• M. A. Alkhadra

Rayleigh–Bénard Convection

Updated: Jun 10, 2018

Try this simple thought experiment: cover the surface of a pan with a layer of cooking oil and heat the pan from below. What do you expect will eventually happen to the oil? The resulting phenomenon is known as Rayleigh–Bénard convection.

In the original experiment, physicist Henri Bénard (1900) studied thermal convection by melting wax in a metal dish, the base of which was hot enough to melt the wax in its entirety. At first, the liquid was completely still, but as the dish was heated above some critical temperature, Bénard observed the formation of a hexagonal pattern of so-called convection cells that appeared on the surface of the wax, as shown in Figure 1.

Above a critical temperature, Bénard observed a hexagonal pattern of so-called convection cells.
Figure 1. Plan view of convection cells forming on the surface of a layer of spermaceti wax heated from below. Image adapted from P. G. Drazin’s text Introduction to Hydrodynamic Stability, 2002.

Lord Rayleigh (1916) modeled this phenomenon using the theory of hydrodynamic stability, which analyses the stability and the onset of instability of fluid motion. (A flow that is unstable typically evolves into the well-known state of motion called turbulence.) The development of these convective cells in the oil, for example, occurs as follows. The temperature of the bottom and top surfaces of the oil is initially the same (this is the stable, unperturbed state). The temperature of the bottom surface is then increased, which establishes a flow of thermal energy—and a concomitant gradient in temperature. This temperature gradient results in a nonuniform density across the liquid; in fact, the density is lowest at the bottom (hot) surface and highest at the top (cold) surface. Natural convection, which is the bulk movement of particles within a fluid, then arises due to this variation in density. In particular, the heavier (more dense) particles of fluid fall, whereas the lighter (less dense) particles rise. The macroscopic Bénard convection cells observed in Figure 1 are the consequence of continuous, ordered rotation of the fluid driven by variations in relative buoyancy. This dynamic mechanism, which describes the formation of Bénard convection cells, is illustrated in Figure 2.

Figure 2. Schematic representation of the experimental setup used to produce Rayleigh–Bénard convection. A container is filled with liquid; the bottom surface is heated, while the top surface is exposed to the cool environment. Image adapted from Alp Yoğurtçuoğlu’s MS thesis.

To summarize, Rayleigh–Bénard convection is flow driven by buoyancy (due to a gradient in density) in a fluid heated from below. Now, what role (stabilizing or destabilizing) do you think the temperature gradient plays in the development of these Bénard convection cells? How about the viscosity of the fluid? In other words, do temperature gradients and viscosity hasten the onset of turbulence, or do they delay it?

Rayleigh–Bénard convection is flow driven by buoyancy in a fluid heated from below.

Although this topic may seem esoteric and of little practical importance, a quick search of “Rayleigh–Bénard convection” on Google returns 77,400 results. According to the late Professor Drazin, “Rayleigh–Bénard convection has been the subject of more theoretical research than its direct physical importance justifies, but it may be regarded as a prototype of many sorts of pattern formation and instability as well as convection.”

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