摘要
This work presents a 1-D simplified steady-state numerical/theoretical model to predict the maximum heat transfer rate (Qmax) and the minimum thermal resistance (Rmin) for an ultra-thin vapor chamber (UTVC). The condensate film is assumed sufficiently thin that its shear effect on the vapor is negligible; wall shear is modeled as for a dry surface. Mass and energy conservation are preserved by further assuming the condensing vapor flow out of the UTVC’s condenser. The remaining task is to numerically solve the steady-state laminar momentum equations for the compressible vapor to flow through the thin vapor duct with numerous support pillars. Although 3-D analysis is conducted for the form drag from the cylindrical pillars, the UTVC can still be regarded as 1-D due to the small pillar distance. The pressure drop and subsequent temperature drop, based on the Clausius-Clapeyron equation, can then be computed numerically. The thermal resistance associated with the vapor flow is determined. Then, the Qmax can be determined by equating the capillary force to the pressure drops from the vapor and liquid flows, and adding with the heat transfer through the sealing edge. The R is calculated considering a theoretical parallel combination for the vapor evaporation through the latent heat and the conduction via the solid pillars. The numerical/theoretical results are validated with experimental data for novel nearly 1-D straight and slender UTVCs with a #200 mesh wick under horizontal and vertical orientations. Afterward, the proportions of the liquid drop and the vapor drop, as well as the values of Qmax under different orientations and values of tv, the vapor velocity, vapor density, and vapor flow rate distributions, decomposition of Qmax into the latent heat, the sensible heat via the evaporator pillars and the heat transfer through the sealing edge, the effects of the effective convection heat transfer coefficient provided by the cold-plate, etc. can all be revealed. The vapor duct thickness (tv) below which the pressure drop increases drastically is also found at about 0.3 mm for the present 1-D 100 × 20 mm2 UTVC. The critical tv,crit beyond which the Qmax hardly increases, is found to be about 0.5 mm.