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In a regeneratively cooled nozzle, there is a transfer of heat from the expanding exhaust to the nozzle (and then into the propellant cooling the nozzle). This is clearly not an adiabatic process. Is flow in regeneratively cooled nozzles still modeled as isentropic flow?

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It's a decent approximation.

The effect of convective heat transfer on the flow is very slight in practical nozzles, since its influence extends only so far as the thermal boundary layer thickness, and this is of the order of the velocity boundary thickness (for typical gases). Radiant heat transfer is also of little importance to propellant behavior, since it is generally smaller than the convective heat transfer.

Hill and Peterson, Mechanics and Thermodynamics of Propulsion, p. 410, 1st edition, 1970 printing.

I found the 2nd edition of this book online (legality unknown) here. The section on nozzles and heat transfer has been extensively rewritten and the quote above does not appear.

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