Mathematical modelling for peristaltic transport of non-newtonian fluid through inclined non-uniform channel under the effect of surface roughness

Document Type : Research Paper

Authors

Department of Applied Science, University of Technology, Baghdad, Iraq

Abstract

The effect of surface roughness on the peristaltic motion of a non-Newtonian Jeffery fluid down a non-uniform inclined channel was carried out, and the analysis has been investigated in two-dimensional channel Cartesian co-ordinates by using a low Reynolds number and a long-wavelength approximation, the governing equations (continuity, motion, and temperature) were modeled and then simplified. Mathematica 11.3 was used to find an analytical solution for the fluid flow i.e. fluid velocity, temperature, pressure gradient, pressure rise, and flow streamlines. The impact of interesting included parameters on axial velocity, stream function, temperature, pressure gradient, and pressure rise is graphically described.

Keywords

[1] Z. Abbas, M.Y. Rafiq, J. Hasnain and T. Javed, Peristaltic transport of a Casson fluid in a non-uniform inclined
tube with Rosseland approximation and wall properties, Arabian J. Sci. Eng. 46 (2021), no. 3, 1997–2007.
[2] F.M. Abbasi, S.A. Shehzad, T. Hayat and M.S. Alhuthali, Mixed convection flow of Jeffrey nanofluid with thermal
radiation and double stratification, J. Hydrodynamics, Ser. B. 28 (2016), no. 5, 840–849.
[3] N.S. Akbar, S. Nadeem and C. Lee, Characteristics of Jeffrey fluid model for peristaltic flow of chyme in small
intestine with magnetic field, Results Phys. 3 (2013), 152–160.[4] N.S. Akbar, S. Nadeem, C. Lee, Z. Hayat Khan and R. Ul Haq, Numerical study of Williamson nanofluid flow in
an asymmetric channel, Results Phys. 3 (2013), 161–166.
[5] S. Akram and S. Nadeem, Influence of induced magnetic field and heat transfer on the peristaltic motion of a
Jeffrey fluid in an asymmetric channel: closed form solutions, J. Magnetism Magnetic Mater. 328 (2013), 11–20.
[6] N. Ali, M. Sajid, Z. Abbas and T. Javed, Non-Newtonian fluid flow induced by peristaltic waves in a curved
channel, Eur. J. Mech.-B/Fluids 29 (2010), no. 5, 387–394.
[7] M. Asgir, A.A. Zafar, A.M. Alsharif, M.B. Riaz and M. Abbas, Special function form exact solutions for Jeffery
fluid: an application of power law kernel, Adv. Differ. Equ. 2021 (2021), no. 1, 1–18.
[8] B.B. Gupta and V. Seshadri, Peristaltic pumping in non-uniform tubes, J. Biomech. 9 (1976), no. 2, 105–109.
[9] D.A.H. Hanaor, Y. Gan and I. Einav, Static friction at fractal interfaces, Tribology Int. 93 (2016), 229–238.
[10] T. Hayat, Y. Wang, K. Hutter, S. Asghar and A.M. Siddiqui, Peristaltic transport of an Oldroyd-B fluid in a
planar channel, Math. Prob. Engin. 2004 (2004), no. 4, 347–376.
[11] T. Hayat, Y. Wang, A.M. Siddiqui and K. Hutter, Peristaltic motion of a Johnson-Segalman fluid in a planar
channel, Math. Prob. Engin. 2003 (2003), no. 1, 1–23.
[12] T. Hayat, Y. Wang, A.M. Siddiqui, K. Hutter and S. Asghar, Peristaltic transport of a third-order fluid in a
circular cylindrical tube, Math. Models Meth. Appl. Sci. 12 (2002), no. 12, 1691–1706.
[13] T. Hayat, H. Zahir, A. Tanveer and A. Alsaedi, Soret and Dufour effects on MHD peristaltic transport of Jeffrey
fluid in a curved channel with convective boundary conditions, PLoS ONE 12 (2017), no. 2, p. 0164854.
[14] P. Lakshminarayana, S. Sreenadh, G. Sucharitha and K. Nandgopal, Effect of slip and heat transfer on peristaltic
transport of a Jeffrey fluid in a vertical asymmetric porous channel, Adv. Appl. Sci. Res. 6 (2015), no. 2, 107–118.
[15] T.W. Latham, Fluid motions in a peristaltic pump, PhD diss. Massachusetts Institute of Technology, 1966.
[16] K.S. Mekheimer, Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels, Biorheology
39 (2002), no. 6, 755–765.
[17] K.S. Mekheimer, Peristaltic flow of blood under effect of a magnetic field in a non-uniform channels, Appl. Math.
Comput. 153 (2004), no. 3, 763–777.
[18] K.S. Mekheimer, E.F. El Shehawey and A.M. Elaw, Peristaltic motion of a particle-fluid suspension in a planar
channel, Int. J. Theor. Phys. 37 (1998), no. 11, 2895–2920.
[19] A. Movassagh, X. Zhang, E. Arjomand and M. Haghighi, A comparison of fractal methods for evaluation of
hydraulic fracturing surface roughness, APPEA J. 60 (2020), no. 1, 184–196.
[20] S. Nadeem and N.S. Akbar, Influence of heat transfer on a peristaltic transport of Herschel–Bulkley fluid in a
non-uniform inclined tube, Commun. Nonlinear Sci. Numerical Simul. 14 (2009), no. 12, 4100–4113.
[21] N.E. Odling, Natural fracture profiles, fractal dimension and joint roughness coefficients, Rock Mech. Rock Engin.
27 (1994), no. 3, 135–153.
[22] N.V. Priezjev, Effect of surface roughness on rate-dependent slip in simple fluids, J. Chem. Phys. 127 (2007), no.
14, p. 144708.
[23] K. Ramesh, Effects of viscous dissipation and Joule heating on the Couette and Poiseuille flows of a Jeffrey fluid
with slip boundary conditions, Propulsion Power Res. 7 (2018), no. 4, 329–341.
[24] M.G. Reddy and O.D. Makinde, Magnetohydrodynamic peristaltic transport of Jeffrey nanofluid in an asymmetric
channel, J. Molecular Liquids 223 (2016), 1242–1248.
[25] M.R. Salman and H.A. Ali, Approximate treatment for the MHD peristaltic transport of Jeffrey fluid in inclined
tapered asymmetric channel with effects of heat transfer and porous medium, Iraqi J. Sci. 2020 (2020), 3342–3354.
[26] A.H. Shapiro, M.Y. Jaffrin and S.L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number,
J. Fluid Mech. 37 (1969), no. 4, 799–825.
[27] R. Shukla, S.S. Bhatt, A. Medhavi and R. Kumar, Effect of surface roughness during peristaltic movement in anonuniform channel, Math. Prob. Engin. 2020 (2020).
[28] A.M. Siddiqui and W.H. Schwarz, Peristaltic motion of a third-order fluid in a planar channel, Rheologica Acta
32 (1993), no. 1, 47–56.
[29] A.M. Siddiqui and W.H. Schwarz, Peristaltic flow of a second-order fluid in tubes, J. Non-Newtonian Fluid Mech.
53 (1994), 257–284.
[30] K. Vajravelu, S. Sreenadh, G. Sucharitha and P. Lakshminarayana, Peristaltic transport of a conducting Jeffrey
fluid in an inclined asymmetric channel, Int. J. Biomath. 7 (2014), no. 6, 1450064.
[31] D.B. Van Dam and C.J. De Pater, Roughness of hydraulic fractures: importance of in-situ stress and tip processes,
Spe J. 6 (2001), no. 1, 4–13.
[32] Y. Wang, T. Hayat and K. Hutter, Peristaltic flow of a Johnson-Segalman fluid through a deformable tube, Theore.
Comput. Fluid Dyn. 21 (2007), no. 5, 369–380.
[33] C. Zhai, Y. Gan, D. Hanaor, G. Proust and D. Retraint, The role of surface structure in normal contact stiffness,
Experim. Mech. 56 (2016), no. 3, 359–368.
Volume 13, Issue 2
July 2022
Pages 117-130
  • Receive Date: 02 March 2022
  • Revise Date: 21 April 2022
  • Accept Date: 18 May 2022