Skip to main content
SpringerLink
Log in

Analyzing the topography of thermosolutal rotating convection of a Casson fluid in a sparsely packed porous channel

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

This paper discusses the thermosolutal rotating convection of a Casson fluid in a sparsely packed porous channel with variable boundaries. For linear analyses, the normal mode method is utilized to solve the governing equations. The system of equations are solved using a one-term Galerkin method for finding critical Rayleigh number. Meanwhile, the eigenvalue problem is numerically solved using the Chebyshev collocation method. Graphical representations are provided of the effects of the Casson fluid (\(\beta \)) and separation parameters (\(\chi \)) on velocity, temperature, and solute concentration profiles for fixed parameter values of Rayleigh number (R), Darcy number (Da), and Taylor number (Ta). Influence of Casson fluid and separation parameters is demonstrated for the system growth rate, stability curves, and critical boundary conditions. However, it turns out that the Darcy number, Taylor number, Lewis number, and Prandtl number all stabilize the system in an unsteady flow. Multiple-scale analysis is used to develop the coupled Landau–Ginzburg equation in weakly nonlinear theory. Furthermore, the study develops amplitude cellular convections in a stability region.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability Statement

The manuscript has associated data in a data repository. [Author’s comment: The data that support the findings in the present study are available from the corresponding author upon request.]

References

  1. D.A. Nield, Onset of thermohaline convection in a porous medium. Water Resour. Res. 4(3), 553–560 (1968)

    Article  ADS  Google Scholar 

  2. A.V. Kuznetsov, D.A. Nield, Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Trans. Porous Media 81, 409–422 (2010)

    Article  MathSciNet  Google Scholar 

  3. S.G. Tagare, Y. Rameshwar, A.B. Babu, J. Brenstensky, Rotating compositional and thermal convection in Earth’s outer core. Contrib. Geophys. Geod. 36(2), 87–113 (2006)

    Google Scholar 

  4. D. Yadav, G.S. Agrawal, R. Bhargava, The onset of convection in a binary nanofluid saturated porous layer. Int J. Theor. Appl. Multiscale Mech. 2(3), 198–224 (2012)

    Article  Google Scholar 

  5. D. Yadav, R. Bhargava, G.S. Agrawal, Boundary and internal heat source effects on the onset of Darcy-Brinkman convection in a porous layer saturated by nanofluid. Int. J. Therm. Sci. 60, 244–254 (2012)

    Article  Google Scholar 

  6. S.G. Tagare, A.B. Babu, Nonlinear convection in a sparsely packed porous medium due to compositional and thermal buoyancy. J. Porous Media 10, 8 (2007)

    Article  Google Scholar 

  7. A. Benerji Babu, G.S. Reddy, S.G. Tagare, Nonlinear magnetoconvection in a rotating fluid due to thermal and compositional buoyancy with anisotropic diffusivities. Heat Transf. 49, 335–355 (2020)

    Google Scholar 

  8. P.H. Roberts, C.A. Jones, The onset of magnetoconvection at large Prandtl number in a rotating layer I. finite magnetic diffusion. Geophys. Astrophys. Fluid Dyn. 92(3–4), 289–325 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. D.R. Fearn, D.E. Loper, Compositional convection and stratification of earth’s core. Nature 289(5796), 393–394 (1981)

    Article  ADS  Google Scholar 

  10. J.B. Gaherty, B.H. Hager, Compositional vs. thermal buoyancy and the evolution of subducted lithosphere. Geophys. Res. Lett. 21(2), 141–144 (1994)

    Article  ADS  Google Scholar 

  11. M.S. Malashetty, M. Swamy, S. Kulkarni, Thermal convection in a rotating porous layer using a thermal nonequilibrium model. Phys. Fluids 19, 054102 (2007)

    Article  ADS  Google Scholar 

  12. S. Agarwal, B.S. Bhadauria, P.G. Siddheshwar, Thermal instability of a nanofluid saturating a rotating anisotropic porous medium. Spec. Top. Rev. Porous Media Int. J. 2, 53–64 (2011)

    Article  Google Scholar 

  13. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961), pp.35–37

    Google Scholar 

  14. S. Dinarvand, M. Behrouz, S. Ahmadi, P. Ghasemi, S. Noeiaghdam, U. Fernandez-Gamiz, Mixed convection of thermomicropolar AgNPs-GrNPs nanofluid: an application of mass-based hybrid nanofluid model. Case Stud. Therm. Eng. 49, 103224 (2023)

    Article  Google Scholar 

  15. S. Dinarvand, M. Behrouz, S. Ahmadi, P. Ghasemi, S. Noeiaghdam, U. Fernandez-Gamiz, Mixed convection of thermomicropolar AgNPs-GrNPs nanofluid: an application of mass-based hybrid nanofluid model. Case Stud. Therm. Eng. 49, 103224 (2023)

    Article  Google Scholar 

  16. S. Shojaee, M. Vahabi, A. Mirabdolah Lavasani, Z. Moinfar, S. Dinarvand S, Turbulent flow of a shear-thinning non-Newtonian CMC-based nanofluid in twisted finned tubes with an elliptical profile. Numer. Heat Transf. Part A Appl. 1–18 (2023)

  17. N. Casson, A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type, in Rheology of Disperse Systems. ed. by C.C. Mill (Pergamon Press, Oxford, 1959), pp.84–104

    Google Scholar 

  18. S. Dinarvand, H. Berrehal, I. Pop, A.J. Chamkha, Blood-based hybrid nanofluid flow through converging/diverging channel with multiple slips effect: a development of Jeffery-Hamel problem. Int. J. Numer. Methods Heat Fluid Flow 33(3), 1144–1160 (2022)

    Article  Google Scholar 

  19. G. Dharmaiah, S. Dinarvand, P. Durgaprasad, S. Noeiaghdam, Arrhenius activation energy of tangent hyperbolic nanofluid over a cone with radiation absorption. Res. Eng. 16, 100745 (2022)

    Google Scholar 

  20. A. Cahyani, J. Kurniasari, R. Nafingah, S. Rahayoe, E. Harmayani, A.D. Saputro, Determining Casson yield value, Casson viscosity and thixotropy of molten Chocolate using viscometer, in IOP Conference Series: Earth and Environmental Science, vol. 355 (2019), p. 012041

  21. U. Gupta, J. Sharma, M. Devi, Casson nanofluid convection in an internally heated layer. Mater. Today Proc. 28, 1748–1752 (2020)

    Article  Google Scholar 

  22. M.S. Aghighi, A. Ammar, C. Metivier, M. Gharagozlu, Rayleigh-Bénard convection of Casson fluids. Int. J. Therm. Sci. 127, 79–90 (2018)

    Article  Google Scholar 

  23. M.S. Aghighi, A. Ammar, H. Masoumi, A. Lanjabi, Rayleigh-Benard convection of a viscoplastic liquid in a trapezoidal enclosure. Int. J. Mech. Sci. 180, 105630 (2020)

    Article  Google Scholar 

  24. S. Parvin, N. Balakrishnan, S.S. Isa, MHD Casson fluid flow under the temperature and concentration gradients. Magnetohydrodynamics 57, 353 (2021)

    Article  Google Scholar 

  25. K.F. Al Oweidi, W. Jamshed, B.S. Goud, I. Ullah, U. Usman, S.S. Mohamed Isa, S.M. El Din, K. Guedri, R.A. Jaleel, Partial differential equations modeling of thermal transportation in Casson nanofluid flow with Arrhenius activation energy and irreversibility processes. Sci. Rep. 12, 20597 (2022)

    Article  ADS  Google Scholar 

  26. S.S. Isa, N. Balakrishnan, N.S. Ismail, N.M. Arifin, F.M. Ali, The velocity, temperature and concentration profiles for triple diffusive Casson fluid flow subjected to the Soret-Dufour parameters. CFD Lett. 16, 15–27 (2024)

    Google Scholar 

  27. R.N. Rudakov, Spectrum of perturbations and stability of convective motion between vertical planes. Appl. Math. Mech. 31, 349–355 (1967)

    Google Scholar 

  28. C.M. Vest, V.S. Arpaci, Stability of natural convection in a vertical slot. J. Fluid Mech. 36, 1–15 (1969)

    Article  ADS  Google Scholar 

  29. S.A. Korpela, D. Gozum, C.B. Baxi, On the stability of the conduction regime of natural convection in a vertical slot. Int. J. Heat. Mass Transf. 16, 1683–1690 (1973)

    Article  Google Scholar 

  30. G.Z. Gershuni, E.M. Zhukhovitskii, Convective Stability of incompressible fluids. J. Appl. Mech. 44(3), 516 (1977)

    Article  ADS  Google Scholar 

  31. B.M. Shankar, I.S. Shivakumara, Gill’s stability problem may be unstable with horizontal heterogeneity in permeability. J. Fluid Mech. 943, A20 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  32. B.M. Shankar, J. Kumar, I.S. Shivakumara, Stability of natural convection in a vertical layer of Brinkman porous medium. Acta Mech. 228, 1–19 (2017)

    Article  MathSciNet  Google Scholar 

  33. B.M. Shankar, J. Kumar, I.S. Shivakumara, Boundary and inertia effects on the stability of natural convection in a vertical layer of an anisotropic Lapwood-Brinkman porous medium. Acta Mech. 228, 2269–2282 (2017)

    Article  MathSciNet  Google Scholar 

  34. A.E. Gill, A proof that convection in a porous vertical slab is stable. J. Fluid Mech. 35, 545–547 (1969)

    Article  ADS  Google Scholar 

  35. B. Straughan, The Energy Method, Stability, and Nonlinear Convection Applied Mathematical Science. (Springer, Berlin, 2004)

    Book  Google Scholar 

  36. D.A.S. Rees, The stability of Prandtl-Darcy convection in a vertical porous layer. Int. J. Heat Mass Transf. 31, 1529–1534 (1988)

    Article  Google Scholar 

  37. S. Lewis, A.P. Bassom, D.A.S. Rees, The stability of vertical thermal boundary layer flow in a porous medium. Eur. J. Mech. 14, 395–408 (1995)

    MathSciNet  Google Scholar 

  38. D.A.S. Rees, The effect of local thermal nonequilibrium on the stability of convection in a vertical porous channel. Transp. Porous Med. 87, 459–464 (2011)

    Article  MathSciNet  Google Scholar 

  39. N.L. Scott, B. Straughan, A nonlinear stability analysis of convection in a porous vertical channel including local thermal nonequilibrium. J. Math. Fluid Mech. 15, 171–178 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  40. K.V. Nagamani, B.M. Shankar, I.S. Shivakumara, Maximum density perspectives on the stability of Brinkman porous convection in a vertical channel. Phys. Fluids 35, 014110 (2023)

    Article  ADS  Google Scholar 

  41. A.B. Babu, D. Anilkumar, N.V.K. Rao, Weakly nonlinear thermohaline rotating convection in a sparsely packed porous medium. Int. J. Heat Mass Transf. 188, 122602 (2022)

    Article  Google Scholar 

  42. B.M. Shankar, S.B. Naveen, I.S. Shivakumara, Stability of double-diffusive natural convection in a vertical porous layer. Transp. Porous Media 141, 87–105 (2022)

    Article  MathSciNet  Google Scholar 

  43. A.C. Newell, J.A. Whitehead, Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279–303 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  44. A.K. Sharma, M.K. Khandelwal, P. Bera, Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium. J. Fluid Mech. 857, 469–507 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  45. A.B. Babu, N. Rao, S.G. Tagare, Weakly nonlinear thermohaline convection in a sparsely packed porous medium due to horizontal magnetic field. Eur. Phys. J. Plus 136, 795 (2021)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Warangal, Telangana, India

    A. Benerji Babu & Sapavat Bixapathi

Authors
  1. A. Benerji Babu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sapavat Bixapathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Benerji Babu.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benerji Babu, A., Bixapathi, S. Analyzing the topography of thermosolutal rotating convection of a Casson fluid in a sparsely packed porous channel. Eur. Phys. J. Plus 139, 408 (2024). https://doi.org/10.1140/epjp/s13360-024-05207-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-024-05207-x

Search

Navigation