The Effect of Internal Temperature Gradients on Regenerator Matrix Performance

Background. One-dimensional regenerator models treat the solid material as a lumped capacitance with negligible temperature gradients. Advanced regenerator geometries operating at low temperatures or active magnetic regenerators which use a liquid heat transfer fluid may have temperature gradients in the solid regenerator that significantly affect performance. It is advantageous to utilize a one-dimensional, or lumped, model of the regenerator that is coupled with a correction factor in order to account for the impact of the internal temperature gradients. Previous work relative to developing such a correction factor is shown here to be inadequate or only valid over a limited range of dimensionless conditions. Method of Approach. This paper describes a numerical model of a sphere subjected to a time varying fluid temperature (representing a passive process) or time varying internal heat generation induced by a magnetic field (representing an active magnetic process). The governing equations are nondimensionalized and the efficiency of the sphere is presented as a function of the Fourier number and Biot number. Results. An approximate correction (or degradation) factor is obtained based on these results that is valid over a wide range of dimensionless conditions and therefore useful to regenerator designers. The degradation factor correlation was developed for a sinusoidal variation in the fluid temperature, however, the same results can be applied to different functional forms of the time variation using the concept of an effective cycle time that is weighted by the magnitude of the driving temperature difference. Conclusions. The heat transfer degradation factor presented here can be applied to one-dimensional regenerator models in order to accurately account for the transient performance of a matrix with finite thermal conductivity. This degradation factor allows regenerator models to approximately account for internal temperature gradients without explicitly modeling them and therefore remain computationally efficient while improving the range of applicability and accuracy.