MHD peristaltic motion of Johnson–Segalman fluid in an inclined channel subject to radiative flux and convective boundary conditions
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 s 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 bywhere 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. Writingand then the solving zeroth and first order systems are as
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:
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Influence of α1 on velocity is decreasing.
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Velocity declines for higher values of H.
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Temperature increases with We whereas it reduces for higher values of Bi, Rn and Fr.
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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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