On oscillatory rotating convection of a couple-stress fluid with chemical reaction

Document Type : Research Article

Authors

1 Department of Mathematics, University College of Science, Osmania University, Telangana, India, 500007

2 Department of Mathematics, University College of Engineering, Osmania University, Telangana, India, 500007

3 Department of Applied Sciences, National Institute of Technology Goa, Goa, India, 403401

4 Area of Decision Sciences, Indian Institute of Management, Sirmaur, India

5 Department of Mathematics, LMNO, CNRS-Universite de Caen-Normandie, Campus II, Science 3, 14032 Caen Cedex, France

Abstract

Newtonian fluids are unable to describe fluid flow behavior in many physical problems because the fluid is non-Newtonian in nature. So, in this article, analytical research is done into the impact of chemical reactions on the onset of rotating convection of a couple-stress fluid. Through the use of linear stability theory, the equations for both stationary and oscillatory Rayleigh numbers are produced. The couple-stress fluid parameter, the solutal Rayleigh number, the Damkohler number, the Lewis number, and the Prandtl number are all graphically represented as their effects at the onset of convection. The system is stabilized by the Lewis and Taylor numbers, while oscillatory and stationary convection are affected differently by the Damkohler number. When the Taylor number is less than $910.331$ and convection is oscillatory otherwise, the stationary instability threshold is reached. When the Damkohler number is less than $1.76455$, oscillatory instability is present; otherwise, stationary convection predominates.

Keywords

Main Subjects

References

References:
Gul, T., Nasir, S., Berrouk, A.S., et al. "Simulation of the water-based hybrid nano fluids  flow through a porous cavity for the applications of the heat transfer", Scientific Reports, 13(1), p. 7009 (2023). https://doi.org/10.1038/s41598-023-33650-w.
2. Nasir, S., Berrouk, A.S., Aamir, A., et al. "Features of  flow and heat transport of MoS2+ GO hybrid nano fluid with nonlinear chemical reaction, radiation and energy source around a whirling sphere", Heliyon, 9(4), pp. 1-13 (2023). https://doi.org/10.1016/j.heliyon.2023.e15089.
3. Nasir, S., Berrouk, A.S., Aamir, A., et al. "Entropy optimization and heat  flux analysis of Maxwell nano fluid configurated by an exponentially stretching surface with velocity slip", Scientific Reports, 13(1), p. 2006 (2023). https://doi.org/10.1038/s41598-023-29137-3.
4. Nasir, S., Berrouk, A.S., Aamir, A., et al. "Significance of chemical reactions and entropy on Darcy-forchheimer  flow of H2O and C2H6O2 convening magnetized nanoparticles". International Journal of Thermo fluids, 17, 100265 (2023). https://doi.org/10.1016/j.ijft.2022.100265.
5. Nasir, S., Berrouk, A.S., Tassaddiq, A., et al. "Impact of entropy analysis and radiation on transportation of MHD advance nano fluid in porous surface using Darcy-Forchheimer model", Chemical Physics Letters, 811, 140221 (2023). https://doi.org/10.1016/j.cplett.2022.140221.
6. Nasir, S., Sirisubtawee, S., Juntharee, P., et al. "Heat transport study of ternary hybrid nano fluid  flow under magnetic dipole together with nonlinear thermal radiation", Applied Nanoscience, 12(9), pp. 2777-2788 (2022). https://doi.org/10.1007/s13204-022-02583-7.
7. Alnahdi, A.S., Nasir, S., and Gul, T. "Ternary Casson hybrid nano fluids in convergent/divergent channel for the application of medication", Thermal .Science, 27(Spec. issue 1), pp. 67-76 (2023). https://doi.org/10.2298/TSCI23S1067A.
8. Alnahdi, A.S., Nasir, S., and Gul, T. "Blood-based ternary hybrid nano fluid  flow-through perforated capillary for the applications of drug delivery", Waves in Random and Complex Media, pp. 1-19 (2022). https://doi.org/10.1080/17455030.2022.2134607.
9. Zeeshan, A., Hussain, F., Ellahi, R., et al. "A study of gravitational and magnetic effects on coupled stress bi-phase liquid suspended with crystal and Hafnium particles down in steep channel", Journal of Molecular Liquids, 286, 110898 (2019). https://doi.org/10.1016/j.molliq.2019.110898.
10. Ellahi, R., Zeeshan, A., Hussain, F., et al. "Two-phase couette flow of couple stress  fluid with temperature dependent viscosity thermally affected by magnetized moving surface", Symmetry, 11(5), p. 647 (2019). https://doi.org/10.3390/sym11050647.
11. Bhatti, M.M., Zeeshan, A., Asif, M.A., et al. "Nonuniform pumping  flow model for the couple stress particle- fluid under magnetic effects", Chemical Engineering Communications, 209(8), pp. 1058-1069 (2022). https://doi.org/10.1080/00986445.2021.1940156.
12. Afzal, Q., Akram, S., Ellahi, R., et al. "Thermal and concentration convection in nano fluids for peristaltic  flow of magneto couple stress  fluid in a nonuniform channel", Journal of Thermal Analysis and Calorimetry, 144, pp. 2203-2218 (2021). https://doi.org/10.1007/s10973-020-10340-7.
13. Khan, A.A., Bukhari, S.R., Marin, M., et al. "Effects of chemical reaction on third-grade MHD  fluid  flow under the influence of heat and mass transfer with variable reactive index", Heat Transfer Research, 50(11), pp. 1-14 (2019). https://doi.org/10.1615/HeatTransRes.2018028397.
14. Ramesh, K., Mebarek-Oudina, F., Ismail, A.I., et al. "Computational analysis on radiative non-Newtonian Carreau nano fluid  flow in a microchannel under the magnetic properties", Scientia Iranica, 30(2), pp. 376-390 (2023). https://doi.org/10.24200/sci.2022.58629.5822.
15. Stokes, V.K. "Couple stresses in  fluids", Phys. Fluids, 9, pp. 1709-1715 (1966). 
16. Rubenstein, D.A. and Yin, W.M.D. "Frame Bio fluid Mechanics", Academic Press, Wyman Street, Waltham, USA (2012).
17. Singh, C. "Lubrication theory for couple stress  fluids and its application to short bearings", Wear, 80(3), pp. 281-290 (1982). https://doi.org/10.1016/0043- 1648(82)90256-3.
18. Srivastava, L.M. "Flow of couple stress  fluid through stenotic blood vessels", Journal of Biomechanics, 18(7), pp. 479-485 (1985). https://doi.org/10.1016/0021-9290(85)90662-1.
19. Soundalgekar, V.M. and Chaturani, P. "Effects of couple-stresses on the dispersion of a soluble matter in a pipe  flow of blood", Rheologica Acta, 19(6), pp. 710-715 (1980). https://doi.org/10.1007/BF01521862.
20. Hsu, C.H., Lin, J.R., and Chiang, H.L. "Combined effects of couple-stresses and surface roughness on the lubrication of short journal bearings", Ind. Lubr. Tribol., 55, pp. 233-243 (2003). https://doi.org/10.1108/00368790310488896.
21. Sunil Devi, R. and Mahajan, A. "Global stability for thermal convection in a couple stress  fluid", Int. Commun. Heat Mass Transf., 38, pp. 938-942 (2011). https://doi.org/10.1016/j.icheatmasstransfer. 2011.03.030.
22. Shivakumara, I.S. "Onset of convection in a couple-stress  fluid-saturated porous medium: effects of nonuniform temperature gradients", Arch. Appl. Mech., 80, pp. 949-957 (2010). https://doi.org/10.1007/s00419-009-0347-5.
23. Shivakumara, I.S., Sureshkumar, S., and Devaraju, N. "Coriolis effect on thermal convection in a couple-stress  fluid-saturated rotating rigid porous layer", Arch. Appl. Mech., 81, pp. 513-530 (2011). https://doi.org/10.1007/s00419-010-0425-8.
24. Gaikwad, S.N. and Kouser, S. "Double diffusive convection in a couple stress  fluid saturated porous layer with internal heat source", Int. J. Heat Mass Transf., 78, pp. 1254-1264 (2014). https://doi.org/10.1016/j.ijheatmasstransfer. 2014.07.021.
25. Shivakumara, I.S. and Naveen Kumar, S.B. "Linear and non-linear triple diffusive convection in a couple stress  fluid layer", Int. J. Heat Mass Transf., 68, pp. 542-553 (2014). https://doi.org/10.1016/j.ijheatmasstransfer. 2013.09.051.
26. Srivastava, A.K. and Bera, P. "Influence of chemical reaction on stability of thermosolutal convection of couple-stress  fluid in a horizontal porous layer", Transp. Porous Media, 97(2), pp. 161-184 (2013). https://doi.org/10.1007/s11242-012-0116-8.
27. Malashetty, M.S. and Biradar, B.S. "The onset of double diffusive reaction- convection in an anisotropic porous layer", Phys. Fluids, 23, 064102 (2011). https://doi.org/10.1063/1.3598469.
28. Ravi, R., Kanchana, C., and Siddheshwar, P.G. "Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids", Appl. Math. Mech. -Engl. Ed., 38(11), pp. 1579-1600 (2017). https://doi.org/10.1007/s10483-017-2280-9.
29. Wollkind, D.J. and Frisch, H.L. "Chemical instabilities: I. A heated horizontal layer of dissociating fluid", The Physics of Fluids, 14(1), pp. 13-18 (1971). https://doi.org/10.1063/1.1693263.
30. Wollkind, D.J. and Frisch, H.L. "Chemical instabilities. III. Nonlinear stability analysis of a heated horizontal layer of dissociating  fluid", The Physics of Fluids, 14(3), pp. 482-487 (1971). https://doi.org/10.1063/1.1693460.
31. Bdzil, John B. and Frisch, H.L. "Chemically driven convection", The Journal of Chemical Physics, 72(3), pp. 1875-1886 (1980). https://doi.org/10.1063/1.439332.
32. Steinberg, V. and Brand, H. "Convective instabilities of binary mixtures with fast chemical reaction in a porous medium", The Journal of Chemical Physics, 78(5), pp. 2655-2660 (1983). https://doi.org/10.1063/1.445024.
33. Steinberg, V. and Brand, H.R. "Amplitude equations for the onset of convection in a reactive mixture in a porous medium", The Journal of Chemical Physics, 80(1), pp. 431-435 (1984). https://doi.org/10.1063/1.446466.
34. Gatica, J.E., Viljoen, H.J., and Hlavacek, V. "Interaction between chemical reaction and natural  convection in porous media", Chemical Engineering Science, 44(9), pp. 1853-1870 (1989). https://doi.org/10.1016/0009-2509(89)85127-9.
35. Pritchard, D. and Richardson, C.N. "The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer", Journal of Fluid Mechanics, 571, pp. 59-95 (2007). https://doi.org/10.1017/S0022112006003211.
36. Wang, S. and Tan, W. "The onset of Darcy-Brinkman thermosolutal convection in a horizontal porous media", Physics Letters A, 373(7), pp. 776-780 (2009). https://doi.org/10.1016/j.physleta.2008.12.056.
37. Hill, A.A. and Morad, M.R. "Convective stability of carbon sequestration in anisotropic porous media". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2170), 20140373 (2014). https://doi.org/10.1098/rspa.2014.0373.
38. Ward, T.J., Cliffe, K.A., Jensen, O.E. et al. "Dissolution-driven porous-medium convection in the presence of chemical reaction", Journal of Fluid Mechanics, 747(20T), pp. 316-349 (2014). https://doi.org/10.1017/jfm.2014.149.
39. Sulaimi, A.B. "The energy stability of Darcy thermosolutal convection with reaction", International Journal of Heat and Mass Transfer, 86, pp. 369-376 (2015). https://doi.org/10.1016/j.ijheatmasstransfer. 2015.03.007.
40. Gautam, K. and Narayana, P.A.L. "On the stability of carbon sequestration in an anisotropic horizontal porous layer with a first-order chemical reaction", Proceedings of the Royal Society A, 475(2226), 20180365 (2019). https://doi.org/10.1098/rspa.2018.0365.
41. Reddy, G.S.K. and Ragoju, R. "Thermal instability of a Maxwell  fluid saturated porous layer with chemical reaction", Spec. Top. Rev. Porous Media Int. J., 13, pp. 33-47 (2022). https://doi.org/10.1615/SpecialTopicsRevPorousMedia. 2021037410.
42. Reddy, G.S.K., Koteswararao, N.V., Ravi, R., et al. "Dissolution-driven convection in a porous medium due to vertical axis of rotation and magnetic field", Mathematical and Computational Applications, 27(3), p. 53 (2022). https://doi.org/10.3390/mca27030053.
43. Ahlers, G., Grossmann, S., and Lohse, D. "Heat transfer and large scale dynamics in turbulent Rayleigh- Benard convection", Rev. Modern Phys., 81, p. 503 (2009). https://doi.org/10.1103/RevModPhys.81.503.
44. Lohse, D. and Xia, K.Q. "Small-scale properties of turbulent Rayleigh-Benard convection", Annu. Rev. Fluid Mech., 42, pp. 335-364 (2010). https://doi.org/10.1146/annurev.fluid.010908.165152.
45. Hassler, D., Dammasch, I., Lemaire, P., et al. "Solar wind out flow and the chromospheric magnetic network", Science, 283(5403), pp. 810-813 (1999). https://doi.org/10.1126/science.283.5403.810.
46. Johnston, J.P. "Effects of system rotation on turbulence structures: a review relevant to turbomachinery  flows", Int. J. Rot. Mach., 4(2), pp. 97-112 (1998). https://doi.org/10.1155/S1023621X98000098.
47. Hartmann, D.L., Moy, L.A., and Fu, Q. "Tropical convection and the energy balance at the top of the atmosphere", J. Clim., 14, pp. 4495-  4511 (2001). https://doi.org/10.1175/1520- 0442(2001)014<4495:TCATEB>2.0.CO;2.
48. Marshall, J. and Schott, F. "Open-ocean convection: observations, theory, and models", Rev. Geophys., 37,  pp. 1-64 (1999). https://doi.org/10.1029/98RG02739.
49. Babu, A.B., Reddy, G.S.K., and 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, pp. 2078-2090 (2019). https://doi.org/10.1016/j.rinp.2019.02.022.
50. Benerji Babu, A., Reddy, G.S.K., and Tagare, S.G. "Nonlinear magnetoconvection in a rotating fluid due to thermal and compositional buoyancy with anisotropic diffusivities", Heat Transfer-Asian Research, 49(1), pp. 335-355 (2020). https://doi.org/10.1002/htj.21615.
51. Rahmstorf, S. "The thermohaline ocean circulation: a system with dangerous thresholds?" Clim. Change, 46, pp. 247-256 (2000). https://publications.pikpotsdam.  de/pubman/item/item-11819.
52. Chandrasekhar, S. "Hydrodynamic and hydromagnetic stability", Courier Corporation (2013). 
Scientia Iranica
Volume 32, Issue 2
Transactions on Mechanical Engineering
January and February 2025 Article ID:6219

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History

  • Receive Date: 19 June 2022
  • Revise Date: 21 August 2023
  • Accept Date: 24 December 2023

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