Vol. 22 No. 3 (2023): Mapana Journal of Sciences
Research Articles

Weakly Non-Linear Stability of Maxwell Fluid in a Porous Layer with the Effect of Magnetic Field

PDF
  • C Bheemudu,
  • T. Ramakrishna Goud
C Bheemudu
Osmania university, Telangana, 500007.
DOI: https://doi.org/10.12723/mjs.66.10

Published 2023-12-13

Keywords

  • Maxwell fluid,
  • Magnetic effect,
  • Porous media,
  • Convection

Copyright (c) 2023

Creative Commons License

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

Abstract

The problem of magnetoconvection over a Maxwell fluid due to porous media with the Darcy–Brinkman model via magnetic field is studied. Analytical results of the critical Darcy–Rayleigh numbers at the onset of stationary convection and oscillatory convection are derived. The governing dimensionless equations are tackled through the normal mode
approach, resulting in an eigenvalue problem within the context of linear stability theory. Furthermore, we harness the power of the Galerkin first-order method in MATLAB R2020a to address and resolve this eigenvalue problem. The behaviour of various parameters, like the Q, Λ, Da, and Pm, has been analyzed. The neutral curves are obtained for different prescribed values of the other physical parameters. The Chandrasekhar and Darcy numbers stabilize the system, and the Critical oscillatory Rayleigh number is a non-monotonic function of Pm. In order to study the heat transport by convection, the well-known Ginzburg-Landau equation has been derived using weakly non-linear analysis.

PDF

References

  1. Alfven, Hannes. ”Discussion of the origin of the terrestrial and solar magnetic fields.” Tellus 2, no. 2, 74-82, (1950).
  2. Thompson, W. B. ”CXLIII. Thermal convection in a magnetic field.” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42, no. 335, 1417-1432, (1951).
  3. Chandrasekhar, S., Hydrodynamic and hydromagnetic stability. Oxford: Oxford University press (1961).
  4. Sparrow, E. M., and R. D. Cess. ”The effect of a magnetic field on free convection heat transfer.” International Journal of Heat and Mass Transfer 3, no. 4, 267-274, (1961).
  5. Nield, D. A. ”Onset of thermohaline convection in a porous medium.” Water Resources Research 4, no. 3, 553-560, (1968).
  6. Taunton, J. W., E. N. Lightfoot, and Theodore Green. ”Thermohaline instability and salt fingers in a porous medium.” The Physics of Fluids 15, no. 5, 748-753, (1972).
  7. Knobloch, E., N. O. Weiss, and L. N. Da Costa. ”Oscillatory and steady convection in a magnetic field.” Journal of Fluid Mechanics 113, 153-186, (1981).
  8. Rudraiah, N., P. Kn Srimani, and R. Friedrich. ”Finite amplitude convection in a twocomponent fluid saturated porous layer.” International Journal of Heat and Mass Transfer 25, no. 5, 715-722, (1982).
  9. Poulikakos, Dimos. ”Double diffusive convection in a horizontal sparcely packed porous layer.” International communications in heat and mass transfer 13, no. 5, 587-598, (1986).
  10. Maxwell, J.C., IV. On the dynamical theory of gases. Philosophical transactions of the Royal Society of London, (157), 49-88, (1987).
  11. Malashetty, M. S. ”Anisotropic thermoconvective effects on the onset of double diffusive convection in a porous medium.” International journal of heat and mass transfer 36, no.9, 2397-2401, (1993).
  12. Kalla, L., P. Vasseur, R. Benacer, H. Beji, and R. Duval. ”Double diffusive convection within a horizontal porous layer salted from the bottom and heated horizontally.” International communications in heat and mass transfer 28, no. 1, 1-10, (2001).
  13. Ingham, D.B. and Pop, I. eds., Transport phenomena in porous media III (Vol. 3). Elsevier, (2005).
  14. Uetake, Hiromichi, Noriyuki Hirota, Jun Nakagawa, Yasuhiro Ikezoe, and Koichi Kitazawa. ”Thermal convection control by gradient magnetic field.” Journal of Applied Physics 87, no. 9, 6310-6312, (2000).
  15. Khuzhayorov, B., Auriault, J.L. and Royer, P., Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media. International Journal of Engineering Science, 38(5), 487-504, (2000).
  16. Sharma, R.C., The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium. Transport in Porous Media, 60(3), pp.251-274, (2005).
  17. Nield, Donald A., and Adrian Bejan. Convection in porous media. Vol. 3. New York: springer, (2006).
  18. Abbas, Z., Sajid, M. and Hayat, T., MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theoretical and Computational Fluid Dynamics, 20(4), 229-238, (2006).
  19. Hayat, T., Abbas, Z. and Sajid, M., Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Physics Letters A, 358(5-6), 396-403, (2006).
  20. Hayat, T., Sajjad, R., Abbas, Z., Sajid, M. and Hendi, A.A., Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium. International Journal of Heat and Mass Transfer, 54(4), 854-862, (2011).
  21. Gaikwad, S. N., and M. Dhanraj. ”Onset of double diffusive convection in a Maxwell fluid saturated anisotropic porous layer with internal heat source.” Special Topics and Reviews in Porous Media: An International Journal 4, no. 4, (2013).
  22. Vad´asz, Peter, ed. ”Emerging topics in heat and mass transfer in porous media: From bioengineering and microelectronics to nanotechnology.” (2008).
  23. Ghosh, S. K., O. Anwar B´eg, and J. Zueco. ”Hydromagnetic free convection flow with induced magnetic field effects.” Meccanica 45, no. 2, 175-185, (2010).
  24. Wang, S. and Tan, W., Stability analysis of soret-driven double-diffusive convection of Maxwell fluid in a porous medium. International Journal of Heat and Fluid Flow, 32(1), 88-94, (2011).
  25. Malashetty, M.S. and Biradar, B.S., The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross-diffusion effects. Physics of Fluids, 23(6), 064109, (2011).
  26. Babu, A. B., Reddy, G. S. K., & Tagare, S. G. . Nonlinear magneto convection due to horizontal magnetic field and vertical axis of rotation due to thermal and compositional buoyancy. Results in Physics, 12, 2078-2090, (2019).
  27. Benerji Babu, A., Reddy, G. S. K., & Tagare, S. G. . Nonlinear magnetoconvection in a rotating fluid due to thermal and compositional buoyancy with anisotropic diffusivities. Heat Transfer—Asian Research, 49(1), 335-355, (2020).
  28. Reddy, Gundlapally Shiva Kumar, Nilam Venkata Koteswararao, Ragoju Ravi, Kiran Kumar Paidipati, and Christophe Chesneau. ”Dissolution-Driven Convection in a Porous Medium Due to Vertical Axis of Rotation and Magnetic Field.” Mathematical and Computational Applications 27, no. 3, 53, (2022).
  29. Raghunatha, K.R., Shivakumara, I.S. and Shankar, B.M., Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer. Applied Mathematics and Mechanics, 39(2), 153-168, (2018).
  30. Karimi, M., Khosravi, M., Fathollahi, R., Khandakar, A., and Vaferi, B. . Determination of the heat capacity of cellulosic biosamples employing diverse machine learning approaches. Energy Science and Engineering, (2022).
  31. Rastegarpouyani, H., Mohebbi, S. R., Hosseini, S. M., Azimzadeh, P., Sharifian, A., Asadzadeh-Aghdaei, H., ... and Zali, M. R. Detection of Parvovirus 4 in Iranian patients with HBV, HCV, HIV mono-infection, HIV and HCV co-infection.Gastroenterology and Hepatology From bed to Bench, 11(2), 138, (2018) .
  32. Hosseinzadeh, K., Gholinia, M., Jafari, B., Ghanbarpour, A., Olfian, H. and Ganji, D.D., Nonlinear thermal radiation and chemical reaction effects on Maxwell fluid flow with convectively heated plate in a porous medium. Heat Transfer—Asian Research, 48(2), 744-759, (2019).
  33. Jahanmahin, O., Rahmati, M. M. M., Mohammadi, T., Babaee, J., and Khosravi, A. Cr (VI) ion removal from artificial waste water using supported liquid membrane. Chemical Papers, 70(7), 913-925, (2016).
  34. Pasha, P., Mirzaei, S., and Zarinfar, M. Application of numerical methods in micropolar fluid flow and heat transfer in permeable plates. Alexandria Engineering Journal, 61(4), 2663-2672, (2022).
  35. Fathollahi, R., Hesaraki, S., Bostani, A., Shahriyari, E., Shafiee, H., Pasha, P., and Ganji, D. D. Applying numerical and computational methods to investigate the changes in the fluid parameters of the fluid passing over fins of different shapes with the finite element method. International Journal of Thermofluids, 15, 100187, (2022).
  36. Faress, F., Yari, A., Rajabi Kouchi, F., Safari Nezhad, A., Hadizadeh, A., Sharif Bakhtiar, L., and Mahmoudi, N. Developing an accurate empirical correlation for predicting anti-cancer drugs’ dissolution in supercritical carbon dioxide. Scientific Reports, 12(1), 1-17, (2022).
  37. Charchi, N., Li, Y., Huber, M., Kwizera, E. A., Huang, X., Argyropoulos, C.,and Hoang, T. Small mode volume plasmonic film-coupled nanostar resonators. Nanoscale advances, 2(6), 2397-2403, (2020).
  38. Abdollahzadeh, M. J., Fathollahi, R., Pasha, P., Mahmoudi, M., Samimi Behbahan, A., and Domiri Ganji, D. Surveying the hybrid of radiation and magnetic parameters on Maxwell liquid with TiO2 nanotube influence of different blades. Heat Transfer, 51(6), 4858-4881, (2022).
  39. Reddy, G.S.K. and Ragoju, R., Thermal instability of a maxwell fluid saturated porous layer with chemical reaction. Special Topics and Reviews in Porous Media: An International Journal, 13(1), (2022).
  40. Ragoju, R., & Shekhar, S. Linear and Weakly Nonlinear Analyses of Magneto-Convection in a Sparsely Packed Porous Medium under Gravity Modulation. Journal of Applied Fluid Mechanics, 13(6), 1937-1947, (2020).
  41. Babu, A. B., Ravi, R., & Tagare, S. . Nonlinear thermohaline magnetoconvection in a sparsely packed porous medium. Journal of Porous Media, 17(1), (2014).
  42. Shadman, P., Parhizi, Z., Fathollahi, R., Zarinfar, M., Anisimova, E. Y., and Pasha, P. Combined septum and chamfer fins on threated stretching surface under the influence of nanofluid and the magnetic parameters for rotary seals in computer hardware. Alexandria Engineering Journal, 62, 489-507, (2023).