Revisiting thermal penetration depth for caloric cooling system

Thermal penetration depth is a physical quantity identifying the distance that heat can diffuse through the domain material, which has been widely adopted for thermoacoustic cryocoolers in the past, where the diffusive thermal resistance is the only dominating factor for gaseous refrigerant. By ignoring the surface convection thermal resistance, we show that the conventional thermal penetration depth significantly overestimates the cooling performance of the caloric material. This paper modifies the conventional thermal penetration depth with the consideration of convection thermal resistance and applies this concept to caloric cooling devices. The modified thermal penetration depth can be computed by the approximate fitting formula, which is numerically validated by CFD simulation results. The influence of physical properties and geometric parameters of materials on thermal penetration depth is discussed. In addition, the modified thermal penetration depth can be visualized on Biot number and Fourier number chart, which can guide design of future caloric cooling systems. This design approach is supported by the experimental data from the literature.