5. Thermoacoustic transfer functions of regenerator and stack

The modeling of the stack or regenerator (associated here with the two end heat exchangers) is based on that of one of the elementary capillary ducts (the assembly constituting the complete porous regenerator or the stack of plates constituting the stack). It can be shown that the wave equation for the channel (non-isothermal this time, since we admit the possibility of heat transfers between the gas and the stack or regenerator wall) under consideration is :