A Validated Time-Stepping Analytical Model for 3D Transient Vapor Chamber Transport

Advances in the computational performance of electronic devices have created a clear need for improved methods of passive thermal management. This has led to renewed interest in the use of vapor chambers as heat spreaders in applications ranging from mobile devices to high-performance-computing and power electronics systems. While there has been significant effort to develop vapor chambers for these applications, their designs have largely relied on steady-state analyses and performance prediction. In many applications, however, the heat load is inherently transient in nature. Heat spreader design must consider transient performance in response to these use-case scenarios. While detailed numerical models of transient vapor chamber operation have been developed, a transient modeling approach with low computational cost is needed for parametric study and quick assessment of vapor chamber performance in system-level models. In the current work, a low-cost, transient vapor chamber model is developed targeting the geometries and operating conditions typical of thermal management applications. The model considers mass, momentum, and energy transport in the vapor chamber wall, wick, and vapor core as well as phase change at the wick-vapor interface. The governing equations are simplified to a system of first-order differential equations based on a scaling analysis and assuming a functional form for the temperature profile along the thickness dimension. The errors in the temperature and pressure fields due to these simplifying assumptions are estimated for a wide range of operating conditions. These estimates indicate low errors in the model predictions over the range considered. For two example cases, the model predictions are compared to a finite-volume-based numerical model. Any deviation from the numerical model prediction is on the same order as the errors estimated based on the simplifying assumptions. The time-stepping analytical model is demonstrated to have a computational cost reduction of three to four orders of magnitude compared to the finite-volume based model