Influence of curvature-dependent channel walls on MHD peristaltic flow of viscous fluid with Hall currents and Joule dissipation

Document Type : Research Note

Authors

1 Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan

2 Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan

Abstract

The prime motive of this study is to assess the behavior of curvature-dependent channel boundaries on the MHD peristaltic flow of viscous liquid with heat transportation effects via a curved channel. The analysis is reported by considering the Hall currents, Joule and viscous dissipations effects. Further, no-slip momentum and thermal conditions are incorporated. Mathematical model is subjected to the implication of large wavelength and weaker magnetic Reynolds number schemes. Galilean transformation is used to convert the problem from laboratory frame to wave frame. The solution of the system of equations is executed by employing the numerical method ND Solve (Built-in command in Mathematica). The volume and mean flow rates are computed and examined. Graphical illustrations are provided to evaluate the nature of distinct constraints on velocity, temperature, and rate of heat transportation. Results show that the curvature constraint has significant influences on the mechanical and thermal features of the flow. The damping effects of the magnetic field improve the temperature and rate of heat transportation at the boundary. Moreover, a reduction in thermal transportation rate is noticed for the increasing curvature constraint values.

Keywords

References

References:
1. Latham, T.W., Fluid Motion in Peristaltic Pump, MIT, Cambridge MA (1966).
2. Whirlow, D.K. and Rouleau, W.T. "Peristaltic flow of viscous liquid in thick-walled elastic tube", Math. Biosci., 27, pp. 355-370 (1967).
3. Shapiro, A.H. "Pumping and retrograde diffusion in peristaltic waves", Proc. Workshop Ureteral Ref., pp. 109-126 (1967).
4. Shapiro, A.H., Jaffrin, M.Y., and Weinberg, S.L. "Peristaltic pumping with long wavelength at low Reynolds number", J. Fluid Mech., 37, pp. 799-825 (1969).
5. Ali, N., Sajid, M., Javed, T., et al. "Heat transfer analysis of peristaltic flow in a curved channel", Int. J. Heat Mass Transf., 53, pp. 3319-3325 (2010).
6. Hayat, T. and Abbasi, F.M. "Variable viscosity effects on peristaltic motion of a third order fluid", Int. J. Numer. Methods Fluids, 67, pp. 1500-1515 (2011).
7. Ali, N., Sajid, M., Javed, T., et al. "An analysis of peristaltic  flow of micropolar fluid in a curved channel", Chin. Phys. Lett., 28, Article ID 014704 (2011).
8. Vajravelu, K., Sreenadh, S., Rajanikanth, K., et al. "Peristaltic transport of a Williamson fluid in asymmetric channel with permeable walls", Non-Liner Anal. Real world Appl., 13, pp. 2804-2822 (2012).
9. Mekheimer, K.S., Abd Elmaboud, Y., and Abdellateef, A. "Particulate suspension flow induced by sinusoidal peristaltic waves through eccentric cylinders: thread annular", Int. J. Biomath., 6, Article ID 1350026 (2013).
10. Tripathi, D., Beg, O.A., Gupta, P.K., et al. "DTM  imulation of peristaltic viscoelastic bio fluid flow in asymmetric porous media: a digestive transport model", J. Bionic Eng., 12, pp. 643-655 (2015).
11. Makinde, O.D. and Reddy, M.G. "MHD peristaltic slip flow of Casson fluid and heat transfer in channel filled with a porous medium", Sci. Iran., 26, pp. 2342-2355 (2019).
12. Hayat, T., Ahmed, B., Abbasi, F.M., et al. "Peristaltic radiative flow of Sisko nanomaterial with entropy generation and modified Darcy's law", J. Therm. Anal. Calorim., 147, pp. 409-419 (2020).
13. Mabood, F., Abbasi, A., Farooq, W., et al. "Thermophoresis effect on peristaltic  flow of viscous nanofluid in rotating frame", J. Therm. Anal. Calorim., 143, pp. 2621-2635 (2021).
14. Hayat, T., Zahir, H., Alsaedi, A., et al. "Hall current and Joule heating effects on peristaltic flow of viscous  fluid in a rotating channel with convective boundary conditions", Resul. Phys., 7, pp. 2831-2836 (2017).
15. Abbasi, F.M., Saba, and Shehzad, S.A. "Heat transfer analysis for peristaltic flow of Carreau-Yasuda fluid through a curved channel with radial magnetic field", Int. J. Heat Mass Transf., 115, pp. 777-783 (2017).
16. Rashidi, M.M., Yang, Z., Bhatti, M.M., et al. "Heat, and mass transfer analysis on MHD blood flow of Casson fluid model due to peristaltic wave", Therm. Sci., 22, pp. 2439-2448 (2018).
17. Asha, S.K. and Sunitha, G. "Effect of joule heating and MHD on peristaltic blood flow of Eyring-Powell nanofluid in a non-uniform channel", J. Taibah Uni. Sci., 13, pp. 155-168 (2019).
18. Ramesh, K. and Devakar, M. "Effect of endoscope on the peristaltic transport of a couple stress fluid with heat transfer: Application to biomedicine", Nonlinear Eng., 8, pp. 619-629 (2019).
19. Selimefendigil, F., Oztop, H.F., and Chamkha, A.J.  "MHD mixed convection in a nanofluid filled vertical lid-driven cavity having a flexible fin attached to its upper wall", J. Therm. Anal. Calorim., 135, pp. 325- 340 (2019).
20. Hayat, T., Nawaz, S., and Alsaedi, A. "Entropy generation analysis of peristaltic flow of magnetonanoparticles suspended in water under second-order slip conditions", Sci. Iran., 27, pp. 3434-3446 (2020).
21. Iqbal, J., Abbasi, F.M., and Shehzad, S.A. "Heat transportation in peristalsis of Carreau-Yasuda nanofluid through a curved geometry with radial magnetic field", Int. Commun. Heat Mass Transf., 177, Article ID 104774 (2020).
22. Mahabaleshwar, U.S., Rekha, M.B., Kumar, P.N.V., et al. "Mass transfer characteristics of MHD Casson fluid flow past stretching/shrinking sheet", J. Eng. Thermophys., 29, pp. 285-302 (2020).
23. Shah, F., Khan, M.I., Chu, Y.M., et al. "Heat transfer analysis on MHD flow over a stretchable Riga wall considering entropy generation rate: A numerical study", Numer. Methods Part. Diff. Eqs. (2020).DOI:https://doi.org/10.1002/num.22694.
24. Kiran, G.R., Shamshuddin, M.D., Krishna, C.B., et al. "Mathematical modelling of extraction of the underground fluids: application to peristaltic transportation through a vertical conduit occupied with porous material", IOP Conf. Series: Mater. Sci. Eng., 981, Article ID 022089 (2020).
25. Salawu, S.O., Kareem, R.A., Shamshuddin, M.D. et al. "Double exothermic reaction of viscous dissipative Oldroyd 8-constant fluid and thermal ignition in a channel", Chem. Phys. Lett., 760, p. 138011 (2020).
26. Shamshuddin, M.D., Salawu, S.O., Ogunseye, H.A., et al. "Dissipative power-law fluid flow using spectral quasi linearization method over an exponentially stretchable surface with Hall current and power-law slip velocity", Int. Commun. Heat Mass Transf., 119, p. 104933 (2020).
27. Akbar, Y., Abbasi, F.M., and Shehzad, S.A. "Effectiveness of Hall current and ion slip on hydromagnetic biologically inspired flow of Cu-Fe3O4/H2O hybrid nanomaterial", Phys. Scrip., 96, p. 025210 (2021).
28. Tripathi, D., Prakash, J., Reddy, M.G., et al. "Numerical simulation of double diffusive convection and electroosmosis during peristaltic transport of a micropolar nano fluid on an asymmetric microchannel", J. Therm. Anal. Calorim., 143, pp. 2499-2514 (2021).
29. Tripathi, D., Prakash, J., Reddy, M.G., et al. "Numerical study of electroosmosis-induced alterations in peristaltic pumping of couple stress hybrid nano fluids through microchannel", Ind. J. Phys., 95, pp. 2411- 2421 (2021).
30. Ranjit, N.K., Shit, G.C., and Tripathi, D. "Electrothermal analysis in two-layered couple stress fluid flow in an asymmetric microchannel via peristaltic pumping", J. Therm. Anal. Calorim., 144, pp. 1325- 1342 (2021).
31. Selimefendigil, F. and Chamkha, A.J. "MHD mixed convection of Ag-MgO/water nano fluid in a triangular shape partitioned lid-driven square cavity involving a porous compound", J. Therm. Anal. Calorim., 143, pp. 1467-1484 (2021).
32. Abdal, S., Siddique, I., Afzal, S., et al. "On development of heat transportation through bioconvection of Maxwell nanofluid  flow due to an extendable sheet with radiative heat flux and prescribed surface temperature and prescribed heat 
flux conditions", Math. Methods Appl. Sci., (2021). DOI: https://doi.org/10.1002/mma.7722.
33. Zhao, T., Khan, M.R., Chu, Y., et al. "Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid", Appl. Math. Mech., 42, pp. 1205-1218 (2021).
34. Hashmi, M.S., Khan, N., Khan, S.U., et al. "Dynamics of coupled reacted flow of Oldroyd-B material induced by isothermal/exothermal stretched disks with Joule heating, viscous dissipation and magnetic dipoles", Alex. Eng. J., 60, pp. 767-783 (2021).
35. Nazeer, M., Hussain, F., Khan, M.I., et al. "MHD two-phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment", Numer. Methods Part. Diff. Eqs. (2021). DOI: https://doi.org/10.1002/num.22766.
36. Nisar, Z., Hayat, T., Alsaedi, A., et al. "Wall properties and convective conditions in MHD radiative peristalsis flow of Eyring-Powell nano fluid", J. Therm. Anal. Calorim., 144, pp. 1199-1208 (2021).
37. Rao, P.S. and Shamshuddin, M.D. "Second-order slip and Newtonian cooling impact on unsteady mixed convective radiative chemically reacting fluid with Hall current and cross-diffusion over a stretching sheet", Heat Transf., 50, pp. 7380-7405 (2021).
38. Saba, Abbasi, F.M. and Shehzad, S.A. "Heat transfer analysis for EMHD peristalsis of ionic-nano fluids via curved channel with Joule dissipation and Hall effects", J. Biolog. Phys., 47, pp. 455-476 (2021).
39. Akram, J., Akbar, N.S., and Tripathi, D. "Thermal analysis on MHD flow of ethylene glycol-based BNNTs nanofluids via peristaltically induced electroosmotic pumping in a curved microchannel", Arab. J. Sci. Eng., 47, pp. 7487-7503 (2022).
40. Akram, J., Akbar, N.S., and Tripathi, D. "Entropy generation in electroosmotically aided peristaltic pumping of MoS2 Rabinowitsch nanofluid", Fluid Dyn. Res., 54, Article ID 015507 (2022).
41. Akram, J., Akbar, N.S., and Tripathi, D. "Electroosmosis augmented MHD peristaltic transport of SWCNTs suspension in aqueous media", J. Therm. Anal. Calorim., 147, pp. 2509-2526 (2022).
42. Luciano, M., Xue, S.L., De Vos, W.H., et al. "Largescale curvature sensing by epithelial monolayers depends on active cell mechanics and nuclear mechanoadaptation", Nature Phys., 17, pp. 1382-1390 (2021).
43. Callens, S.J., Uyttendaele, R.J., Fratila-Apachitei, L.E., et al. "Substrate curvature as a cue to guide spatiotemporal cell and tissue organization", Biomater., 232, p. 119739 (2020).
44. Augustin, C.M., Fastl, T.E., Neic, A., et al. "The impact of wall thickness and curvature on wall stress in patient-specific electromechanical models of the left atrium", Biomech. Model. Mechanobiology, 19, pp. 1015-1034 (2020).
45. Saba, Abbasi, F.M. and Shehzad, S.A. "Impact of curvature-dependent channel walls on peristaltic  flow of Newtonian fluid through a curved channel with heat transfer", Arab. J. Sci. Eng., 45, pp. 9037-9044 (2020).
Scientia Iranica
Volume 29, Issue 6 - Serial Number 6
Transactions on Mechanical Engineering (B)
November and December 2022
Pages 3107-3118

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