Sorry Zeranin but Kleinstein is right - that 40mm square peltier will have a thermal conductivity of around .3W/K, so for 5/6 of the time when the power is off approx 12W will be flowing back to the cold side which means it couldn't maintain a 40C deltaT for very long under those operating conditions.
The thermal conductivity can be calculated from the information on page 13 of Laird Tecnologies handbook THR-BRO-Thermal Handbook 0110.pdf. Their CP14,127,10 module is similar to the one you quoted so it has a geometry factor of .077 and 127 elements.
Kleinsten's original posting wan't clear to me, but his later posting, and your posting, are absolutely correct! Thank you. As you say, the correct reason that PWM falls down is because of ‘thermal leakage’ when the peltier is OFF. Everything I said was impeccably correct,
except that I neglected to consider what happens when the PWM peltier is OFF. Ooops.
The correct conclusion then is that for any given Peltier, non-PWM operation provides the best efficiency for all combinations of required cooling power and differential. That said, it would be instructive to look at just
how much worse is PWM operation under typical operating conditions. The good news is that Linear or PWM operation converge to the same thing at full cooling requirement, 100% duty cycle, which is arguably where efficiency matters most. If PWM turns out to be significantly worse only at very low duty cycles, then it’s no big deal. Unfortunately though, the following example, chosen to be a real-world as possible, shows that PWM gives really horrible efficiency under typical partial-load conditions.
Referring to the Peltier plots attached previously, I have chosen an operating condition of Thot=50 DegC, deltaT=40, so Tcold=10 DegC. For this particular Peltier, typical full-power cooling would be at 4A, producing 16W of cooling, and I will analyse the efficiency at 5.33W of cooling power (1/3 of full) using both Linear and PWM voltage drive. The peltier thermal conductivity is taken as 0.3W/K, for a back-leakage of 12W when peltier is OFF. From the peltier data :-
deltaT=40 DegC
I=4A
V=11.2V
Pin = 44.8W
Cooling = 16W
Eff = 36%
Now here is the operating point that gives 5.33W of cooling :-
deltaT = 40 DegC
I = 2A
V = 6V
Pin = 12W
Cooling = 5.33W
Eff = 44%
Now for the crunch, to see how PWM compares at producing 5.33W of cooling :-
Duty cycle = 0.62
Cooling = 0.62 x 16 = 9.92W (while peltier is ON)
Back leakage = (1-0.62) x 12 = 4.56W (while peltier is OFF)
Net Cooling = 9.92-4.56 = 5.36W
Pin = 0.62 x 44.8 = 27.8W (average input power)
Eff = 5.36/27.8 = 19%
Yuk! That is really horrible. To get our 5.3W of cooling, we are pumping in 28W of electrical power, compared to only 12W using a non-PWM input of 6V. To put it another way, the efficiency is worse by a factor of x2.3 I am an efficiency nut, so I do find this very offensive, but we need to keep in mind that the cooling performance of the fridge or whatever won’t be any worse because the 2 drive methods provide the same maximum cooling power, so the only consequence, actually, is that the PWM implementation will consume more electrical power under partial load. Whether this matters depends on the application.
Another interesting point arises on account of that damned back leakage. Usually, it’s good engineering to ‘oversize’ within limits, be it a resistor, power semiconductor, heatsink or whatever. Peltiers are cheap, and we know they are not very efficient, so there is a great temptation (at least for me) to use more or bigger of them than strictly necessary. At worst, it might be thought, you spend a little more on the peltiers than was needed, but in terms of performance and efficiency, intuition suggests you can’t go wrong with using more or bigger peltiers, so each one doesn’t work as hard. That’s the way I always design things! In this case though, for any given requirement of cooling power and differential, there is an
optimum size of peltier that maximizes efficiency. Of course, you need to allow some reserve capacity, but if you greatly oversize the total area of Peltiers, then the efficiency goes to pot, essentially because it takes a significant overhead of electrical power input just to stop the heat flowing backwards through the peltier thermal resistance, before you even get to the stage of pumping the heat in the correct direction. There is no analog of this with compressor cooling systems, and it’s not a nice feature of Peltiers.
Edited in later: Note to Kleinstein. I hadn't read your posting #47 when I wrote this, but we are independently saying the same thing.