Hydrodynamic Stability Analysis for MHD Casson Fluid Flow through a Restricted Channel

Abstract:

Flow instability is a major challenge experienced in medical, engineering and industrial settings globally. For instance, flow instability linked with irregular cardiac output of the heart leads to organ malfunctioning in the medical field, it also encourages mechanical vibrations in the case of fluctuating flow rate, and several other applications. In this study, linear stability analysis is conducted to monitor the behavior of a small disturbance that is imposed on hydromagnetic Casson fluid that flows steadily through a saturated porous medium. A new variant of the Orr-Sommerfield equation is obtained and solved numerically by using spectral point collocation weighted residual approach with eigenfunction expansion of the Chebyshev polynomial as the admissible trial function. Based on the QZ algorithm, numerical results are obtained for wave and Reynold’s numbers, wave velocity as functions of Magnetic field intensity and porosity shape parameters. Results are validated against previously released data. The biophysics of the heart, particularly in cardiac rhythm analysis, as well as several other medicinal and technical applications, is among the areas where the current work has applicability.

• Periodical: Defect and Diffusion Forum (Volume 426)
• Pages: 115-126
• DOI: https://doi.org/10.4028/p-np7v6f
• Online since: June 2023
• Authors: Samuel Olumide Adesanya, Tunde AbdulKadri Yusuf, Adesina Taofeek Adeosun, Lazarus Rundora*
• Keywords: Brinkman Model, Casson Fluid, Chebyshev Spectra-Collocation Method, Modified Orr-Sommerfield Equation, Stability Analysis

References

[1] O.D. Makinde, Magneto-Hydrodynamic Stability of Plane-Poiseuille Flow Using Multideck Asymptotic Technique, Mathematical and Computer Modelling. 37 (2003) 251-259.

DOI: 10.1016/s0895-7177(03)00004-9

[2] O.D. Makinde, Temporal stability of small disturbances in MHD Jeffery–Hamel flows, Computers and Mathematics with Applications. 53 (2007) 128–136

DOI: 10.1016/j.camwa.2006.06.014

[3] O.D. Makinde, On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium, Int. J. Numer. Meth. Fluids. 59 (2009) 791–799

DOI: 10.1002/fld.1847

[4] O.D. Makinde, P. Y. Mhone, on temporal stability analysis for hydromagnetic flow in a channel filled with a saturated porous medium, Flow, Turbulence and Combustion. 83 (2009) 21-32.

DOI: 10.1007/s10494-008-9187-6

[5] M. Takashima, The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field. Fluid Dyn. Res. 17, 293–310 (1996). doi:10.1016/0169-5983(95) 00038-0

DOI: 10.1016/0169-5983(95)00038-0

[6] B. M. Shankar, J. Kumar, I. S. Shivakumara, Magnetohydrodynamic stability of natural convection in a vertical porous slab, Journal of Magnetism and Magnetic Materials 421 (2017) 152– 164.

DOI: 10.1016/j.jmmm.2016.08.010

[7] V. Poply, P. Singh, A. K. Yadav, Stability analysis of MHD outer velocity flow on a stretching cylinder, Alexandria Engineering Journal. 57 (2018) 2077–(2083)

DOI: 10.1016/j.aej.2017.05.025

[8] X. Zhai, K. Chen, B. Song, Linear instability of channel flow with microgroove-type anisotropic superhydrophobic walls. (2022) physics.flu-dyn. arXiv:2209.05091

DOI: 10.1103/physrevfluids.8.023901

[9] K. H. Yu, C. J. Teo, and B. C. Khoo. Linear stability of pressure-driven flow over longitudinal superhydrophobic grooves. Phys. Fluids, 28:022001, 2016.

DOI: 10.1063/1.4940336

[10] C. Chai and B. Song. Stability of slip channel flow revisited. Phys. Fluids, 31:084105, 2019.

[11] X. Xiong and J. Tao. Linear stability and energy stability of plane Poiseuille flow with isotropic and anisotropic slip boundary conditions. Phys. Fluids, 32 (2020) 094104.

DOI: 10.1063/5.0015737

[12] J. O. Pralits, E. Alinovi, and A. Bottaro. Stability of the flow in a plane microchannel with one or two superhydrophobic walls. Phys. Rev. Fluids, 2 (2017) 013901.

DOI: 10.1103/physrevfluids.2.013901

[13] S. Ceccacci, S. A. W. Calabretto,  C. Thomas, and  J. P. Denier, The linear stability of slip channel flows, Physics of Fluids. 34(7) (2022)

DOI: 10.1063/5.0098609

[14] A. Rafiki and A. Hifdi Stability of plane Poiseuille flow of viscoelastic fluids in the presence of a transverse magnetic field, MATEC Web of Conferences 1 06006 (2012), DOI: 10.1051/ matecconf 0106006

DOI: 10.1051/matecconf/20120106006

[15] Z. Hussain, S. Hussain, T. Kong, and Z. Liu, Instability of MHD couette flow of an electrically conducting fluid, AIP Advances 8 (2018) 105209.

DOI: 10.1063/1.5051624

[16] A. Laouer, E Mezaache and S. Laouar, Stability analysis of MHD fluid flow over a moving plate with pressure gradient using the Chebyshev spectral method, International Journal of Engineering Research in Africa. 49 (2020) 29-38

DOI: 10.4028/www.scientific.net/jera.49.29

[17] Drazin, P.G.: Introduction to Hydrodynamic Stability. Cambridge University Press, Cambridge (2002)

[18] P. Sibanda, O.D. Makinde, A Mathematical Introduction to Incompressible Flow, University of Zimbabwe publisher (2000)

[19] Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, New York (1998)

[20] Khorrami, M.R., Malik, M. R., Ash, R. R. Application of spectral techniques to the stability of swirling flows. J. Comput. Phys. 81 (1989) 206–229

DOI: 10.1016/0021-9991(89)90071-5

[21] Orszag, S.A.: Accurate solution of the Orr–Sommerfield stability equation. J. Fluid Mech. 50(4) (1971) 689–703

DOI: 10.1017/S0022112071002842

[22] Z. Shah, S. Islam, H. Ayaz, and S. Khan, "Radiative heat and mass transfer analysis of micropolar nanofluid flow of Casson fluid between two rotating parallel plates with effects of Hall current," ASME Journal of Heat Transfer (2018).

DOI: 10.1115/1.4040415

[23] Z. Shah, S. Islam, T. Gul, E Bonyah, and M. A. Khan, "The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates," Results in Physics 9 (2018) 1201–1214.

DOI: 10.1016/j.rinp.2018.01.064

[24] G. Ishaq, Z. Ali, S. Shah, Islam and S. Muhammad, "Entropy generation on nanofluid thin film flow of Eyring–Powell fluid with thermal radiation and MHD effect on an unsteady porous stretching sheet, Entropy 20 (2018) 412. doi.org/

DOI: 10.3390/e20060412

[25] H. Hammed, M. Haneef, Z. Shah, S. Islam, W. Khan, and S. Muhammad, "The combined magnetohydrodynamic and electric field effect on an unsteady Maxwell nanofluid flow over stretching surface under the influence of variable heat and thermal radiation," Applied Sciences 8 (2018) 160

DOI: 10.3390/app8020160

[26] T.A Yusuf, R. Naveen Kumar, R. J. Punith Gowda, U.D Akpan, Entropy generation on flow and heat transfer of a reactive MHD Sisko fluid through inclined walls with porous medium, International Journal of Ambient Energy. 43(1) (2022) 6307-6317.

DOI: 10.1080/01430750.2021.2013941

[27] M. I. Anwar, K. Rafique, M. Misiran S A Shehzad, Numerical study of hydrodynamic flow of a Casson nanomaterial past an inclined sheet under porous medium, Heat Transfer-Asian Res. (2019) 1-28.

DOI: 10.1002/htj.21614

[28] H B Lanjwani, S. Saleem, M. S Chandio, M. I Anwar and N Abbas, Stability analysis of triple solutions of Casson nanofluid past on a vertical exponentially stretching/shrinking sheet, Advances in Mechanical Engineering. 13(11) (2021) 1–13.

DOI: 10.1177/16878140211059679