An Experimentally Validated Model for Transport in Thin, High Thermal Conductivity, Low CTE Heat Spreaders

Passive phase-change thermal spreaders such as vapor chambers have been widely employed to spread the heat from small-scale high-flux heat sources to larger areas. In the present work, a numerical model for ultra-thin vapor chambers has been developed which is suitable for reliable predictions of the operation at high heat fluxes and small scales. The effects of boiling in the wick structure on the thermal performance are modeled and the model predictions are compared with experiments on custom-fabricated devices. The model predictions agree reasonably well with experimental measurements and reveal the input parameters to which thermal resistance and vapor chamber capillary limit are most sensitive. NOMENCLATURE A area, m C specific heat capacity at constant pressure, J/kg K CE Ergun’s coefficient, 0.55 CTE coefficient of thermal expansion g acceleration due to gravity, m/s hevap convection heat transfer coefficient defined for evaporation, W/mK hfg latent heat, J/kg k thermal conductivity, W/m K keff effective thermal conductivity, W/m K K permeability of the porous medium, m L length, m '' m mass flux, kg/ms M mass, kg M molecular weight, g/mol P pressure, Pa '' q heat flux, W/m R gas constant, J/kgK R universal gas constant, J/molK r radius, m t time, s T temperature, K TGP thermal ground plane u x-direction velocity, m/s v y-direction velocity, m/s V  velocity vector, m/s w z-direction velocity, m/s x axial coordinate; axial distance, m y, z transverse direction coordinates; transverse distance, m Greek symbols α thermal diffusivity, m/s γlv surface tension between liquid and vapor phases, N/m Ω area on the upper surface of the vapor chamber   accommodation coefficient ρ density of liquid, kg/m ε porosity of the wick θ contact angle between liquid and solid surface ν kinematic viscosity, m/s μ dynamic viscosity, Ns/m Subscripts a adiabatic section c condenser e evaporator equ equilibrium eff effective i, lv interface Proceedings of the ASME 2011 Pacific Rim Technical Conference & Exposition on Packaging and Integration of Electronic and Photonic Systems InterPACK2011 July 6-8, 2011, Portland, Oregon, USA InterPACK2011-52039 I Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/13/2013 Terms of Use: http://asme.org/terms 2 Copyright © 2011 by ASME l liquid max maximum op operating pressure ref reference s solid sat saturation condition v vapor w wall