Numerical calculation of the temperature difference between the extremities of a thermoacoustic stack plate

When a plate is placed in a thermoacoustic resonator, one extremity of the plate heats up while the other cools down due to the thermoacoustic effect. In the present work the temperature difference between the extremities of the plate is calculated numerically. The computed temperature difference is compared to the one predicted by the linear theory. Some discrepancies are found even at low acoustic Mach numbers. These discrepancies can not be attributed to non-linear effects, rather they exist because of thermal effects. In particular the mean temperature in the fluid and in the plate are not equal. The discrepancies can be eliminated using corrective coefficients. Some deviations between the linear theory predictions and numerical results also occur at higher Mach numbers and are due to non-linearities, and especially temperature non-linearities that are generated in the vicinity of the plate.