Modeling of Subcooled Boiling Heat Transfer to Cool Electronic Components in a Micro-Channel

This paper aims to model a subcooled flow boiling in a vertical stainless-steel micro-channel with an upward flow in 1 mm diameter, 40 mm length and 0.325 mm thickness tube. Water has been considered as a working fluid. The heat flux varies from 600 - 750 kW∙m −2 , input velocity from 1 - 2 m∙s −1 , and the subcooled temperature varies from 59.6 - 79.6 K. The working pressure and saturation temperature are 1 atm and 372.75 K, respectively. The results show that, the flow boiling keeps the temperature of the channel wall lower and more uniform than a single-phase flow, as long as the flow boiling does not reach the dry-out point. The onset point of dry-out depends on three factors, heat flux, inlet velocity, and subcooled temperature. In addition, the dry-out occurs at a point near the channel inlet with increased heat flux and subcooled temperature. Decreasing the inlet velocity would also cause the dry-out point to shift closer to the inlet of the channel.


Introduction
The amount of heat removal of electronic chips is considered as one of the challenges and limitations for shrinking the size of the electronic components. Presently, most chips and electronic circuits are cooled by fins and air fans that have limited heat transfer capabilities. Boiling heat transfer because of high heat transfer capabilities while maintaining at a constant temperature seems a solution for this obstacle. Especially if liquids of low boiling temperature could be used or take advantages of subcooled boiling condition of higher boiling temperature of water. It is well known that the latent heat of boiling is much greater than the sensible heat transferred to liquids. The corresponding heat transfer coefficients in boiling are much greater than the same coefficient in single-phase condition while keeping the temperature at a constant value of boiling condition. Keeping the temperature of electronic elements and circuits at a constant value would influence the service life of these components. Use of boiling heat transfer in reducing the operating temperature of the electronic components while increasing the amount of heat transfer by a significant amount with relatively small surface areas have been under considerable research in recent years. Boiling heat transfer in milli-and micro-channels constitutes numerous studies carried out in which some of them will be reviewed in the following.
Falsetti et al. [1] have experimentally studied two-phase flow boiling to cool a micro-pin fan. Ethanol and acetone with a boiling point of 78.4˚C and 56˚C respectively were used as working fluids by Radwan et al. [2] for cooling concentrator photovoltaic Forced boiling heat transfer in horizontal and vertical mini-channels with upward flow have been experimentally investigated by Saisorn et al. [3]. Channel with 1.7 mm diameter and length of 600 mm was used as a test section with mass flow rate of 200 -1000 kg•m −2 •s −1 , a heat flux ranging from 1 -80 kW•m −2 and saturation pressure of 7 -13 bar have been examined. They reported that the heat transfer coefficient depends on flow pattern as well as direction of the flow.
The effects of channel dimension, heat flux, and the flow rate on flow boiling regimes in micro-channels have been experimentally investigated by Harirchian and Garimella [4]. In their work, Fluorinert FC-77a, perfluorinated dielectric fluid, have been used as a working fluid with mass flux ranging from 225 -1420 kg•m −2 •s −1 . Channel width ranging from 100 -5850 μm, and all with a depth of 400 μm and a length of 12.7 mm have been considered. They reported that flow pattern for micro-channel of 400 μm depth and larger are similar and nucleate boiling is dominated. However, flow patterns in smaller channels differ from those of 400 μm depth and bubble nucleation at the wall is suppressed. In addition, their results show that as channel width increases, bubble flow replaces by slug flow and intermittent churn/wispy-annular flow replaces intermittent churn/annular H. Abbasinejad, R. Hosseini Abardeh Journal of Electronics Cooling and Thermal Control flow. Furthermore, for microchannel of 400 μm and larger the heat transfer coefficient is almost independent of the channel size.
Ong and Thome [5] have investigated the flow boiling of R134a, R236fa, and R245fa in a horizontal circular channel with a diameter of 1.030 mm. This study was performed with a heat flux range of 2.3 -250 kW•m −2 , mass flux range of 200 -1600 kg•m −2 •s −1 , and a subcooled temperature range of 2 -9 K at a saturation temperature of 31˚C. A correlation between the boiling heat transfer coefficients, the mass flow rate and heat fluxes have been presented. They reported that the subcooled temperature did not affect the heat transfer coefficient.
Owhib et al. [6] conducted an experimental work on saturated flow boiling in microchannels. They have measured the heat transfer coefficients for saturated boiling of R134a in vertical channels with internal diameters of 1.7, 1.224, and 0.826 mm. A uniformly heated length of 220 mm, with a mass flow rate ranging from 50 -400 kg•m −2 •s −1 , and the heat flux ranging from 3 -34 kW•m −2 with two different pressures of 8.626 and 6.458 bar have been investigated. Their results show that the heat transfer coefficient is a strong function of the heat flux and system pressure, while it is almost independent of mass flux and vapor quality.
Yu et al. [7] have examined the boiling heat transfer of water in a small-diameter horizontal tube with an inner diameter of 2.98 mm and a heated length of 0.91 m. mass flux in a range of 50 -200 kg•m −2 •s −1 , inlet temperature from ambient to 80˚C, and a system pressure of 200 Kpa have been considered. Their findings suggest that the heat transfer coefficients and pressure drop for this channel differ from those in wider channels. In addition, the boiling heat transfer depends on heat flux and independent of mass flow rate.
The numerical and experimental study of Zhang et al. [8] indicates a very good agreement between their results. The flow boiling in rectangular channels with hydraulic diameters between 25 -60 μm and aspect ratios 1 to 3.5 have been considered.
Hosseini et al. [9]   As mentioned above, the boiling heat transfer mechanism would be one of the possible solution for increasing the amount of heat removal from electronic components and integrated circuits. An obstacle presently exists in reducing the size of the electronic components. This implies more serious studies about this mechanism and parameters affecting the process, especially in milli-and micro-channels. The main aim of the present work therefore is, investigation of the flow boiling in a stainless steel microchannel with a diameter of 1 mm, length of 40 mm, and a thickness of 0.325 mm. The heat applied to the channel wall is considered equivalent to the heat generated by all electronic components exists in a chip or integrated circuit. Of course, in order to get better understanding on how the boiling heat transfer affects the temperature of the channel wall, a comparison will be made between single-phase and two-phase flow boiling. The parameters affecting the mechanism of the boiling heat transfer and the dry-out phenomenon on the flow boiling and heat transfer will be addressed in next sections.

Governing Equations
The Eulerian-Eulerian model in the fluent code was used to model the flow field and boiling process. Equations for each phase (liquid and vapor) are presented and solved separately. The Rensselaer Polytechnic Institute (RPI) model is also applied for boiling on the channel wall.

Continuity Equations
In the Eulerian multiphase boiling model, the continuity equation is defined as follow [11] [12]: where q v is the phase velocity, pq m  is mass transfer from p th to q th phase, qp m  is mass transfer from q th to p th phase, and q S is an external mass source on the q th phase that here has been considered 0 [11] [12].

Momentum Equation
The momentum equation is given by [12] ( ) ( ) virtual mass exchange force, and , td q F is a turbulent dispersed force, and pq R is the interaction drag force between the two-phases.

of Electronics Cooling and Thermal Control
where q τ , q µ and q λ are shear stress tensor, shear viscosity and bulk viscosity of q th phase, respectively.

Energy Equation
The energy equation is expressed as follows [12]: where q h , q q and q S are specific enthalpy, heat flux and an external heat source of q th phase, respectively. pq Q and pq h are heat transfer and enthalpy between p th and q th phases, respectively.

Turbulence Model Equation
In this study, turbulence κ-ɛ model has been used for the mixture; these two parameters are expressed as following [12]: (6) where the density, molecular viscosity, and velocity are given by Equations (7) to The turbulence viscosity and turbulence kinetic energy are defined by the following Equations (10) and (11) respectively: The terms m k Π and m ε Π in Equations (5) and (6)

Equations Governing RPI Model
According to the RPI model, a well-known model developed by Kurul & Podowski [13], the total heat flux transferred from the wall to the fluid mixture includes three parts: the convective heat flux ( C q  ), the quenching heat flux ( Q q  ), and the evaporation heat flux ( E q  ): where convective heat flux is shown in Equation (13): In Equation (13), c h is the liquid phase heat transfer coefficient, b A is the influence area, w T and l T are the wall and the liquid temperature, respectively.
Quenching heat flux is defined in Equation (14): where l k is the thermal conductivity, bw f is the frequency of bubble departure Evaporation heat flux is defined in Equation (15): In Equation (15) The parameters required in Equations (13) to (15) are defined below: The Influence area in Equation (13) is defined in Equation (16): where k, is the empirical coefficient and is determined by the relation suggested by Del Valle and Kenning [14] as given in Equation (17): where sub Ja is the subcooled Jacob number given by Equation (18): The frequency of Bubble departure is defined in Equation (19) Active nucleate site density is calculated from Equation (21).
V q  and G q  are given in Equations (25) and (26) according to [12]: The function ( ) l f α in Equation (24) depends on the local liquid/vapor volume fraction that can be calculated by the relation proposed by Loilev et al. [19]: where the breakpoints have been set to

Problem Statement and Boundary Conditions
In this work, the subcooled boiling heat transfer is investigated in a vertical microchannel with an upward flow in 1 mm diameter channel with 40 mm length and stainless-steel material. The thickness of the channel is 0.325 mm. Figure 1 provides  Table 1.  the thermophysical properties of the fluid due to the change in temperature was considered linear, and modeling was performed in a two-dimensional, steady state and no-slip boundary condition for two phases. Coupled algorithm (pressure based coupled algorithm) has been used for pressure-velocity coupling. Constants temperature at inlet and constant heat flux on wall channel have been use as boundary conditions. The κ-ɛ model was used for turbulence. It should be noted that because of symmetry, a half channel was simulated to reduce the computational time.

Validation and Grid-Independence
For validation of the two-phase flow modeling, the experimental work of Owhaib et al. [6] first was modeled and the results obtained were then compared with their given experimental findings. The information of experimental work of Owhaib et al. [6] on the flow boiling in the vertical microchannel are presented in Table 2. Figure 2 and Figure 3 represent the modeling and the experimental results for two channels with diameters of 1.224 and 0.826 mm, respectively. Based on these figures, the results from modeling are reasonably comparable to those of experimental outcome. Table 3 Figure 4 presents the wall temperature of the channel at outlet position for these two mesh sizes. According to Figure 4, it is clear that     Figure 4. Examination of the mesh sizing on wall temperature of the channel at outlet position. Journal of Electronics Cooling and Thermal Control the mesh size does not affect the modeling results, so that it can be claimed that the obtained result is independent of the mesh sizing. Therefore, a mesh size of (15 * 521) will be used in remaining part of this study.

Results
The results will be shown in this section. First, the superiority of the flow boiling for cooling of the electronic components over a single phase heat transfer will be addressed. Since the dry-out phenomenon has a severe impact on the flow boiling heat transfer, it will be addressed next.   As Figure 6(a) shows, before reaching the dry-out point, the wall temperature all over the length of the channel in the flow boiling condition is lower than that of the single-phase flow. Although the variation of the subcooled temperature do not significantly affect the wall temperature in a single-phase flow, it is clear that the wall temperature will increase as the subcooled temperature decreases in the flow boiling. By decreasing subcooled temperature from 79.6 K to 69.6 K, the wall temperature at the end of the channel rises by 2.1%. Figure 6(b) indicates that T.U.C. in the two-phase flow (boiling), before dry-out point is lower than that of single-phase flow. In the case of dry-out, the temperature difference increases considerably.
With respect to the above results, it is clear that in the flow boiling and away from dry-out point, the wall temperature and its variation is lower than single-phase flow. Accordingly, the flow boiling in microchannel for electronic components cooling is suggested. In the following subsections, the results of the investigated effects of the heat flux, subcooled temperature, and inlet velocity on the flow boiling inside the microchannel will be fully reported.

Effect of Heat Flux on Flow Boiling Heat Transfer
The     the related boiling heat transfer coefficient, which is shown in Figure 12 examined by Kim and Mudawar [21]. By comparison between these two Figures ( Figure 11 and Figure 12), the different flow regimes are clear. According to Kim and Mudawar, the forced convective heat transfer is dominant in this case. The design of the system to be efficiently and effectively used the mechanism of flow boiling heat transfer in cooling electronic equipment and chips, must be such that the system is working in the nucleate boiling region (close to the CHF point).

Effect of Inlet Velocity on Flow Boiling Heat Transfer
Obviously, the fluid inlet velocity is one of the factors influencing the boilingheat transfer. In this section, the effect of the fluid inlet velocity is reported by changing it from 1 -2 m•s −1 . The turbulence in the flow will increase with increasing the fluid inlet velocity which in turn causes the increase of the liquid single-phase heat transfer, while leads to a decrease in the boiling heat transfer as illustrated in Figure 13. Decreasing the boiling heat transfer affect the vapor quality, as illustrated in Figure 14. As can be seen in Figure 14, when inlet velocity increases from 1 to 2 m•s −1 , the vapor quality considerably decreases at the end of the channel.

Effect of Inlet Subcooled Temperature on Flow Boiling Heat Transfer
The subcooled temperature is also one of the parameters influencing the boiling heat transfer, the higher the subcooled temperature means the higher temperature differences between inlet and saturation temperature. Thus, the fluid needs more heat to reach the saturation point. Here, the heat flux of 610 kW•m −2 and inlet velocity of 1 m•s −1 is considered. In Figure 16 the initial point of boiling shown with filled circles indicating that boiling occurs at a point farther from the channel inlet as subcooled temperature increases. In fact, the single-phase heat transfer increases with increasing subcooled temperature. Figure 17 indicates that in the microchannels, the subcooled temperature may significantly affect the vapor quality, such that decreased subcooled temperature from 69.6-59.6 K leads to an increase vapor quality at the end of the channel from 0.000934 to 0.86.    This means that an excessive increase in the vapor quality causes to create early formation of dry-out region. This would in turn greatly increase the wall temperature ( Figure 18) that leads to decrease the effect of flow boiling heat transfer and this is not acceptable for temperature control of the electronic components.

Conclusion
The present paper demonstrates the forced boiling heat transfer inside a micro-channel with upward flow. Results indicate that in the case of flow boiling, the wall temperature is more uniform and lower than the single-phase flow, which positively influences the service life of the electronic components. When the flow boiling reaches the dry-out point the wall temperature increases significantly and therefore it should be avoided the operating condition to reach the dry-out condition. In order to prevent the dry-out condition from happening, the heat flux, inlet velocity, and inlet-subcooled temperatures of the liquid should be carefully controlled. Based on the present results, the probability of dry-out occurrence will increase with increasing the heat flux. Under a high heat flux condition, the dry-out may happen near the channel inlet. The inlet velocity significantly affects the boiling heat transfer and is a key for controlling the dry-out. The dry-out occurs in the case of the inlet velocity of 1 m•s −1 , while it does not occur along the channel with increasing the inlet velocity of 1.5 m•s −1 , and in excess of this velocity. It means that the inlet velocity is one of the most important parameters in the system to prevent dry-out to occur. The subcooled inlet temperature also affects the flow condition and the heat transfer, so that the closer the inlet temperature to the fluid saturation temperature, the higher the probability of dry-out occurrence. Although the application of the flow boiling is recommended for keeping the electronic components working temperature constant and lower value, however, the design conditions should be so that to avoid the dry-out along the channel length. In fact, the system should be designed in such a way that the operating condition be closed in nucleate boiling near the CHF point and region before that.