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ISSN Online: 2377-424X

ISBN Print: 978-1-56700-421-2

International Heat Transfer Conference 15
August, 10-15, 2014, Kyoto, Japan

Analytical Prediction of the Transition Point to Weak Turbulent Convection in a Porous Layer Subject to Feedback Control

Get access (open in a dialog) DOI: 10.1615/IHTC15.pmd.009303
pages 6693-6705

Аннотация

The transition point from steady to weak turbulent convection in a porous layer heated from below and subject to feedback control is predicted analytically via the a weak nonlinear analysis using an asymptotic expansion. The analysis builds on previous investigations showing that the transition from steady convection to chaotic convection does not occur at the Hopf bifurcation point, but earlier depending on the initial conditions. The results are being compared to numerical solutions indicating an excellent match as long as the asymptotic expansion is valid and consistent with the basic assumptions. The feedback control is used to promote or suppress the transition to weak turbulence. It is further shown that the feedback control model can be transformed into a corresponding model without feedback control through a simple transformation of variables implying that the main effect the feedback control has on the solution is equivalent to altering the initial conditions. Since the initial conditions affect the transition point to weak turbulence (chaos) and the controller acts as to alter these initial conditions one may use the controller to promote or supress the transition point.