We are working on a wearable headband device which gives cold therapy to specific locations on head using Thermoelectric Peltier element. We currently have a very reliable control circuitry for the level of cold when we use large heatsink at hot side of the Peltier. Since it will be a wearable device, it should be portable, lightweight and not too big in size. So, heatsink for the hot side should be as small as possible- if possible without fan.
How do I make a good heat sink without a fan?
A good heat sink without a fan needs to be large (lots of surface area) and have low thermal resistance (high thermal conductivity material & thick) so that the whole heat sink surface is working for you. Fins can't be too close together.
Usually that means a heavy heat sink because you need a thick metal (eg. aluminum) base and fins.
There are exotic materials, namely diamond, that can be used to reduce the mass of the heat spreader but they may not be affordable enough. You still need the fins to transfer heat to the air, ideally they could also be CVD.
Alternately, you could consider a relatively quiet/small fan as used in a notebook or tablet computer, or use liquid to transfer the heat to a bulkier heat sink worn elsewhere on the body.
TE coolers are quite inefficient so there is a lot of heat to dispose of, much more than is being removed from the target area. Mechanical refrigeration is more efficient.
Unfortunately to make the cold side cold you will need a way to dissipate the heat into air. You can do this with a fan a heat sink or combination of the two. The more surface area you give to heat sink the better heat dissipation to air you will have.
Another option is maybe a water cooled solution to spread the heat out similar to PC water cooling circuits.
If fans and excessive weight are out, then you might want to consider heat pipes as heat spreaders, to get the heat from the small TEC hot side, and out to a large lightweight heatsink.
