  The unsteady response of nozzles with steady heat transfer forced by acoustic
and/or entropy waves is modelled. The approach is based on the
quasi-one-dimensional linearised Euler equations. The equations are cast in
terms of three variables, namely the dimensionless mass, stagnation temperature
and entropy fluctuations, which are invariants of the system at zero frequency
and with no heat transfer. The resulting first-order system of differential
equations is then solved using the Magnus expansion method, where the
perturbation parameters are the normalised frequency and the volumetric heat
transfer. In this work, a measure of the flow non-isentropicity (in this case
the steady heat transfer) is used for the first time as an expansion parameter.
The solution method was applied to a converging-diverging nozzle with constant
heat transfer for both sub-critical and super-critical flow cases, showing good
agreement with numerical predictions. It was observed that the acoustic and
entropy transfer functions of the nozzle strongly depend on the frequency and
heat transfer.
