Rayleigh-Benard Convection in a Dielectric Liquid : Imposed Time-Periodic Boundary Temperatures
We discuss the thermal instability in a layer of dielectric ﬂuid when the boundaries of the layer are subjected to synchronous/asynchronous time-periodic temperatures. Only inﬁnitesimal disturbances are considered. Perturbation solution in powers of the amplitude of the applied temperature ﬁeld is obtained. In the case when the Imposed Time-periodic Boundary Temperatures (ITBT) at the two walls are synchronized then for moderate values of frequency the role of the electric Rayleigh Number in inducing subcritical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The dielectric parameters and Prandtl number have the opposite eﬀect at large frequencies. The system is most stable when the ITBT is asynchronous. The problem has relevance in many dielectric ﬂuid applications wherein regulation of thermal convection is called for.