Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel
Introduction
Peristaltic transport is a form of material transport induced by a progressive wave of area contraction or expansion along the length of a distensible tube, mixing and transporting the fluid in the direction of the wave propagation. This phenomenon is known as peristalsis. It plays an indispensable role in transporting many physiological fluids in the body such as urine transport from kidney to bladder, the movement of chyme in the gastrointestinal tracts, the transport of spermatozoa in the ductus efferentes of the male reproductive tract, the movement of ovum in the fallopian tubes, the swallowing of food through esophagus and the vasomotion of small blood vessels. Many modern mechanical devices have been designed on the principle of peristaltic pumping for transporting fluids without internal moving parts, for example, the blood pump in the heart–lung machine and the peristaltic transport of noxious fluid in nuclear industry. The problem of the mechanism of peristaltic transport has attracted the attention of many investigators. Since the first investigation of Latham [1], a number of analytical, numerical and experimental studies of peristaltic flow of different fluids have been reported under different conditions with reference to physiological and mechanical situations (Refs. [1], [2], [15], [27], [28], [29], [30], [31], [32] and references therein).
There are also a few studies available about the peristaltic flow of non-Newtonian fluids in asymmetric channels. Some recent interesting investigations in this direction are given in Refs. [3], [4], [5], [6], [7]. Due to the flow behaviour of non-Newtonian fluids, the governing equations become more complex to handle as additional non-linear terms appear in the equations of motion. There is also no universal constitutive model available which exhibits the characteristics of the all non-Newtonian fluids. Mention may be made to some interesting studies done previously, pertaining to non-Newtonian fluids, which may give insights into their behaviour (Refs. [8], [9], [10], [11], [12], [13] and references therein). Some recent studies [14], [16], [17] have considered the peristaltic motion of magnetohydrodynamic (MHD) Newtonian and non-Newtonian fluids in asymmetric channels. The MHD flow of a fluid in a channel with elastic, rhythmically contracting walls is of interest in connection with certain problems of the movement of conductive physiological fluids, e.g., the blood, and with the need for theoretical research on the operation of a peristaltic MHD compressor. The effect of a moving magnetic field on blood flow was studied by Stud et al. [18], and they observed that the effects of a suitable moving magnetic field accelerate the speed of blood. Srivastava and Agarwal [19] considered the blood as an electrically conducting fluid that constitutes a suspension of red cells in the plasma. Recently, Mekheimer [20] analysed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. Srinivas and Kothandapani [14] have analysed the MHD peristaltic flow of a viscous fluid in asymmetric channel with heat transfer. More recently, Kothandapani and Srinivas [15] have studied the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium. Hayat et al. [16] have examined the effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space. Literature survey bears witness to the fact that the information on MHD peristalsis of non-Newtonian fluids in an asymmetric channel is scant. To the best of our knowledge only Wang et al. [17] have studied the MHD peristaltic motion of a Sisko fluid in an asymmetric channel.
In the present analysis, the liquid considered is of Jeffrey type and is electrically conducting. The Jeffrey model is a relatively simpler linear model using time derivatives instead of convected derivatives for example the Oldroyd-B model and it represents a rheology different from the Newtonian. The main purpose of the present study is to investigate the peristaltic pumping of MHD flow of a Jeffrey fluid in a two-dimensional asymmetric channel having electrically insulated walls. The channel asymmetry is produced by choosing the peristaltic wave train on the walls which have different amplitudes and phase due to the variation in channel width, wave amplitudes and phase differences. The governing equations of fluid flow are solved subject to relevant boundary conditions. The comparison among the four waveforms is also made carefully and influence of several pertinent parameters on the stream function and pressure drop have been studied and numerical results obtained are presented. The results and discussions presented in this study may be helpful to further understand MHD peristaltic motion for non-Newtonian fluids in an asymmetric channel.
Section snippets
Mathematical formation and solution
We consider the motion of an incompressible viscous fluid in a two-dimensional channel induced by sinusoidal wave trains propagating with constant speed along the channel wallswhere are the amplitudes of the waves, is the wavelength, is the width of the channel, the phase difference varies in the range , corresponds to symmetric channel with waves out of phase and the waves are in
Results and discussion
To study the effects of Hartmann number , Material parameter , mean flux and phase difference on the axial velocity, we have plotted Fig. 1. From Figs. 1(a) and (b), it can be observed that the increasing of magnetic field and material parameter act as an increasing resistant against the flow in the central part of the channel. Fig. 1(c) shows that influence of the mean flow rate on the axial velocity. Axial velocity increases with the increase of . From Fig. 1(d), we can
Conclusion
The influence of applied magnetic field on the peristaltic flow of a Jeffrey fluid in asymmetric channel and different wave forms has been analysed. The analytical expressions are constructed for the stream function and pressure gradient. Numerical investigation is used to analyse the pumping characteristics. Streamlines are plotted to discuss the phenomena of trapping. The main findings can be summarized as:
- •
The axial velocity for the MHD fluid is less when compared with hydrodynamic fluid in
Acknowledgements
This work was supported in part by DRDO Grant no. ERIP/ER/0304285/M/01 and Grant no. ERIP/ER/0304284/M/01. Authors sincerely thank the referees and Professor K.R. Rajagopal, for their valuable comments and suggestions which helped us to improve the quality of the present paper.
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2022, Materials Today CommunicationsCitation Excerpt :Peristaltic activity by considering lubrication approach has been studied by Shapiro et al. [20]. After these fundamental studies, the peristalsis has been addressed through different perspectives (see studies [21–30] among others). It is well recognized fact that non-Newtonian fluid rheology has recently gained popularity among scientists due to its interdisciplinary nature involvement in pharmaceutical and other engineering processes.