Analytical investigation of oscillating flow heat transfer in pulse tubes

In the present paper, a two-dimensional compressible oscillating flow in the tube section of a pulse tube refrigerator system is modeled, based on the successive approximation method. In this respect, the variables are expanded up to second-order terms. For pulse tubes with an outer adiabatic surface, the conservation equations of mass, momentum, energy, and the equation of state for the ideal gas are applied. The effects of operating frequency and taper angle on the temperature distribution, heat transfer behavior, and time-averaged enthalpy flow during a cycle are investigated. Increasing the frequency leads to a higher heat transfer rate in the pulse tube. The enthalpy flow, as the cooling performance representative of the pulse tube, reaches maximum for an optimum convergent taper angle. The temperature distribution and heat transfer process along the axial direction, as well as the phase behavior of the heat transfer coefficient, are also studied. It is shown that, moving from the cold to the hot end of the pulse tube, the temperature variation domain and heat transfer rate decrease.