Thermoacoustic Heat Transfer in a Cylinder under Non-Uniform Thermal Flow

Abstract

In this paper, the effect of non-uniform main thermal flow on thermoacoustic heat transfer in a cylinder is investigated. In order to model thermoacoustic phenomenon, the hydrodynamic and thermal parameters of the flow are considered as the decomposition of a main flow and oscillating flow. The general and particular governing equations, including continuity, momentum, energy, and the ideal gas law, are developed assuming transient two-dimensional viscous flow in cylindrical coordinate. Various functions (linear, exponential, logarithmic, sine, and Bessel) are considered for the main flow temperature. From the simplification of the governing equations, a series of ordinary differential equations have been obtained, which have been solved semi-analytically. The semi-analytical results of the present study are in good agreement with the analytical results of previous studies. The results of the present study show that the logarithmic temperature function for the main flow provides the highest gain of work flux density. However, the linear temperature function also provides a relatively good gain and can be created more easily than the logarithmic function.