Maximum Temperature Rise in the Reacted Zone of Electrochemical Devices for Space Applications

A model to predict the temperature rise in the reacted zone of discharging electrochemical devices has been developed. The model assumes that electrode kinetics are fast and concentration gradients are negligible. In the reacted zone, a thermal boundary layer grows, and its thickness is proportional to the reacted zone thickness. In the model, the temperature rise is predicted using the one-dimensional heat diffusion equation for a porous medium. The effective heat capacity per unit volume and effective thermal conductivity are defined as a function of electrode porosity. The instantaneous power per unit area dissipated in the reacted zone is used as a source term in the heat diffusion equation. With fixed parameters such as discharge current density, charge capacity per unit volume, electrode electrical conductivity, electrode porosity, and thermophysical properties of the pore-space fluid and electrode, the transient temperature distribution in the reacted zone is derived in closed-form. Subsequently, the maximum electrode temperature is readily obtained, and the maximum electrode temperature at complete discharge is derived. A new dimensionless parameter, the electro-thermal number, emerges as one of the most important parameters controlling the discharge time and maximum temperature rise.