Numerical analysis and experimental verification on thermal fluid phenomena in a vapor chamber

doi:10.1016/j.applthermaleng.2005.11.012

Applied Thermal Engineering

Volume 26, Issues 14–15, October 2006, Pages 1669-1676

https://doi.org/10.1016/j.applthermaleng.2005.11.012 Get rights and content

Abstract

A numerical analysis is carried out on a flat-plate type heat pipe called “vapor chamber”. The vapor chamber is an advanced cooling heat spreader for high-performance microchips, such as new generation CPUs in personal computers and workstations. The mathematical model of the vapor chamber formulated in this study is a two-phase closed disk-shaped chamber and is placed between a small heat source and a large heat sink. Wick sheets and a wick column are provided inside the vapor chamber to circulate the working fluid. By solving the equations of continuity, momentum and energy numerically, the velocity, pressure and temperature distributions inside the vapor chamber are obtained. From the numerical results, the capillary pressure head necessary to circulate the working fluid is estimated and the temperature drop inside the vapor chamber is determined. These numerical results are useful for the design and improvement of the vapor chamber. Experimental investigation is also carried out, and fairly good agreement is obtained with the numerical results, which confirms the validity of the present numerical analysis.

Introduction

In recent years, data processing performance of microchips, such as central processing units (CPUs) in personal computers and workstations, have progressed dramatically, resulting in a significant increase in heat fluxes generated in these microchips. Mochizuki et al. [1] predicted that the heat fluxes generated in microchips, which were about 10–15 W/cm² in the year 2000, will reach 100 W/cm² in the late 2000s. Therefore, advanced cooling devices are becoming more necessary in electronic industries.

In response to this, a flat-plate type heat pipe called “vapor chamber” has been developed. The vapor chamber is placed between the heat source and the heat sink, which is generally much larger than the former; it works as a heat spreader to spread the heat from the heat source to the heat sink, resulting in the low thermal resistance between them. In addition, the thickness of the vapor chamber is less than 5 mm and it is lighter than the conventional solid copper heat spreaders. Furthermore, the structure of the vapor chamber is so simple that it can be manufactured easily with low cost.

Several experimental research works on the vapor chamber have been already carried out. Koito et al. [2] examined the thermal resistance of the vapor chamber with the changes in the heat flux applied from the heat source, the temperature of cooling air and the inclination angle of the vapor chamber. Mochizuki et al. [3] investigated the cooling performance of the vapor chamber and concluded that the use of the vapor chamber was one of the most effective ways to cool personal computers. On the other hand, various numerical research works on heat pipes have also been carried out. Chen and Faghri [4] presented the numerical analysis on the steady-state cylindrical heat pipes with a single or multiple heat sources. Faghri and Buchko [5] introduced the complete two-dimensional numerical model of the low-temperature cylindrical heat pipes with multiple heat sources. Compared to the model by Chen and Faghri [4], the effect of the liquid flow in the liquid-wick region was included in the model by Faghri and Buchko [5] because the effect is very important in case of the low-temperature heat pipes. Gutierrez et al. [6] carried out the numerical analysis on the transient behavior of the cylindrical heat pipe. Vadakkan et al. [7] developed the three-dimensional mathematical model to analyze the transient and steady-state performance of the flat heat pipes.

Previous numerical analyses on heat pipes are helpful in the development of the mathematical model of the vapor chamber and its numerical solution procedure. However, the previous numerical results on the heat pipes cannot be applied to the design of the vapor chamber because the geometrical and operating conditions of the vapor chamber are essentially different from those of the heat pipes. Furthermore, although the information on the thermal fluid phenomena occurring inside the vapor chamber is necessary to improve the performance of the vapor chamber, very few analytical studies have been published in this respect. In the present study, therefore, a numerical analysis is carried out to investigate the thermal fluid phenomena occurring inside the vapor chamber. Velocity, pressure and temperature distributions inside the vapor chamber are obtained by solving the equations of continuity, momentum and energy numerically. Experimental study is also carried out to investigate the temperature distribution in the vapor chamber, and the experimental results are compared with the numerical results to verify the validity of the mathematical model.

Section snippets

Vapor chamber

A photograph of the heat sink with the vapor chamber is shown in Fig. 1. The vapor chamber is a two-phase closed flat chamber. It is made of copper and water is used as the working fluid. Sintered sheets and sintered columns made of small copper powders (size: 100–200 mesh, porosity: 40%) were used as the wick inside the vapor chamber. The vapor chamber was placed between the heat source and the heat sink, which is much larger than the former (see Fig. 3). Details of the vapor chamber are given

Mathematical modeling and numerical solution procedure

Based on the discussion made by Lee et al. [8], the following equivalent radii of the vapor chamber, r_vc, and the heat source, r_h, are used, and the numerical analysis is carried out in the cylindrical coordinate: $r_{vc} = \sqrt{\frac{A_{vc}}{π}}$ $r_{h} = \sqrt{\frac{A_{h}}{π}}$ where A_vc is the top surface area (=bottom surface area) of the actual vapor chamber, and A_h the contact area of the actual heat source at the bottom of the actual vapor chamber.

The mathematical model of the vapor chamber is formulated as shown in Fig. 2. Although several

Experimental set-up and procedure

The same experimental set-up as described in the authors’ previous paper [2] is used in the present study. Fig. 3 shows the experimental set-up, which consists of a wind tunnel, a heat sink with a vapor chamber, a heater used as the heat source, a blower, an orifice manometer set-up and a damper. The vapor chamber shown in Fig. 1 is placed between the top of the heater and the bottom of the heat sink. The bottom surface area of the heat sink, which is equal to the top and bottom surface areas

Evaluation of thermal resistance of heat sink

Using the authors’ previous experimental results [2] as well as the present experimental results, the value of the thermal resistance of the heat sink, R_hs, is calculated from Eq. (14) and the result is shown in Fig. 5. The average of measured T_t,1–T_t,5 is used to evaluate 〈T_t,exp〉. As expected, R_hs is found to be hardly affected by the heat flux applied from the heat source, q, and the temperature of cooling air, T_air, for q = 16–32 W/cm² and T_air = 20–30 °C. Therefore, the averaged value of R_hs,

Conclusions

The mathematical model of the vapor chamber has been developed. The model consists of the vapor region, the liquid-wick region and the solid wall region. The heat flux was applied from the small heat source to a part of the bottom of the vapor chamber and the top of the vapor chamber was cooled by the large heat sink. Velocity, pressure and temperature distributions inside the vapor chamber were obtained by solving the equations of continuity, momentum and energy for each region numerically.

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