Wall and fluid inlet temperature effect on heat transfer in incompressible laminar oscillating flows

This paper deals with the problem of oscillating flows occurring in devices such as Stirling or thermoacoustic engines and refrigerators. Since the global governing equations cannot be solved, the authors propose to introduce a few simplifications; the most simplifying reduction is that the fluid is assumed to be incompressible. However, specific attention is paid to describing the flow characteristics that's why the Lagrangian formalism which allows the individual study of each fluid particle is adopted. Thereby each particle contribution to global thermal effects can be evaluated and the gas temperature profiles along the exchanger can be computed. Various situations are presented including the case of a non-uniform temperature at the wall and a phase lag between pressure and temperature at the fluid entrance. The efficiency of the wall to fluid thermal exchange is analyzed. The authors show that this exchange depends upon two important parameters: the geometric ratio between the exchanger length and the particle oscillating displacement, and a thermal parameter “β”, governing the temperature profiles and related to the Prandtl number, the operating frequency and the phase lag between the instantaneous heat flux and the wall to fluid temperature difference.