving backward, then longitudinal contraction to shove it ahead. Therefore, we have conducted a theoretical investigation on peristaltic transport in flow of Johnson-Segalman liquid subject to inclined magnetic field. The energy equation is developed with extra heat transport assumptions like thermal radiative flux and dissipation. The channel walls are heated convectively.

Methods: Dimensionless problems subject to small Reynolds number and long wavelength are tackled. Perturbation technique is implemented for small Weissenberg number.

Results: The physical importance of involved parameters that directly affect the heat transfer rate temperature and velocity. The pertinent variables are amplitude ratio, wave number, Reynolds number, Hartman number, Prandtl number, Weissenberg number, thermal radiative heat flux, Biot number, elasticity variables and Froude number are graphically discussed. The obtained outcome shows that the velocity field increases against higher values of elasticity variables but velocity the material decays through higher fluid parameter. Temperature field declines through higher Hartman number. Furthermore, it is also examined that the heat transfer rate decays against rising Hartman number.

Conclusions: The impact of complaint walls on radiative peristaltic transport of Johnson–Segalman liquid in symmetric channel subject to inclined angle. The influence of Johnson–Segalman variable on the velocity field shows decreasing behavior. Velocity also declines against larger Hartman number. Temperature and heat transfer rate boosts through rising values of E1 E2 while decays versus larger E3. Furthermore, reduction in heat transfer coefficient is observed when the values of α and Br are increased.

Introduction

Research on studying the characteristics of non-Newtonian nature materials during last few decades has achieved much consideration of numerous researchers and analyst owing to its meaningful utilizations in industry, biology, physiology and engineering. There are several challenges raised in the mathematical modeling of constitutive expressions due to nonlinearities. Therefore, frequent non-Newtonian liquid models are proposed by the analyst to investigate the relationship between rate of deformation and stress. But, there is no solo mathematical model which interprets the attribute of real-life materials in the literature. Thus, frequent constitutive expressions for numerous non-Newtonian materials are presented by the researchers [1], [2], [3], [4], [5]. Analysis of peristaltic transport subjected to nonlinear nature materials have obtained ample consideration owing to its meaningful utilizations in industry and physiology. Gastrointestinal tract, stomach and intestines are examples of peristalsis within human body. This activity is also used to design various devices for example dialysis machine, heart lung machine and blood pump machine to pump blood during frequent bio-medical processes. With these applications in mind numerous analyst and investigators put their efforts forward to examine flow of non-Newtonian nature materials with various flow assumptions can be seen through the Refs. [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20].

MHD has attained much consideration of investigators and analyst due to its meaningful utilization in industry and bio-engineering like purification of molten metals from nonmetallic inclusions, power generators and fluid droplet sprays etc. Furthermore, a flow with shear rate less than 100 s1 characterizes peristaltic flows in the coronary arteries [21]. Cancer treatment, bleeding reduction during surgeries, magnetic resonance imaging is some application of MHD in physiology. Hayat et al. [22] scrutinized peristaltic flow of Williamson material (non-Newtonian fluid) subject to magnetohydrodynamic in an inclined channel. Peristaltic transport with partial slip effects in flow of Jeffrey material is studied by Ellahi and Hussain [23]. Behavior of peristaltic motion in flow of non-Newtonian material subject to magnetic effects in a tapered asymmetric channel is discussed by Kothandapani et al. [24]. Some other works on MHD flow are mentioned in Refs. [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40].

Peristaltic movement with heat transport can be seen in many scientific and industrial applications like radiation between environment and surface, convection phenomenon in blood flow from pores of tissues etc. The processes of hemodialysis and oxygenation have also been imagined through peristaltic flows subject to heat transport. With all such inspirations in mind, many researchers are engaged to evaluate the mutual impacts of magnetohydrodynamic and heat transfer on peristaltic transport mentioned in refs. [41], [42], [43]. Heat transport through radiative heat flux is different from convection and conduction. In the presence of radiative heat flux, the energy transfer by electromagnetic waves through material medium e.g. radio waves, X-rays and gamma radiation. Radiation is widely used in industry and medical fields such as high energy X-rays which externally applied to treat cancer. In biomedical applications the X-rays have broad significance in skin absorptions, cancer detection and tissue reflecting. Among industries radioactive materials are utilized in aircraft and automobile manufacturers, construction and oil and mining companies. Industry has utilized radioisotopes to advance highly sensitive gauges. Motivated by such detail the radiative peristaltic flows in a asymmetric or symmetric channel are extensively investigated (see Refs. [44], [45], [46], [47], [48]).

With the aforementioned results and importance, The main theme of present communication is to examine radiated peristaltic flow of Johnson-Segalman material with convective conditions. MHD liquid is considered. The viscous dissipation is also observed. Channel walls are compliant. Lubrication approximation is utilized for mathematical development. Perturbation technique is used for the solutions of coupled equations. Finally the graphs are interpreted physically. Trapping phenomenon is also explored.

Section snippets

Formulation

Here we have considered a symmetric channel having width 2d. The channel inclination is denoted by α (see Fig. 1). An electrically conducting incompressible Johnson–Segalman fluid fills the channel. Applied magnetic field has inclination Θ. The complaint properties of channel walls are accounted. Sinusoidal waves propagating along the channel walls induce peristalsis. The wave shape is represented byy=±η(x,t)=±[d+asin2πλ(xct)],where a highlights the amplitude, c wave speed, t time,  ± η

Perturbation solution

We intend to solve the resulting systems of stream function and temperature by taking Weissenberg number as perturbation quantity. Writingψ=ψ0+(We)2ψ1+.,Syx=S0yx+(We)2S1yx+,θ=θ0+(We)2θ1+,Z=Z0+(We)2Z1+.and then the solving zeroth and first order systems are asψ0=C3+C4y+eHycos2[Θ]1+α1(C2+C1e2Hycos2[Θ]1+α1)(1+α1)sec2[Θ]α1H2,ψ1=B3+B4ye3Hycos2[Θ]1+α18H21+α1cos2[Θ](e6Hycos2[Θ]1+α1A111+α1×(8e2Hycos2[Θ]1+α1(B2+B1e2Hycos2[Θ]1+α1)(1+α1)+C23(α1q2α1))×cos2[Θ]A12e4Hycos2[Θ]1+α1A13e2Hycos2[Θ]

Analysis

This section addresses the effectiveness of involved variables on thermal field (θ), velocity field (u), coefficient of heat transfer (Z) and stream function (ψ).

Closing remarks

Effect of complaint walls on radiated peristaltic activity in non-Newtonian (Johnson-Segalman) material in a symmetric channel inclined at angle α is studied. Convective boundary conditions are considered. Inclined magnetic field is accounted. The prime theme of this communication is listed as:

  • Influence of α1 on velocity is decreasing.

  • Velocity declines for higher values of H.

  • Temperature increases with We whereas it reduces for higher values of Bi, Rn and Fr.

  • Coefficient of heat transport,

Declaration of Competing Interest

The authors declared that they have no conflict of interest and the paper presents their own work which does not been infringe any third-party rights, especially authorship of any part of the article is an original contribution, not published before and not being under consideration for publication elsewhere.

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