Heat exchangers are of key importance in overall performance and commercialization of thermoacoustic devices. The main goal in designing efficient thermoacoustic heat exchangers (TAHXs) is the achievement of the required heat transfer rate in conjunction with low acoustic energy dissipation. A numerical investigation is performed to examine the effects of geometry on both the viscous and thermal-relaxation losses of shell-and-tube TAHXs. Further, the impact of the drive ratio as well as the temperature difference between the oscillating gas and the TAHX tube wall on acoustic energy dissipation are explored. While viscous losses decrease with d i / δ κ , thermal-relaxation losses increase; however, thermal relaxation effects mainly determine the acoustic power dissipated in TAHXs. The results indicate the existence of an optimal configuration for which the acoustic energy dissipation minimizes depending on both the TAHX metal temperature and the drive ratio.