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Convective heat and mass transports and chaos in two-component systems: comparison of results of physically realistic boundary conditions with those of artificial ones

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Abstract

Linear and weakly nonlinear stability analyses of double-diffusive convection in two-component liquids with either potassium chloride (KCl) or sodium chloride (NaCl) aqueous solution, and heat being present is investigated in the paper for free, and rigid, isothermal, iso-solutal boundaries. Using the thermophysical values of the aqueous solutions, we have shown that the stationary convection is the preferred mode at onset and that sub-critical motion is possible. We found that the critical thermal Rayleigh number for water + NaCl + heat is higher compared to that of water + KCl+ heat. The study shows that for water + KCl + heat, the transition from convective motion to chaotic motion occurs at \(r_{\mathrm{H}}=27.2\) for free boundaries and at 48.5 for rigid boundaries. Here, \(r_{\mathrm{H}}\) denotes the Hopf thermal Rayleigh number. Further, the existence of windows of mildly chaotic points and fully periodic intervals are reported using Lyapunov exponents and bifurcation diagrams. Chaotic motions in both the aqueous solutions are nearly identical. The percentage increase in heat transport in the double-diffusive system involving NaCl is nearly 1% more than that of KCl in the case of free boundaries, whereas in the case of realistic boundaries it is nearly 1.6%. The comparison of the Nusselt and the Sherwood numbers between water + KCl and water + NaCl leads us to the conclusion that the aqueous solution with lower Lewis number transports maximum heat in the case of free boundaries and opposite is seen in the case of rigid boundaries due to the boundary effect. The many qualitative similarities between the results of artificial and realistic boundaries are highlighted.

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  • 25 March 2022

    The fourth author’s affiliation was incorrectly published as 1, 4. The corrected affiliation of fourth author is 4 which was corrected.

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Acknowledgements

The author(KC) is grateful to the Universidad de Tarapacá, Chile for supporting her research work with the University of Tarapaca, Arica (UTA) Fellowship. The author BS expresses his gratitude to Jawaharlal Nehru Technological University College of Engineering, Hyderabad (JNTUCEH) for financial support under Technical Education Quality Improvement Program (TEQIP)-3 for a year. The authors are grateful to the Reviewers and the Editor for their most valuable comments.

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Authors and Affiliations

  1. Instituto de Alta Investigación, CEDENNA, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren, 2477, Iquique, Chile

    C. Kanchana

  2. Department of Mathematics, CHIRST (Deemed to be University), Bengaluru, 560029, India

    P. G. Siddheshwar

  3. Department of Mathematics, CVR College of Engineering, Ibrahimpatnam, Ranga Reddy District, Telangana, 501510, India

    B. Shanker

  4. Instituto de Alta Investigación, CEDENNA, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    D. Laroze

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  1. C. Kanchana
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  4. D. Laroze
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Correspondence to C. Kanchana.

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Kanchana, C., Siddheshwar, P.G., Shanker, B. et al. Convective heat and mass transports and chaos in two-component systems: comparison of results of physically realistic boundary conditions with those of artificial ones. J Therm Anal Calorim 147, 3247–3266 (2022). https://doi.org/10.1007/s10973-021-10662-0

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