next up previous
Next: The exact equations of Up: Rayleigh-Benard Convection Previous: Rayleigh-Benard Convection

Intrduction

Consider a layer of fluid heated from below. As a result the density at the bottom layer becomes lighter than at the top. The system is thus bottom heavy but does not necessarily undergoes convective motion since viscosity and thermal diffusivity of the fluid try to prevent the convective motion. If the fluid is heated sufficiently large enough (higher temperature gradient across the layer), than only the top heavy state becomes unstable and convective motion ensues. Here we shall consider the condition necessary for the onset of thermal instability.

The first intensive experiments were carried by Benard in 1900. He experimented on a fluid of thin layer and observed appearance of hexagonal cells when the instability in the form of convection developed. Rayleigh in 1916 developed the theory which found the condition for the instability with two free surface. He showed that the instability would results if the temperature gradient $ \beta=-dT/dz$ was large enough so that the so called Rayleigh number

$\displaystyle R_a=\frac{\alpha \beta g d^4}{k\nu}
$

exceeds a certain (critical value). Here $ g$ is the acceleration due to gravity, $ \alpha$ is the coefficient of thermal expansion, $ d$ is the depth of the chamber and $ k,\nu$ are the thermal diffusivity and kinematic viscosity respectively. The parameter $ R_a$ represents the ratio of destabilizing buoyance force to the stabilizing viscous force.

Experiments in the early stage were carried out with fluid heated from bottom at the top surface is open to atmosphere. Thus the top surface is free to move and deform. It was later (around 1960) realized that this can lead to another instability mechanism (Benard-Marangoni convection) due to gradient in surface tension. This mechanism coexists with the Rayleigh's mechanism but dominates in thin layer. Most of the findings reported by Benard were actually due this second instability mechanism. The instabilities driven by surface tension decreases as the layer becomes thicker. Later experiments on thermal convection (with or without free upper surface) have obtained convective cells of many form such as rolls, square and hexagons.


next up previous
Next: The exact equations of Up: Rayleigh-Benard Convection Previous: Rayleigh-Benard Convection
A/C for Homepage of Dr. S Ghorai 2003-01-16