One-dimensional models for heat and mass transfer in pulse-tube refrigerators

This paper studies systems of partial differential equations modelling puls e-tube refrigerators. Through a regular asymptotic expansion, the pressure is found to be a known function of time. Therefore, models for heat and mas s transfer are derived neglecting the equation for conservation of momentum ; the cooling mechanism being highlighted in terms of this model. New appro ximate formulas are derived for the velocity in the tube and the non-linear thermal wave speed in the porous medium (known as the regenerator) on the short (piston oscillation) time-scale. The temperature dependence of the th ermal wave speed is proposed as one measure of the efficiency of the transp ort of heat away from the cold heat exchanger. Progress is limited on the l ong time-scale, however, the importance of the difference between the gas t emperature averaged over an oscillation and heat exchanger temperature is i dentified. (C) 2001 Elsevier Science Ltd. All rights reserved.