The Leidenfrost Effect, or how I didn't burn myself in the kitchen

The transfer of heat, the energy content of materials tied to the disorganized motion of their constituents, is big business.  A typical car engine is cooled by conducting heat to a flowing mixture of water and glycol, and that mixture is cooled by transferring that heat to gas molecules that get blown past a radiator by a fan.  Without this transfer of heat, your engine would overheat and fail.  Likewise, the processor in your desktop computer generates about 100 W of thermal power, and that's carried away by either a fancy heat-sink with air blown across it by a fan, or through a liquid cooling system if you have a really fancy gaming machine.

Heat transfer is described quantitatively by a couple of different parameters.  The simplest one to think about is the thermal conductivity \(\kappa_{T}\).  If you have a hunk of material with cross-sectional area \(A\) and length \(L\), and the temperature difference between the hot side and the cold side is \(\Delta T\), the thermal conductivity (units of W/m-K in SI) tells you the rate (\(\dot{q}\), units of Watts) at which thermal energy is transferred across the material:  \( \dot{q} = \kappa_{T} A \Delta T/L\).

Where things can get tricky is that \(\kappa_{T}\) isn't necessarily just some material-specific number - the transport of heat can depend on lots of details.  For example, you could have heat being transferred from the bottom of a hot pot into water that's boiling.  Some of the energy from the solid is going into the kinetic energy of the liquid water molecules; some of that energy is going into popping molecules from the liquid and into the gas phase.  The motion of the liquid and the vapor is complicated, and made all the more so because \(\kappa_{T}\) for the liquid is \(>> \kappa_{T}\) for the vapor.  (There is a generalized quantity, the heat transfer coefficient, that is defined similarly to \(\kappa_{T}\) but is meant to encompass all this sort of mess.)  If you think about \(\dot{q}\) as the variable you control (for example, by cranking up the knob on your gas burner), you can have different regimes, as shown in the graph to the right (from this nice wikipedia entry).  

At the highest heat flux, the water right next to the pan flashes into a layer of vapor, and because that vapor is a relatively poor thermal conductor, the liquid water remains relatively cool (that is, because \(\kappa_{T}\) is low, \(\Delta T\) is comparatively large for a fixed \(\dot{q}\)).    This regime is called film boiling, and you have seen it if you've ever watched a droplet of water skitter over a hot pan, or watched a blob of liquid nitrogen skate across a lab floor.  The fact that the liquid stays comparatively cool is called the Leidenfrost Effect.   This comparatively thermal insulating property of the vapor layer can be very dramatic, as shown in this Mythbusters video, where they show that having wet hands allows you to momentarily dip your hand in molten lead (!) without being injured. Note that this demo was most famously performed by Prof. Jearl Walker, author of the Flying Circus of Physics, former Amateur Scientist columnist for SciAm, and inheritor of the mantle of Halliday and Resnick.  The Leidenfrost Effect is also the reason that I did not actually burn my (wet) hand on the handle of a hot roasting pan last weekend.

This heat transfer example is actually a particular instance of a more general phenomenon.  When some property of a material (here \(\kappa_{T}\)) is dramatically dependent on the phase of that material (here liquid vs vapor), and that property can help determine dynamically which phase the material is in, you can get very rich behavior, including oscillations.  This can be seen in boiling liquids, as well as electronic systems with a phase change (pdf example with a metal-insulator transition, link to a review of examples with superconductor-normal metal transitions ).