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Turbocharger-Non-adiabatic compression

Turbocharger-Non-adiabatic compression

Turbocharger-Non-adiabatic compression

(OP)
I have a question regarding the compresion occring in compressor of a turbocharger under non adiabati conditions.
If you look at the attached file a diagrama of a non adiabatic compression is reported.
The real non-adiabatic process is 1>2
The adiabatic process is 1-2adi

I would like to know if we can consider the non adiabatic process as a sum of the processes (1>2adi)+(2adi>2): from the diagram it seems clear tha this assumption seems to be right but is there a way to demonstarte this mathematically? Could the polytropic process describe the non-adiabatic compression 1>2?
This diagram was taken bt Seume and Shabaan that dealt with the effects of heat transfer on a turbocharger. However they did not explain on which physical basis it was erlying.

many thanks

Ax

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