Semi-Analytical Solution of Thermoacoustic Heat Transfer in a Pulse Tube in the Presence of Pulsating Internal Heat Source

Abstract

In this paper, thermoacoustic flow and heat transfer in a pulse tube are investigated. The driving force of thermoacoustic flow is a pulsating internal heat source. The governing equations for the problem include continuity, momentum, energy, and the ideal gas law. The governing equations are solved semi-analytically by considering the decomposition of a main flow and a two-dimensional oscillating flow with variable thermophysical properties. The semi-analytical solution method is the Leibniz-Maclaurin power series method. The semi-analytical solution of the present study is in good agreement with the analytical solution of previous studies. The results show that there is a maximum point for pressure and an inflection point for velocity. The locations of these points are around the middle of the pulse tube length. Increasing the internal heat source increases the pressure and temperature and reduces the density. Fluid friction losses reduce the gain of work flux density and radial velocity gradients increase the gain fluctuations. The results of the present research can be considered as an augment heat transfer tool to improve the performance of pulse tube engines, pulsating heat pipes, electronic device coolers, and so on.