A pulse combustion heat exchanger that is configured to accept oxidant (1A1) and fuel (1A2) and output a cooled combustion stream (1A5), including: (a) an oxidant inlet section that is configured to accept oxidant (1A1); (b) a fuel inlet section that is configured to accept fuel (1A2); (c) a mixing section including a first plurality of aerovalves (A, A', A") that are configured to accept and mix oxidant (1A1) from the oxidant inlet section with fuel (1A2) from the fuel inlet section to create an oxidant and fuel mixture (1A3); (d) a combustion section configured to receive oxidant and fuel mixture (1A3) from each of the first plurality of aerovalves of the mixing section and combust the oxidant and fuel mixture (1A3) to produce a pulsating combustion stream (1A4); (e) a heat transfer section configured to receive the combustion stream (1A4) from the combustion section, the heat transfer section including a second plurality of resonance conduits (502, 502A, 502B, 502C, 502D, 502E) that are configured to transfer heat from the combustion stream (1A4) to an energy sink, wherein combustion of the oxidant and fuel mixture (1A3) may continue to take place within the second plurality of resonance conduits of the heat transfer section; (f) a first transition section positioned between the combustion section and the heat transfer section, the first transition section comprising a first coolant path configured to receive a first coolant; (g) a second transition section connected to the heat transfer section and configured to receive the combustion stream (1A4) from the heat transfer section and output a cooled combustion stream (1A5), the second transition section comprising a second coolant path configured to receive a second coolant; and (h) a decoupler section connected to the second transition section and configured to accept the cooled combustion stream (1A5) from the second transition section and output the cooled combustion stream (1A5) via a combustion stream outlet. (a) an oxidant inlet section that is configured to accept oxidant (1A1); (b) a fuel inlet section that is configured to accept fuel (1A2); (c) a mixing section including a first plurality of aerovalves (A, A', A") that are configured to accept and mix oxidant (1A1) from the oxidant inlet section with fuel (1A2) from the fuel inlet section to create an oxidant and fuel mixture (1A3); (d) a combustion section configured to receive oxidant and fuel mixture (1A3) from each of the first plurality of aerovalves of the mixing section and combust the oxidant and fuel mixture (1A3) to produce a pulsating combustion stream (1A4); (e) a heat transfer section configured to receive the combustion stream (1A4) from the combustion section, the heat transfer section including a second plurality of resonance conduits (502, 502A, 502B, 502C, 502D, 502E) that are configured to transfer heat from the combustion stream (1A4) to an energy sink, wherein combustion of the oxidant and fuel mixture (1A3) may continue to take place within the second plurality of resonance conduits of the heat transfer section; (f) a first transition section positioned between the combustion section and the heat transfer section, the first transition section comprising a first coolant path configured to receive a first coolant; (g) a second transition section connected to the heat transfer section and configured to receive the combustion stream (1A4) from the heat transfer section and output a cooled combustion stream (1A5), the second transition section comprising a second coolant path configured to receive a second coolant; and (h) a decoupler section connected to the second transition section and configured to accept the cooled combustion stream (1A5) from the second transition section and output the cooled combustion stream (1A5) via a combustion stream outlet.