1.) Condenser
2.) TXV or capillary tube.
3.) Vortex tube
4.) Heat-exchanger (vortex tube directly connected here)
What size TXV or cap tube?
What refrigerant?
How many CFM at what pressure do you need fro the vortex to operate?
How many CFM do yo anticipate through the HX?
WIth the "hot" end of the vortex tube sealed, how are you going to get enogh "hot exhaust" to have flow? Dont tell me that the heat sink will be enough, It wont.

I am not asking these questions to help you along with your "project". I am asking you these questions to show you that you are missing some basic understanding of refrigeration. You should stop using your superior google fu for this advanced cooling system and put it to work on your basic understanding of refrigeration. If you dont believe me when I tell you that you need this, then please start buying parts and assembling this unit. Then you can tell me I was wrong.

Here it is in BIG Letters

Crawl, Walk, Run

You are trying to do a marathon at this time.