Is it more efficient to stack two Peltier modules or to set them side by side? Is it more efficient to stack two Peltier modules or to set them side by side?
And why?
I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing.
(I want to keep my camera cool, so I'm putting in this cool box.
The camera looks through a flat glass window on one side of the box).
The heatsink I have on hand is about twice as wide as the widest Peltier module I originally planned on using.
So there's room to put 2 Peltier modules side-by-side under the heatsink.
Or I could center a stack of 2 Peltier modules under the heatsink.
Which arrangement is more efficient?
I have to cut a bigger hole in the insulation for the side-by-side arrangement, so the unwanted heat that "back-flows" through the side-by-side arrangement is worse.
On the other hand, other effects are worse for the stacked arrangement.
(Is https://electronics.stackexchange.com/ a better place to post questions about Peltier coolers?)
 A: If efficiency is the issue, then definitely parallel TECs (or use a single unit rated for twice the power, same thing).  The only reason for stacking TECs is to get a lower temperature.  However that comes at great expense to efficiency and overall power consumption.
Another point is that paralleling TECs is actually more efficient overall.  The reason is that TECs are more efficient at lower power.  The cooling power is proportional to the current, but the internal heating is due to internal I2R losses, so goes with the square of the current.  At low currents a small increment in current causes more cooling than additional internal heating.  However, eventually the squared term wins and at the top of the parabola a small current increment causes the same heating as the additional current is able to cause the device to remove.  That's the maximum cooling point, but is also the least efficient point along the normal operating range.
Two indetical TECs in parallel therefore need less than 1/2 the current each than a single one would need for the same cooling power.  Another way to put this is that except for money and space constraints, you want to oversize the TEC for efficiency.
A: You'll want a much bigger heatsink!!
(and maybe just one TEC)
If it's being cooled only by convection then maybe a heat sink area* that is 10 times that of the TEC.  (maybe bigger)  
The classic mistake with a TEC is to make the heat sink too small.  With too small a heatsink the hot side of the TEC gets hotter, more thermal leakage through the TEC, it has to work harder to keep the same temperature.. and the whole thing goes into thermal runaway.
*one should really talk about the volume of the heatsink.  
A: An efficiency of 10% does not mean you require 100W to produce 10W of cooling.  This is complete nonsense.  Efficiency is comparing the amount of heat shifted with the ideal Carnot cycle. In the ideal Carnot cycle 'coefficient of performance' (COP) values of over 5 are possible. That is why the efficiency of a TEM can be low but the COP actually quite reasonable, just no where as good as a vapour compression cycle.  In most applications 100W of power supplied will shift about 50W of heat, give or take.
A: For a 20 degree Celsius differential, parallel devices will be more efficient, if the devices are operating in their normal range of heat removal. If your camera box is extraordinarily well insulated and you can wait for hours and hours for it to cool down, then a series arrangement with both devices running at less than about 10% of maximum power is most efficient.
The reason has to do with the graphs supplied by the manufacturer of your module. Typically you can get efficiencies of better than 200% for delta T of 10 degrees at low heat flow, so that's 100% for 2 in series. Double the heat flow and the required power almost quadruples, so efficiency is 110% per module or 55% overall.
In parallel, 2 devices with a delta T of 20 degrees might be 75% efficient at the total heat flow of the first case in the previous paragraph. With the doubled heat flow of the second case, the efficiency might be 85%.
Running Peltier devices at near their rated power is very inefficient and requires a lot of care to prevent thermal runaway and device destruction. Avoid it if possible.
Heat sinks on both sides need to be very effective, and you should consider a fan for the hot side, vibration isolated from the camera.
A: Thermoelectric coolers (TECs) are horrendously inefficient (slightly better now than a decade ago, but not really by that much).  Cooling a hunk of inert material is the easiest.  Cooling and controlling the temperature of an active, power dissipating device is harder.  Much harder.
Example:  back in the optical telecom boom days, I was working on the packaging for an optical switching device.  The main designers were all excited because they had worked a design that integrated the active optical material and the rf drive circuits onto a little substrate perhaps a square centimeter or so.  I asked for the specs on how cold, and how much power the circuits would need, and they said is was only 10W, and it didn't need to be that cold, just controlled.
Well, commercially available TECs were roughly 10% efficient at that time.  So, to pump 10W off the substrate required 100W of power to the TEC.  This in turn meant that 110W was dumped to the heatsink at room temperature.  That meant a roughly 4"x4" TEC, and a huge honking 6"x6" heatsink with giant fan.  So, that beautiful tightly integrated device meant a giant package.
What does this mean for you?  Well, you stack TECs in order to make your cold object colder.  But it comes at a big penalty in how much power your "cold" object is allowed to expend.  That first stage is only 10% efficient.  The second stage has to be sized so that all the power of the device AND the first TEC can be pumped through it, and at only 10% efficiency again.  Ouch.  In the case above, a second stage would have been pumping 110W, so it would have needed about 1100W  to pump that, meaning 1210W overall.  Your efficiency goes to hell with stacked TECs - each additional stage has to inefficiently pump the inefficiencies of all the previous stages.
If you want to be as efficient as possible, use a single stage.  That will limit your ultimate temperature, but will pull the most power off the cooled device.  If you want the lowest temperature possible, stack your TECs, but understand that the maximum power your can dissipate will drop like a stone.
