The following research and patent proves the idea that I've stated. That using the heat of the vortex tube can be applied in a practical manner to assist in the actual cooling process. The heat of the vortex tube is used to drive a pulse refrigeration cycle.
This is what I was ultimately looking for!
Double inlet arrangement for pulse tube refrigerator with vortex heat exchanger
The heat and sound are combined to produce a rapid compression/decompression wave in a chamber. That alternating wave functions like a sterling engine, but with no moving parts. The result is the heated gas is cooled and sent back into the vortex tube. This is a common feedback device. AND IT WORKS!!
Shingoshi
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