Skip to main content
SpringerLink
Log in

The Effect of Variable Gravity and Chemical Reaction on Double Diffusive Convection in a Sparsely Packed Porous Layer

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The present investigation is aimed to study the joint effect of the variable gravity field and chemical reaction on the onset of convection in a sparsely packed porous layer. Linear, parabolic, cubic and exponential functions are considered to account for the variable gravity field. The normal mode technique is used to study the linear stability of the problem. The corresponding eigenvalue problem is solved for the free-free, rigid-free, and rigid-rigid boundaries. The influence of the Damkohler number Dm, the solutal Rayleigh number Rs, the Lewis number Le, the Darcy number Da and the variable gravity field parameter \({{{{\delta }}}_{1}}\) on stability of the system in a sparsely packed porous layer is investigated. The results show that the onset of convection is delayed due to increase in the solutal Rayleigh number, the variable gravity parameter, and the Lewis number. In contrast, the onset of convection is enhanced by increase in the Darcy number and the Damkohler number. It is also observed that the system becomes more stable for exponential variation in the gravity field and less stable for cubic variation in the gravity field.

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.

Similar content being viewed by others

REFERENCES

  1. Wollkind, D.J. and Frisch, H.L., Chemical instabilities. I. A heated horizontal layer of dissociating fluid, Phys. Fluids, 1971, vol. 14, no. 1, pp. 13–17.

    Article  ADS  Google Scholar 

  2. Wollkind, D.J. and Frisch, H.L., Chemical instabilities. III. Nonlinear stability analysis of a heated horizontal layer of dissociating fluid, Phys. Fluids, 1971, vol. 14, no. 3, pp. 482–487.

    Article  ADS  Google Scholar 

  3. Bdzil, J.B. and Frisch, H.L., Chemical instabilities. II. Chemical surface reactions and hydrodynamic instability, Phys. Fluids, 1971, vol. 14, no. 3, pp. 475–481.

    Article  ADS  MATH  Google Scholar 

  4. Bdzil, J.B. and Frisch, H.L., Chemically driven convection, J. Chem. Phys., 1980, vol. 72, no. 3, pp. 1875–1886.

    Article  ADS  Google Scholar 

  5. Gitterman, M. and Steinberg, V., Onset of convective instabilities in binary liquid mixtures with fast chemical reactions, Phys. Fluids, 1983, vol. 26, no. 2, pp. 393–396.

    Article  ADS  MATH  Google Scholar 

  6. Gatica, J.E., Vjljoenz, H.J., and Hlavacek, V., Interaction between chemical reaction and natural convection in porous media, Chemical Engg. Sci., 1989, vol. 44, no. 9, pp. 1853–1870.

    Article  Google Scholar 

  7. Steinberg, V. and Brand, H.R., Convective instabilities of binary mixtures with fast chemical reaction in a porous medium, J. Chem Phys., 1983, vol. 78, no. 5, pp. 2655–2660.

    Article  ADS  Google Scholar 

  8. Pritchard, D. and Richardson, C.N., The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer, J. Fluid Mech., 2007, vol. 571, pp. 59–95.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Yadav, D., The onset of longitudinal convective rolls in a porous medium saturated by a nanofluid with non-uniform internal heating and chemical reaction, J. Thermal Anal. Calorimetry, 2019, vol. 135, no. 2, pp. 1107–1117.

    Article  Google Scholar 

  10. Malashetty, M.S. and Gaikwad, S.N., Onset of convective instabilities in a binary liquid mixtures with fast chemical reactions in a porous medium, Heat Mass Trans., 2003, vol. 39, no. 5, pp. 415–420.

    Article  ADS  Google Scholar 

  11. Mahajan, A. and Tripathi, V.K., Effects of spatially varying gravity, temperature and concentration fields on the stability of a chemically reacting fluid layer, J. Engg. Math., 2020, vol. 125, no. 1, pp. 23–45.

    Article  MathSciNet  MATH  Google Scholar 

  12. Harfash, A.J., Magnetic effect on convection in a porous medium with chemical reaction effect, Trans. Porous Med., 2015, vol. 106, no. 1, pp. 163–179.

    Article  MathSciNet  Google Scholar 

  13. Huppert, H.E. and Turner, J.S., Double-diffusive convection, J. Fluid Mech., 1981, vol. 106, pp. 299–329.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Huppert, H.E. and Moore, D.R., Nonlinear double-diffusive convection, J. Fluid Mech., 1976, vol. 78, no. 4, pp. 821–854.

    Article  ADS  MATH  Google Scholar 

  15. Costa, L.N., Knobloch, E., and Weiss, N. O., Oscillations in double-diffusive convection, J. Fluid Mech., 1981, vol. 109, pp. 25–43.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Sibgatullin, I.N., Gertsenstein, S.I., and Sibgatullin, N.R., Some properties of two-dimentional stochastic regimes of double-diffusive convection in plane layer, Chaos, 1976, vol. 13, no. 4, pp. 1231–1241.

    Article  ADS  MATH  Google Scholar 

  17. Afanasyev, A., Onset of Darcy–Bénard convection in a horizontal layer of dual permeability medium with isothermal boundaries, J. Fluid Mech., 2020, vol. 899, no. A18, pp. 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  18. Shekhar, S., Rogoju, R., Reddy, G.J., and Sheremet, M.A., The Coriolis effect on thermal convection in a rotating sparsely packed porous layer in presence of crossdiffusion, Coatings, 2022, vol. 12, no. 1, pp. 1–20.

    Google Scholar 

  19. Horton, C.W. and Rogers, F.T., Convection currents in a porous medium, J. Appl. Phys., 1945, vol. 16, no. 6, pp. 367–370.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Lapwood, E.R., Convection of a fluid in a porous medium, Proc. Cambridge Philos. Soc., 1948, vol. 44, no. 4, pp. 508–521.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Homsy, G.M. and Sherwood, A.E., Convective instabilities in porous media with through flow, AlChE J., 1976, vol. 22, no. 1, pp. 168–174.

    Article  Google Scholar 

  22. Nield, D.A. and Bejan, A., Convection in Porous Media, New York: Springer, 2006.

    MATH  Google Scholar 

  23. Babu, A.B., Ragoju, R., and Tagare, S.G., Nonlinear rotating convection in a sparsely packed porous medium, Commun. Nonlinear Sci. Numer Simulat, 2012, vol. 17, no. 12, pp. 5042–5063.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Yadav, D., Numerical investigation of the combined impact of variable gravity field and throughflow on the onset of convective motion in a porous medium layer, Int. Comm. Heat Mass Trans., 2019, vol. 108, p. 104274.

  25. Ragoju, 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., 2017, vol. 38, no. 11, pp. 1579–1600.

    Article  MathSciNet  Google Scholar 

  26. Ragoju, R., Kanchana, C., Reddy, G.J., and Basha, H., Study of Soret and Dufour effects and secondary instabilities on Rayleigh-Benard convection in a couple stress fluid, Eur. Phys. J. Plus, 2018, vol. 133: 513, pp. 1–14.

    Google Scholar 

  27. Pradhan, G.K. and Samal, P.C., Thermal stability of a fluid layer under variable body forces, J. Math. Anal. Applications, 1987, vol. 122, no. 2, pp. 487–495.

    Article  MathSciNet  MATH  Google Scholar 

  28. Harfash, A.J. and Alshara, A.K., Chemical reaction effect on double diffusive convection in porous media with magnetic and variable gravity effects, Korean J. Chem. Engg., 2015, vol. 32, no. 6, pp. 1046–1059.

    Article  Google Scholar 

  29. Rionero, S. and Straughan, B., Convection in a porous medium with internal heat source and variable gravity effects, Int. J. Engg. Sci., 1990, vol. 28, no. 6, pp. 497–503.

    Article  MathSciNet  MATH  Google Scholar 

  30. Straughan, B., Convection in a variable gravity Field, J. Math. Anal. Applications, 1989, vol. 140, no. 2, pp. 467–475.

    Article  MathSciNet  MATH  Google Scholar 

  31. Harfash, A.J., Three-dimensional simulations for convection in a porous medium with internal heat source and variable gravity effects, Transp. Porous Med., 2014, vol. 101, no. 2, pp. 281–297.

    Article  MathSciNet  Google Scholar 

  32. Deepika, N. and Narayana, P.A.L., Effects of vertical throughflow and variable gravity on Hadley–Prats flow in a porous medium, Transp. Porous Med., 2015, vol. 109, no. 2, pp. 455–468.

    Article  MathSciNet  Google Scholar 

  33. Mahabaleshwar, U.S., Basavaraja, D., Wang, S., Lorenzini, G., and Lorenzini, E., Convection in a porous medium with variable internal heat source and variable gravity, Int. J. Heat Mass Trans., 2017, vol. 111, pp. 651–656.

    Article  Google Scholar 

  34. Chand, R., Rana, G.C., and Kango, S.K., Effect of variable gravity on thermal instability of rotating nanofluid in porous medium, FME Transactions, 2015, vol. 43, no. 1, pp. 62–69.

    Article  Google Scholar 

  35. Shekhar, S., Ragoju, R., and Yadav, D., The effect of variable gravity on rotating Rayleigh–Bénard convection in a sparsely packed porous layer, Heat Trans., 2022, vol. 51, no. 5, pp. 4187–4204.

    Article  Google Scholar 

  36. Kaloni, P.N. and Qiao, Z., Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects, Int. J. Heat Mass Trans., 2001, vol. 44, pp. 1585–1591.

    Article  MATH  Google Scholar 

  37. Alex, S.M. and Patil, P.R., Effect of variable gravity field on soret driven thermosolutal convection in a porous medium, Int. Comm. Hear Mass Trans., 2001, vol. 28, no. 4, pp. 509–518.

    Article  Google Scholar 

  38. Alex, S.M., Patil, P.R., and Vankatakrishan, K.S., Variable gravity effects on thermal instability in a porous medium with internal heat source and inclined temperature gradient, Fluid Dyn. Res., 2001, vol. 29, no. 1, pp. 1–6.

    Article  ADS  Google Scholar 

  39. Yadav, D., The onset of Darcy–Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects, Heat Trans., 2020, vol. 49, no. 5, pp. 1–10.

    Article  Google Scholar 

  40. Alex, S.M. and Patil, P.R., Effect of a variable gravity field on convection in an anisotropic porous medium with an internal heat source and inclined temperature gradient, J. Heat Trans., 2002, vol. 124, no. 1, pp. 144–150.

    Article  Google Scholar 

  41. Yadav, D., Numerical solution of the onset of buoyancy-driven nanofluid convective motion in an anisotropic porous medium layer with variable gravity and internal heating, Heat Trans., 2020, vol. 49, no. 3, pp. 1170–1191.

    Article  Google Scholar 

  42. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, New York: Dover, 1961.

    MATH  Google Scholar 

Download references

ACKNOWLEDGMENTS AND FUNDING

One of the authors (Ravi Ragoju) gratefully acknowledges the assistance for this research work provided by “Science and Engineering Research Board”, Department of Science & Technology, India, under the Grant no. ECR/2017/000357 and another author (Dhananjay Yadav) gratefully acknowledges the University of Nizwa Research Grant (Grant no.: A/2021-2022-UoN/3/CAS/IF), the Sultanate of Oman for supporting this work.

Author information

Authors and Affiliations

  1. Department of Applied Sciences, National Institute of Technology Goa, Goa, India

    S. Shekhar & R. Ragoju

  2. Department of Mathematical and Physical Sciences, University of Nizwa, Nizwa, Oman

    D. Yadav

Authors
  1. S. Shekhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Ragoju
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to S. Shekhar, R. Ragoju or D. Yadav.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shekhar, S., Ragoju, R. & Yadav, D. The Effect of Variable Gravity and Chemical Reaction on Double Diffusive Convection in a Sparsely Packed Porous Layer. Fluid Dyn 57, 1065–1079 (2022). https://doi.org/10.1134/S0015462821101201

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462821101201

Keywords:

Search

Navigation