Thermal Rectification in Lumped and Nonlumped Multilayer Oscillating Thermomagnetic Devices

Abstract Thermomagnetic devices can exhibit time-periodic oscillations between stationary substrates due to temperature-dependent magnetic forces. These oscillations shuttle thermal energy across the device and can be leveraged for thermal rectification and thermomagnetic energy harvesting applications. If the shuttle is thin and made from a high thermal conductivity material, simple thermally lumped modeling can be used to find the time-averaged heat flow. However, there are no existing analytical solutions that describe the full spatiotemporal temperature and heat flow profiles during time-periodic oscillations of multilayered devices with layers of arbitrary thickness and thermal conductivity. Here, we present experimental measurements of such thermomagnetic devices along with analytical solutions for an arbitrary number of stationary hot-side, stationary cold-side, and oscillating layers. We show that the exact solution for the dc component of the heat flow is in good agreement with a simple closed-form approximate expression that spans the lumped and nonlumped regions. We use the analytical solution to interpret experimental measurements of heat flows in multilayer thermal diode devices made with aluminum, steel, or acrylic materials. The aluminum and steel shuttle devices are well-described by the simple lumped thermal model and have thermal rectification ratios near 3 in air, while the acrylic shuttle displays a nonlumped thermal behavior and has thermal rectification ratios of only 1.6 in air. The measurements and analytical solutions developed here provide insight into the thermal performance of thermomagnetic devices for energy scavenging and thermal rectification applications.