Radial buoyancy effects on momentum and heat transfer in a circular Couette flow

Onset of thermal convection in non-colloidal suspensions

“…2013; Kang et al. 2017)

Figure 13.Profiles of the heat current normalized by for . Here, Ra * = 2245.92 for Ra = 3000, Ra * = 4491.84 for Ra = 6000, and Ra * = 6737.76 for Ra = 9000.

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“…To characterize the critical states of the flow, we use the Landau equation, which describes the evolution of the flow perturbation in its weakly nonlinear regime, and it can be determined as (Landau & Lifshitz 1976; Guckenheimer & Holmes 1983; Kang et al. 2017, 2019 a , b ) Here, is the linear growth rate of the perturbation and l is the Landau constant, where the sign of l indicates the nature of the bifurcation (i.e. supercritical versus subcritical).…”

“…They both can be determined from the linear stability analysis (Kang et al. 2017, 2019 a , b ). In this study, the coefficients are zero (i.e.…”

“…The bifurcation is supercritical (non-hysteretic) if l is positive , while a negative value of l indicates a subcritical (hysteretic) transition (Kang et al. 2017, 2019 a , b ). The sign of l can be identified practically from the behaviour of the instantaneous growth rate as a function of at a vanishing .…”

“…To evaluate the heat transfer caused by the convective flow, the conserved heat current yielded by averaging the energy equation (2.4) in the x -direction has been estimated as follows (Kang et al. 2017): …”