Thermodynamics of active magnetic regenerators: Part I

Abstract

Cycle-averaged relationships for heat transfer, magnetic work, and temperature distribution are derived for an active magnetic regenerator cycle. A step-wise cycle is defined and a single equation describing the temperature as a function of time and position is derived. The main assumption is that the convective interaction between fluid and solid is large so that thermal equilibrium between fluid and solid exists during a fluid flow phase (regeneration). Relations for the temperatures at each step in the cycle are developed assuming small regenerative perturbations and used to derive the net cooling power and magnetic work at any location in the AMR. The overall energy balance expression is presented with transformations needed to relate the boundary conditions to effective operating temperatures. An expression is derived in terms of operating parameters and material properties when each location is regeneratively balanced; this relation indicates needed conditions so the local energy balance will satisfy the assumed cycle. By solving the energy balance expression to determine temperature distribution one can calculate work, heat transfer, and COP.