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I am confused about the theorem quite much.

The theorem says that the time rate of change of a property of a system is equal to the local rate of such property in a control volume plus the efflux of the respective intensive property across its control surface.

I am wondering the effect of the influx and efflux in this theorem. Apparently, the efflux was accounted for in the second term, the control surface integral. However, when we are studying the local rate of a property in a control volume, isn't the effect of influx and efflux has alredy been accounted for?

To me, I think

the local rate of change of a property in a control volume = net production rate in the control volume + net influx across the control surface am I wrong?

So, to put back all the thing into the Reynolds Transport Theorem:

Rate of chnge in a system = net production rate in the control volume + net influx across the control surface + the efflux of the respective intensive property across its control surface??

the net influx and net efflux term shall cancel each other? It sounds strange.

Can anyone tell me if the local rate of change has incorporate the effect of the flux across the control surface?

And please help clear my concept about the theorem. Thanks in advance.

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# Reynolds Transport Theorem

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