Gain and efficiency of a short traveling wave heat engine

Gain and efficiency equations are derived for a short regenerator in a travelling wave heat engine. The following are assumed: small amplitude waves, nonturbulent flow, a constant heat exchange coefficient, and no regenerator end effects. Since the short regenerator has a minimal effect on the wave impedance, the wave impedance is determined by the acoustical circuit exterior to the regenerator. The normalized acoustic power gain and the second-law efficiency are calculated and graphed as functions of dimensionless variables. For acoustical impedances of free waves, and a Prandtl number of 0.7, the efficiency is 10 percent of Carnot efficiency due to viscous losses in the regenerator. For higher impedances, that is, if the impedance is multiplied by 10, the efficiency rises to 76 percent. Methods to increase the wave impedance are discussed. Traveling wave heat pumps are similarly modeled and have comparable potential efficiencies.