I'm not a physicist so if I'm saying Very Silly Things below, I'd appreciate if you left a comment to set me straight.
Fans are devices to move ambient-temperature coolant fluid (read: air) into contact with heat sink fins, so as to maximize heat conduction from the heat sink to the environment. Heat conduction = thermal conductivity * area * temperature difference / distance between the different temperatures [according to Wikipedia]. If you think of the heat sink surface–ambient air -system in terms of that model, a fan would be trying to minimize the distance between the hot heat sink and the cool air. In practice, pushing off the boundary layer of hot air and replacing it with cooler air.
There are also other methods for optimizing the heat conduction equation, here's a small roundup. Endothermic reactions for soaking up heat and transporting it away: heat pipes. Maximize the temperature difference: dry ice, LN2 (plus the boiling is endothermic). Increase thermal conductivity of the coolant fluid: water cooling, mineral oil cooling. Increase conducting area: finned heat sinks, larger heat sinks - and I guess the increased mass acts as a thermal buffer that soaks up spikes in heat production. Decrease distance between the different temperatures: fan pushing in cold air, chimney enhancing natural convection. (Natural convection: hot air expands, making it less dense than cool air, which lets cool air fall below hot air. As long as you have gravity, that is.)
Sci-fi, where our Author reveals his lack of understanding in The Art of Physicks
- You could also get cold air close to the heat sink fins by ionizing air and charging the heat sink with reverse polarity to attract the cool air to the heat sink (hopefully neutralizing the air in the process). Maybe that could get cold air more effectively through the boundary layer than mechanical pushing with a fan? They're doing some commercial research into that, and there's also a DIY Ion Cooler.
- Some sort of channels on the heat sink surface to require less airflow to replace the boundary layer. Funnel the air to a higher velocity to push through the boundary layer more efficiently.
- This is neat: vibrating piezoelectric heat sink fins.
- Heat travels as phonons, maybe you could somehow create a heat waveform and sap it out through destructive interference with an audio source. Sort of like noise cancelling headphones. Audible noise is in the kilohertz range, heat is in the gigahertz range. Apparently these guys at MIT are making phononic mirrors.
- Make the heat do work, cooling the heat sink down in the process. Stuff a heat sink full of piezoelectric crystals to convert the thermal expansion of the heat sink into electricity, conduct the electricity away to cool the heat sink.
- Can heat be focused? Heat up a small region of the heat sink to a high enough temperature for blackbody radiation to really kick in, use mirrors to transport the resulting photons away. (Intensity of blackbody radiation grows as fourth power of absolute temperature, temperature grows roughly linearly with power input (apart from phase changes).
- A meter-high 0.1x0.1m chimney with 50C internal air and 20C room temperature could generate 0.01 m^3/s airflow, or 22 CFM? Plugging in values to Q = C*A*sqrt(2*g*H*(Ti/T0-1)): 0.7 * 0.01m^2 * sqrt(2*9.81m/s^2*1m*(323K/293K-1)) = 0.0099 m^3/s.
- Rotate the chimney, get a fire tornado!
- An interesting page on thermal design