Caloric materials exhibit significant entropy variations when applying appropriate excitation, pushing forward the development of solid-state cooling systems. Their development includes materials' properties optimization, with a focus on their adiabatic temperature change when driven at their limit. In order to sustain the device development, an analytical model for regenerative cooling systems is presented in this work. It consists of a caloric material driven cyclically so that it exhibits harmonic temperature variations, whereas an oscillating fluid layer is exchanging heat with the caloric material, leading to a net heat flux along one given direction. The heat transfer equation was solved analytically for harmonic excitation along the direction perpendicular to caloric materials layers separated by fluid layers. In a second step, the problem was solved along an axis parallel to the layers. In order to validate the model, an experimental proof of concept was developed based on a natural rubber tube inside which water flows harmonically. The comparison between model and experiment is given, while the model highlights the importance of the thermal boundary layer, and how the geometry of the device compensates easily the low thermal conductivity of natural rubber.