Analytical solution for temperature profiles at the ends of thermal buffer tubes

The distortion of temperature profiles at the ends of thermal buffer tubes is related to the time-dependent gas pressure and motion in both nearly adiabatic and nearly isothermal environments during one acoustic cycle. The analytical solution for the mean temperature distribution is derived assuming zero heat conduction between gas parcels and linear acoustics with the acoustic wavelength much longer than other system dimensions. Theoretical results are compared with some experimental data and with results of numerical simulations that assume high heat conductivity.