# Stirling Engine: LDT and high heat input?

1. Oct 28, 2007

### zytrahus

Hello,
I am working toward my new Stirling engine prototype for a particular application. Let me start with a small description of what I am going to try anyways:

I will experiment this with a small electrical heater:
- heat input: 50-100 W (heater thermall insulated on all sides but the die)
- die size: 20x20 mm
- die material: Copper
- thermocouple in the geometrical center of the die (top surface)

I will not control the hot side temperature as I will control the heat input (50-100 W). Depending on the overall thermal resistance of the device, I expect a temperature of 75-80 C on the hot side of the engine. Basically I would like to keep my heater temperature (thermocouple on top of the die) below 80 C.

I will keep water temperature between 20 and 30 C. So I expect a maximum temperature delta of 45-60 C.

I have equipment to measure/control heat input as well as cold temperature (chilled water). I can also measure output RPM.

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Now my problem:
I know that stirling engine are be very good for thermal dissipation as it uses a gas that is pumped cycle-ly. But let's imagine a stirling engine that is thermally good, i.e. with a low overall thermal resistance... You can give it a lot of heat input and the hot side of the engine will not get too hot, which means a low delta of temperature between the two sides, hence a bad efficiency (cf Carnot). Anyways, even if the efficiency is like 5%, 200 W heat input, you could get 10 W output power.
Now since it's a LDT stirling engine, 'it is said'* that RPM are low. (*I have read about it but never actually seen equations - personnaly I think it's more of a design choice = choice of volumes sizes in order to reduce RPM...).

But here is my problem/understanding: low RPM = big thermal resistance: with low RPM I don't see how we can keep a low delta of temperature between the two sides because the gas used will not move enough energy per second to leep a low temperature. So the hot side temperature will increase, increasing the RPM, decreasing the thermal resistance. The efficiency is also increasing with the hot side temperature (cold side kept constant).
To me, it ends up like this: there is no real way to have both a low delta of temperature and also a large amount of heat input. I know it's possible in the range of DT=60-70C but I am not sure what the heat capacity would be ( check this out: http://www.bsrsolar.com/core1-1.php3 )

What I want, is to use a defined amount of heat and keep my die temperature below one defined maximum (cf description above). I would like to design a stirling engine capable of this job: thermal resisance of xxx C/W (according to my constraints, I already have a good idea of my goal). I know it's a little backward from usual designs as it's always all about delta of temperature and never about heat input...

But anyways, I would like to get advices to design the engine knowing the heat input and a rough idea of the DT.