Regular and chaotic Rayleigh-Bénard convective motions in methanol and water

• Published in: Communications in nonlinear science & numerical simulation 2020-04, Vol.83, p.105129, Article 105129
• Main Authors: Kanchana, C., Su, Yongqing, Zhao, Yi
• Format: Article
• Language: English
• Subjects: Bifurcation diagram; Chaos; Convection modes; Fourier series; Hopf bifurcation; Liapunov exponents; Lyapunov exponent; Mathematical models; Methanol; Periodic; Rayleigh number; Rayleigh-Bénard convection; Regular; Studies; Water
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.105129

•Regular, chaotic and periodic Rayleigh-Benard convective motions in methanol and water are reported.•The comparison of heat transport between water and methanol is presented.•The merits of methanol and the demerits of water as coolants in thermal systems are documented.•From the study it is evident that methanol is stable in regular and periodic regimes and quite vigorously active in the chaotic regime compared to water.•The percentage of enhanced heat transport in water compared to methanol is just around 0.17%.•The possibility of having a transition region between regular convection and chaotic motions is demonstrated. The study of regular and chaotic Rayleigh-Bénard convective motions in methanol and water is made. The stationary mode of convection is shown to be the preferred one at the onset of convection in the case of both the liquids. Using a higher-order truncated Fourier series representation we arrive at the energy-conserving penta-modal Lorenz model and then the tri-modal Lorenz model is obtained as a limiting case of it. To keep the study analytical the Ginzburg-Landau model is derived from the penta-modal Lorenz model. It is shown that the tri- and the penta-modal Lorenz models predict exactly the same results leading to the conclusion that the tri-modal Lorenz model is a good enough truncated model for a weakly nonlinear study of convection. The Rayleigh numbers at which the onset of regular convective and chaotic motions occur are reported for both methanol and water. The behavior of the dynamical system is studied using the spectrum of Lyapunov exponents, the maximum Lyapunov exponent, the bifurcation diagram and the phase-space plots. The Hopf bifurcation Rayleigh number is obtained analytically. It is shown that the thresholds for onset of regular and chaotic motions are smaller in the case of methanol compared to water. Another very important finding of the paper is to show the existence of a developing region for chaos before becoming fully-developed.