Everyone is familiar with the Carnot cycle for both heat engines and heat pumps.
In an effort to simplyfy developing working systems based on the Stirling engine/pump, I developed the concept of thermal torque.
Paralleling the simple concept of a mechanical lever, one can more quickly determine thermal properties needed to achieve certain goals. The diagram below illustrates the concept. The formulas in the diagram are all constants of any given system for ideal carnot engines/pumps.
The lever is drawn as a simple mechanical lever but in reality will be a more complicated system. It may be comprised of a Stirling engine connected to a Stirling heat pump
Here's an example:
Example:
A group of picnickers wish to keep a refrigerated container at 45 degrees throughout the day.
The air temperature is 90 degrees F. There is a small stream flowing through their picnic area with a constant temperature of 60 degrees F. They know that the refrigerated container will require about 250 BTU/hr to stay at 45 degrees.
To use the above formula temperatures must be converted to an absolute scale (one where 0 is absolute 0). For calculation purposes we will use the Rankine scale.
The conversion formula is ﹾR= ﹾF + 459.67
They’ll use the air as TH1, The stream will provide the sink TL1 and and also Tdest.
The refrigerated container is Tsource which is set 45ﹾ F
Converting all temperatures to rankine we get:
TH1 = 549.67 ﹾR TL1= 519.67 ﹾR
Tsource = 504.67 ﹾR Tdest = 519.67 ﹾR
ΔT1 = 30 ﹾR and ΔT2 = 15 ﹾR
QH2 is 250 BTU/hr
QH2 divided by Tsource times ΔT2 equals 62.5. 62.5 is now the required thermal Torque.
QH1 can be calculated by simple algebra QH1 =( 62.5 *549.67) /30.
QH1 = 1145.15 BTU/hr And QL1 = 1082.65 BTU/hr
Result: They’ll need to absorb about 1145 BTU/hr from the air and dump 1083 into the creek in order to get 250 BTU/hr of cooling at 45 ﹾF
The benefit is that it’s a free 250 BTUs/hr.
This can be improved by increasing TH1 by using a solar absorber.
For example by using a solar absorber at 120 ﹾF (579.67 ﹾR) for TH1, the amount of heat needed for QH1 is reduced to only 622.57 BTU/hr which can be achieved with a panel of about 2.5 square feet. The solar absorber could be nothing more than a flat black piece of metal connected to something that can transmit the heat into the input of the lever.
To date, as far as I know there is nothing commercially available that can be used for a “Thermal Lever”.
The most promising devices available are built around the Stirling engine. Stirling engines are already being used in Arizona to achieve solar efficiency of about 30 %.
The Stirling engine has a cousin called a Stirling heat pump. By coupling a Stirling engine to a Stirling heat pump a thermal lever can be created.
There is an excellent Utube video describing the process and the device https://www.youtube.com/watch?v=X1fiABe4x08
Hi David,
Thanks for sharing "The concept of direct thermal leveraging and thermal torque". It is quite an interesting concept. Can you please elaborate more on QL1, QH1, and other notations?
I am unable to understand the direction of the flow of heat on the heat pump side.