Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Be´nard problem of an infinite fluid layer heated from below with Joule heating and cooled from above can be significantly increased through the use of feedback control strategies effecting small perturbations in the boundary data. The bottom of the layer is heated by a network of heaters whose power supply is modulated in proportion to the deviations of the temperatures at various locations in the fluid from the conductive, no-motion temperatures. Similar control strategies can also be used to induce complicated, time-dependent flows at relatively low Rayleigh numbers.

Issue Section:
Natural Convection
Keywords:
Materials Processing and Manufacturing Processes, Natural Convection
Topics:
Fluids, Heating, Joules, Rayleigh number, Temperature, Bifurcation, Computer simulation, Feedback, Flow (Dynamics), Heat conduction, Manufacturing, Materials processing, Natural convection, Stability
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