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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.

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. [^{2} heated area composed of 66 rows of cylindrical in-line micro-pin fins with 50 μm diameter, height of 100 μm, and pitch of 91.7 μm have been used as micro-evaporator. The heat flux from 20 - 44 W∙cm^{−2}, the mass flux from 750 - 1750 kg∙m^{−2}∙s^{−1}, and the dielectric refrigerant R134a have been considered as a working fluid. They reported a very stable flow boiling behavior for R134a. They found that the heat transfer coefficients are strongly depended on the vapor quality and the heat flux but slightly influenced by mass flux.

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} has been considered. Their findings indicate that the counter flow operation of forced convective boiling achieved temperature uniformity as low as 1.6˚C and 1.8˚C with the velocity range of 25 - 100 ml∙h^{−1} for ethanol and 50 - 300 ml∙h^{−1} for acetone, respectively.

Forced boiling heat transfer in horizontal and vertical mini-channels with upward flow have been experimentally investigated by Saisorn et al. [^{−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 [^{−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 flow. Furthermore, for microchannel of 400 μm and larger the heat transfer coefficient is almost independent of the channel size.

Ong and Thome [^{−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. [^{−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. [^{−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. [

Hosseini et al. [^{−2}. The heat transfer coefficients were calculated by measuring wall superheat of the samples and the input heat flux. The obtained results have shown significant effect of surface material, with copper providing the highest heat transfer coefficient among the samples, and aluminum the least. Concerning the roughness effect, the results show significant improvement of the heat transfer coefficient as the surface roughness is increased. The samples were treated by different sand paper grit sizes to achieve different surface roughness (Ra). It was found that the heat transfer coefficient of the sample with Ra = 0.901 is 3.4%, 10.5%, and 38.5% higher in comparison with surfaces with Ra of 0.735, 0.65, and 0.09 respectively at heat flux of 170 kW∙m^{−2}.

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.

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.

In the Eulerian multiphase boiling model, the continuity equation is defined as follow [

∂ ∂ t ( α q ρ q ) + ∇ ⋅ ( α q ρ q v q ) = ∑ p = 1 n ( m ˙ p q − m ˙ q p ) + S q . (1)

where v q is the phase velocity, m ˙ p q is mass transfer from p^{th} to q^{th} phase, m ˙ q p is mass transfer from q^{th} to p^{th} phase, and S q is an external mass source on the q^{th} phase that here has been considered 0 [

The momentum equation is given by [

∂ ∂ t ( α q ρ q v q ) + ∇ ⋅ ( α q ρ q v q v q ) = − α q ∇ p + ∇ ⋅ τ ¯ ¯ q + α q ρ q g

∑ p = 1 n ( R p q + m ˙ p q v p q − m ˙ q p v q p ) + ( F q + F l i f t , q + F w l , q + F v m , q + F t d , q ) (2)

where F q is external body force, F l i f t , q is lift force, F w l , q is wall lubrication force, F v m , q virtual mass exchange force, and F t d , q is a turbulent dispersed force, and R p q is the interaction drag force between the two-phases.

τ ¯ ¯ q = α q μ q ( ∇ v q + ∇ v q T ) + α q ( λ q − 2 3 μ q ) ∇ ⋅ v q I ¯ ¯ (3)

where τ ¯ ¯ q , μ q and λ q are shear stress tensor, shear viscosity and bulk viscosity of q^{th} phase, respectively.

The energy equation is expressed as follows [

∂ ∂ t ( α q ρ q h q ) + ∇ ⋅ ( α q ρ q v q h q ) = α q ∂ p q ∂ t + τ ¯ ¯ q : ∇ v q − ∇ ⋅ q q + ∑ p = 1 n ( Q p q + m ˙ p q h p q − m ˙ q p h q p ) + S q (4)

where h q , q q and S q are specific enthalpy, heat flux and an external heat source of q^{th} phase, respectively. Q p q and h p q are heat transfer and enthalpy between p^{th} and q^{th} phases, respectively.

In this study, turbulence κ-ɛ model has been used for the mixture; these two parameters are expressed as following [

∂ ∂ t ( ρ m k ) + ∇ ⋅ ( ρ m v m k ) = ∇ ⋅ ( ( μ m + μ t , m σ k ) ∇ k ) + G k , m − ρ m ε + Π k m (5)

∂ ∂ t ( ρ m ε ) + ∇ ⋅ ( ρ m v m ε ) = ∇ ⋅ ( ( μ m + μ t , m σ ε ) ∇ ε ) + ε k ( C 1 ε G k , m − C 2 ε ρ m ε ) + Π ε m (6)

where the density, molecular viscosity, and velocity are given by Equations (7) to (9):

ρ m = ∑ i = 1 N α i ρ i (7)

μ m = ∑ i = 1 N α i μ i (8)

v m = ∑ i = 1 N α i ρ i v i ∑ i = 1 N α i ρ i (9)

The turbulence viscosity and turbulence kinetic energy are defined by the following Equations (10) and (11) respectively:

μ t , m = ρ m C μ k 2 ε (10)

G k , m = μ t , m ( ∇ v m + ( ∇ v m ) T ) : ∇ v m (11)

The terms Π k m and Π ε m in Equations (5) and (6) relate the turbulence interactions between the dispersed and continues phases of the flow. In this modeling, the values of constant coefficients are assumed equal to those of the used software.

According to the RPI model, a well-known model developed by Kurul & Podowski [

q ˙ W = q ˙ C + q ˙ Q + q ˙ E (12)

where convective heat flux is shown in Equation (13):

q ˙ C = h c ( T w − T l ) ( 1 − A b ) (13)

In Equation (13), h c is the liquid phase heat transfer coefficient, A b is the influence area, T w and T l are the wall and the liquid temperature, respectively.

Quenching heat flux is defined in Equation (14):

q ˙ Q = 2 k l π λ l f b w ( T w − T l ) (14)

where k l is the thermal conductivity, f b w is the frequency of bubble departure and λ l = k l ρ l C p l is the liquid phase diffusion coefficient.

Evaporation heat flux is defined in Equation (15):

q ˙ E = π 6 d b w 3 f b w N w ρ v h l v (15)

In Equation (15), d b w , N w , ρ v , h l v are bubble departure diameter, active nucleate site density, density of the vapor phase, and latent heat of evaporation, respectively.

The parameters required in Equations (13) to (15) are defined below:

The Influence area in Equation (13) is defined in Equation (16):

A b = min ( 1 , k N w π d b w 2 4 ) (16)

where k, is the empirical coefficient and is determined by the relation suggested by Del Valle and Kenning [

k = 4.8 e − J a s u b 80 (17)

where J a s u b is the subcooled Jacob number given by Equation (18):

J a s u b = ρ l C p l Δ T s u b ρ v h l v (18)

where Δ T s u b = T s a t − T l .

The frequency of Bubble departure is defined in Equation (19) based on the model developed by Cole [

f b w = 1 T = 4 g ( ρ l − ρ v ) 3 ρ l d b w (19)

Bubble departure diameter is calculated from Equation (20) based on the model developed by Tolubinski-Kostanchuk [

d b w = min ( 0.0014 , 0.0006 exp ( − Δ T s u b 45 ) ) (20)

Active nucleate site density is calculated from Equation (21).

N w = C n ( T w − T s a t ) n (21)

where n = 1.805 and C = 210 based on Lemmert-Chawla correlation [

Other relations for active nucleate site density provided by Kocamustafaogullari and Ishii [

N w * = f ( ρ * ) r c * − 4.4 (22)

where

N w * = N w d b w 2 r c * = 2 r c d b w r c = 2 σ T s a t ρ v h l v ( T w − T s a t ) ρ * = ρ l − ρ v ρ v

The density function in Equation (22) is calculated from Equation (23):

f ( ρ * ) = 2.157 × 10 − 7 ρ * − 3.2 ( 1 + 0.0049 ρ * ) 4.13 (23)

According to the base model of RPI, the vapor temperature is assumed constant and equal to the saturation temperature. The vapor temperature and the amount of heat transferred are needed in the solution process in order to model non-equilibrium boiling and critical heat flux (CHF). The modified RPI relation to contain a term for the diffusive heat flux of the vapor phase q ˙ V and the heat flux to any other possible gas phases q ˙ G , is given in Equation (24):

q ˙ W = ( q ˙ C + q ˙ Q + q ˙ E ) f ( α 1 ) + ( 1 − f ( α 1 ) ) q ˙ V + q ˙ G (24)

q ˙ V and q ˙ G are given in Equations (25) and (26) according to [

q ˙ V = h V ( T W − T V ) (25)

q ˙ G = h G ( T W − T G ) (26)

The function f ( α l ) in Equation (24) depends on the local liquid/vapor volume fraction that can be calculated by the relation proposed by Loilev et al. [

f ( α v ) = 1 − f ( α l ) = max ( 0 , min { 1 , α v − α v , 1 α v , 2 − α v , 1 } ) (27)

where the breakpoints have been set to α v , 1 = 0.9 and α v , 2 = 0.95 .

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. ^{−1}, inlet subcooled temperature of 59.6 - 79.6 K, and heat flux in the range of 600 - 750 kW∙m^{−2}. Water was used as a working fluid at a pressure of 1 bar and saturation temperature of 372.75 K. The thermophysical properties of stainless steel and water in the two liquid and vapor phases at the different inlet and saturation temperatures are provided in

First of all, modeling was performed in the single-phase flow without applying the energy equation; a velocity profile obtained from this single-phase flow was applied as a boundary condition for boiling flow. Then, enable the energy equation and take Eulerian model to simulate boiling heat transfer. Non-equilibrium

μ (kg/(m∙s)) | K (W/(m∙K)) | C_{p} (J/(kg∙K)) | ρ (kg/m^{3}) | Material |
---|---|---|---|---|

0.0001001 | 0.5985 | 4185 | 998.2 | Water (T = 293.15 K) |

0.000797 | 0.6155 | 4180 | 995.6 | Water (T = 303.15 K) |

0.000653 | 0.631 | 4178 | 992.2 | Water (T = 313.15 K) |

0.0002829 | 0.679 | 4216 | 958.64 | Liquid Water (T = 372.75 K) |

0.000012256 | 0.025 | 2076 | 0.59 | Vapor Water (T = 372.75 K) |

- | 16.27 | 502.48 | 8030 | stainless steel |

model has been applied to calculate the temperature of the vapor. The change in 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.

For validation of the two-phase flow modeling, the experimental work of Owhaib et al. [

Two mesh sizes (15 * 521) and (25 * 869) have been used in order to examine the grid dependent results.

T_{in} (˚C) | T_{sat} (˚C) | G (kg/(m^{2}∙s)) | q (kW/m^{2}) | Channel diameter (mm) | Fluid |
---|---|---|---|---|---|

34 | 34 | 300 & 400 | 10 - 35 | 1.224 & 0.826 | Water |

d = 1.224 | d = 0.826 | Diameter (mm) | |||
---|---|---|---|---|---|

400 | 300 | 400 | 300 | Mass Flux (kg/(m^{2}∙s)) | |

10% | 5.38% | 5% | 16.66% | 10 | Heat Flux (kW/m^{2}) |

10.52% | 10.47% | 8.33% | 4.54% | 15 | |

12% | 4.16% | 5.55% | 15.38% | 20 | |

10.34% | 7.93% | 4% | 4.76% | 25 | |

9.37% | 11.7% | 12.38% | 4.16% | 30 | |

5.88% | 9.16% | 17.39% | 1.85% | 35 |

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.

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. The results considered here are for the velocity in the range of 1 - 2 m∙s^{−1}, subcooled temperature in the range of 59.6 - 79.6 K, and heat flux in the range of 600 - 750 kW∙m^{−2}.

^{−2} in both single-phase and two-phase flows. The inlet velocity of fluid is V I n l e t = 1 m ⋅ s − 1 and the subcooled temperature is Δ T s u b = 69.6 K .

from inlet to outlet. A sudden increase in temperature of the wall observed as the heat flux reaches to 700 kW∙m^{−2} and over, indicates a severe decrease in the heat transfer coefficients due to the dry-out. It is well known that, the life times of the electronic components are dependent strongly on their operating temperatures. According to ^{−2}, respectively. However, in the case of heat flux of 750 kW∙m^{−2}, the temperature at the end of the channel in two-phase flow is 74.5% higher than that of single-phase flow, because of entering to the dry-out condition. Therefore, if the operating temperatures can be controlled at lower range by use of the flow boiling as indicated in

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.

The amount of heat flux applied to the channel wall is one of the parameters influencing the heat transfer coefficients. To study this issue, the heat flux applied to the channel were changed from 650 - 750 kW∙m^{−2}, while the inlet velocity and subcooled temperature remain constant at 1 m∙s^{−1} and 69.6 K, respectively.

As can be seen in ^{−2}, a sudden increase in the wall temperature observed which is an indication of reaching to the dry-out point. The dry-out point would get closer to the channel inlet as the heat flux increases. To better represent the distribution of heat transfer,

^{−2}. Based on this figure, the vapor volume fraction will increase as the heat flux increases. By increasing the heat flux from 600 to 750 kW∙m^{−2}, the vapor volume fraction goes up 188 times. Dry-out occurs in the channel as the value of vapor quality increases causing a sharp drop in the heat transfer coefficients in the channel, which is illustrated in

the boiling heat transfer coefficient decreases significantly as the vapor covers the whole surface of the channel wall. In

^{−2}. According to this figure, there are three distinct regions, single-phase liquid heat transfer, nucleate boiling heat transfer, and the dry-out. This figure illustrates the relationship between these three regions and the related boiling heat transfer coefficient, which is shown in

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 ^{−1}, the vapor quality considerably decreases at the end of the channel.

^{−1}, it is not observed with increasing the inlet velocity to 1.5 m∙s^{−1} and 2 m∙s^{−1}. As a result, the flow inlet velocity is one of the important parameters influencing the dry-out, so that the inlet velocity can be used to control the flow and avoid the dry-out condition.

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

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 (

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.

The authors declare no conflicts of interest regarding the publication of this paper.

Abbasinejad, H. and Hoseini Abardeh, R. (2020) Modeling of Subcooled Boiling Heat Transfer to Cool Electronic Components in a Micro-Channel. Journal of Electronics Cooling and Thermal Control, 9, 1-21. https://doi.org/10.4236/jectc.2020.91001