Analytical Approach to Nonlinear Oscillatory Flow Through a Semi-Infinite Vertical Permeable Wall in a Porous Medium with MHD Mixed Convection

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Authors

  • Vijaya Kumar
    Department of Mathematics, M S Ramaiah Institute of Technology, Bengaluru – 560054, Karnataka ,IN
  • P. A. Dinesh
     Department of Mathematics, M. S. Ramaiah Institute of Technology, Bengaluru – 560054, Karnataka ,IN
  • A. S. Aruna
     Department of Mathematics, M. S. Ramaiah Institute of Technology, Bengaluru – 560054, Karnataka ,IN
  • G. S. Prasad
     Department of Mathematics, AMCEC, Bengaluru – 560083, Karnataka ,IN
  • M. Suresha
     Department of Mathematics, Vemana Institute of Technology, Bengaluru - 560034, Karnataka ,IN

DOI:

https://doi.org/10.18311/jmmf/2023/43602

Keywords:

Linear Stability Analysis, Magneto Hydrodynamics (MHD), Porous Media.

Abstract

The present work illustrates mixed MHD convection flow of an unstable two-dimensional viscous incompressible fluid flow in a porous material under the following conditions: semi-infinite vertical permeable wall support (i) There is a constant mean oscillation in the suction velocity normal to the wall throughout time. (ii) A constant mean velocity of the free stream; (iii) a constant wall temperature; and (iv) a somewhat high temperature differential between the wall and the free stream, which generates free convection currents. Conservation of mass, energy and momentum are used to obtain the governing equations. These equations are non-linear in nature and connected with one another. The nonlinear differential equations are non-dimensionalized employing non-dimensionalized parameters such as Prandtl number Pr, Grashof number Gr, Eckert number Ek, Hartmann number Mh, and Viscous ratio. An analytical method is used to solve approximate solutions for nonlinear PDEs utilizing the double regular perturbation technique. The numerical results for temperature, skin friction, heat flow, velocity, and skin friction are computed for various parameters and are demonstrated to be in good agreement with previous findings.

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Published

2023-12-30

How to Cite

Kumar , V., Dinesh, P. A., Aruna, A. S., Prasad, G. S., & Suresha, M. (2023). Analytical Approach to Nonlinear Oscillatory Flow Through a Semi-Infinite Vertical Permeable Wall in a Porous Medium with MHD Mixed Convection. Journal of Mines, Metals and Fuels, 71(12A), 326–334. https://doi.org/10.18311/jmmf/2023/43602

Issue

Volume 71, Issue 12A , 2023

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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References

Shojaefard MH, Noorpoor AR, Avanesians A, Ghaffarpour M. Numerical investigation of flow control by suction and injection on a subsonic airfoil. American Journal of Applied Sciences. 2005; 2(10):1474-80. https://doi.org/10.3844/ajassp.2005.1474.1480 DOI: https://doi.org/10.3844/ajassp.2005.1474.1480

Uwanta IJ, Hamza MM. Effect of suction/injection on unsteady hydromagnetic convective flow of reactive viscous fluid between vertical porous plates with thermal diffusion. Hindawi Publishing Corporation. International Scholarly Research Notices. 2014; 980270:14. https://doi.org/10.1155/2014/980270 DOI: https://doi.org/10.1155/2014/980270

Jhaa BK, Isahb BY, Uwantab I J. Combined effect of suction/ injection on MHD free-convection flow in a vertical channel with thermal radiation. Ain Shams Engineering Journal. 2016. https://doi.org/10.1016/j.asej.2016.06.001 DOI: https://doi.org/10.1016/j.asej.2016.06.001

Mazzuoli M, Vittori G. Transition to turbulence in an oscillatory flow over a rough wall. J Fluid Mech. 2016; 792:6797. https://doi.org/10.1017/jfm.2016.61 DOI: https://doi.org/10.1017/jfm.2016.61

Faladea JA, Ukaegbub JC, Egereb AC, Adesanyab SO. MHD oscillatory flow through a porous channel saturated with porous medium. Alexandria Engineering Journal. 2016. https://doi.org/10.1016/j.aej.2016.09.016 DOI: https://doi.org/10.1016/j.aej.2016.09.016

Oni MO. Combined effect of heat source, porosity and thermal radiation on mixed convection flow in a vertical annulus: An exact solution. Engineering Science and Technology, An International Journal. 2017; 20(2):518- 27. https://doi.org/10.1016/j.jestch.2016.12.009 DOI: https://doi.org/10.1016/j.jestch.2016.12.009

Upreti H, Pandey AK, Kumar M. MHD flow of Ag-water nanofluid over a flat porous plate with viscous Ohmic dissipation, suction/injection and heat generation/ absorption. Alexandria Engineering Journal. 2018; 57(3):1839-47. https://doi.org/10.1016/j.aej.2017.03.018 DOI: https://doi.org/10.1016/j.aej.2017.03.018

Jha BK, Aina B. Role of suction/injection on steady fully developed mixed convection flow in a vertical parallel plate microchannel. Ain Shams Engineering Journal. 2018; 9(4):747-55. https://doi.org/10.1016/j. asej.2016.05.001 DOI: https://doi.org/10.1016/j.asej.2016.05.001

Jha BK, Oni MO, Aina B. Steady fully developed mixed convection flow in a vertical micro-concentric annulus with heat generating/absorbing fluid: An exact solution. Ain Shams Engineering Journal. 2018; 9(4):1289-301. https://doi.org/10.1016/j.asej.2016.08.005 DOI: https://doi.org/10.1016/j.asej.2016.08.005

Suresh Babu R, Rushi Kumar B, Dinesh PA. Effects of mixed convection on the oscillatory flow of a couple stress fluid through a vertical plate with variable fluid properties. Defect and Diffusion Forum. 2018; 388:328-43. https://doi.org/10.4028/www.scientific.net/ DDF.388.328 DOI: https://doi.org/10.4028/www.scientific.net/DDF.388.328

Amaratunga M, Rabenjafimanantsoa HA, Time RW. Comparison of oscillatory flow conditions in Newtonian and non-Newtonian fluids using PIV and high-speed image analysis. Flow Measurement and Instrumentation. 2019; 70:101628. https://doi.org/10.1016/j.flowmeasinst. 2019.101628 DOI: https://doi.org/10.1016/j.flowmeasinst.2019.101628

Ullah A, Alzahrani E, Shah Z, Ayaz, M, Islam, S. Nanofluids thin film flow of Reiner-Philippoff fluid over an unstable stretching surface with Brownian motion and thermophoresis effect. Coatings. 2019; 9(1):21. https://doi.org/10.3390/coatings9010021 DOI: https://doi.org/10.3390/coatings9010021

Upreti H, Kumar M. Influence of non-linear radiation, Joule heating and viscous dissipation on the boundary layer flow of MHD nano fluid flow over a thin moving needle. Multidiscipline Modeling in Materials and Structures. 2019; 16(1):208–24. https://doi.org/10.1108/ MMMS-05-2019-0097 DOI: https://doi.org/10.1108/MMMS-05-2019-0097

Vo DD, Shah Z, Sheikholeslami M, Shafee A, Nguyen TK. Numerical investigation of MHD nanomaterial convective migration and heat transfer within a sinusoidal porous cavity. Physica Scripta. 2019; 94(11):115225. https://doi.org/10.1088/1402-4896/ab2ced DOI: https://doi.org/10.1088/1402-4896/ab2ced

Javaid M, Imran M, Imran MA, Khan I, Nisar KS. Natural convection flow of a second-grade fluid in an infinite vertical cylinder. Second-Gradeeports. 2020; 8327. https://doi.org/10.1038/s41598-020-64533-z DOI: https://doi.org/10.1038/s41598-020-64533-z

Upreti H, Pandey AK, Kumar M. Thermophoresis and suction/injection roles on free convective MHD flow of Ag–kerosene oil nanofluid. Journal of Computational Design and Engineering. 2020; 7(3):386–96. https://doi. org/10.1093/jcde/qwaa031 DOI: https://doi.org/10.1093/jcde/qwaa031

Ajibade AO, Umar AM, Kabir TM. Analytical study on effects of viscous dissipation and suction/injection on a steady MHD natural convection couette flow of heat generating/absorbing fluid. Advances in Mechanical Engineering. 2021; 13(5):1–12. https://doi. org/10.1177/16878140211015862 DOI: https://doi.org/10.1177/16878140211015862

Basavaraj MS, Shobha T, Aruna AS, Kumar V. MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis. Heat Transfer. 2021. https://doi. org/10.1002/htj.22148 DOI: https://doi.org/10.1002/htj.22148

AlmukhtarAllafia W, Al Zahrah Mohd Saata F, Maoc X. Fluid dynamics of oscillatory flow across parallel-plates in standing-wave thermoacoustic system with two different operation frequencies. Engineering Science and Technology, An International Journal. 2021; 24:41-9. https://doi.org/10.1016/j.jestch.2020.12.008 DOI: https://doi.org/10.1016/j.jestch.2020.12.008

Sincomb S, Coenen W, Sanchez AL, Lasheras JC. A model for the oscillatory ow in the cerebral aqueduct. arXiv:2201.07568v1, Physics.flu-dyn. 2022. https://arxiv. org/abs/2201.07568

Sowbhagya. Outlook of density maximum on the onset of Forchheimer-Bénard convection with through flow. Journal of Mines, Metals and Fuels. 2022; 70(8A):32– 40. https://doi.org/10.18311/jmmf/2022/32007 DOI: https://doi.org/10.18311/jmmf/2022/32007

Vijaya Kumara VM, Aswatha, Banu Prakash Reddy V, Amit Datta D, Balaji V, Ashik AV. A numerical investigation of natural convection in a porous enclosure with lower wall heating. Journal of Mines, Metals and Fuels. 2023; 70(10A):195–201. https://doi.org/10.18311/ jmmf/2022/31225 DOI: https://doi.org/10.18311/jmmf/2022/31225