Investigation on Critical Heat Flux of Flow Boiling in Rectangular Microchannels: A Parametric Study and Assessment of New Prediction Method

Abstract

The critical heat flux (CHF) of minichannel heat sinks is crucial, as it helps prevent thermal safety incidents and equipment failure. However, the underlying mechanisms of CHF in minichannels remain poorly understood, and existing CHF prediction models require further refinement. This study systematically investigates the characteristics and influencing factors of critical heat flux (CHF) in rectangular minichannels through combined experimental and theoretical approaches. Experiments were conducted using microchannels with hydraulic diameters ranging from 0.5 to 2.0 mm, with ethanol employed as the working fluid. Key parameters-including mass flux, channel geometry, system pressure, and inlet subcooling-were analyzed to assess their influence on CHF. Results indicate that CHF increases with mass flux; however, the increase rate diminishes under higher mass flux. Larger channel dimensions significantly enhance CHF by delaying liquid film dryout. System pressure further improves CHF by reducing bubble detachment frequency and promoting flow stability. Increased inlet subcooling enhances CHF by delaying the onset of nucleate boiling and improving convective heat transfer. Four classical CHF prediction models were evaluated, revealing significant overprediction-up to 148.69% mean absolute error (MAE)-particularly for channels with hydraulic diameters below 1.0 mm. An ANN deep learning model was developed, achieving a reduced MAE of 8.93%, with 93% of predictions falling within ±15% error. This study offers valuable insights and a robust predictive model for optimizing microchannel heat sink performance in high heat flux applications.

1. Introduction

Rapid advancements in micro/nanotechnology have led to the miniaturization of industrial components, resulting in unprecedented heat fluxes during operation and presenting substantial challenges for thermal management systems [1,2]. Microchannel two-phase flow boiling, leveraging the latent heat of vaporization, has gained prominence as an efficient thermal management solution owing to its exceptional heat transfer performance, uniform temperature distribution, and compact structural design [3]. These systems are especially vital for high-power electronics, aerospace thermal control systems, and advanced energy conversion technologies [4,5]. However, the occurrence of CHF in microchannels significantly limits their continued advancement. CHF not only limits heat transfer enhancement but also induces flow instabilities, localized dryout, and equipment overheating, thus constituting a major bottleneck for the practical deployment of microscale flow boiling technologies [6]. Consequently, comprehensive theoretical and experimental investigations of CHF are vital to ensure the safety and performance of heat transfer systems. This applies to diverse applications, from thermal-hydraulic components in nuclear reactors to thermal management systems in hydrogen fuel cell vehicles. Moreover, accurate CHF prediction is indispensable for designing reliable cooling systems.

CHF mechanisms and affecting factors have been extensively investigated in the context of flow boiling heat transfer [7,8]. Experimental investigations have primarily focused on identifying influencing factors, including fluid properties [9,10], flow parameters [11,12,13,14], structural configurations [15,16,17], and surface treatments [18,19,20]. Although critical heat flux (CHF) is a pivotal phenomenon in flow boiling, the fundamental heat transfer mechanism responsible for its occurrence remains elusive. Qu and Mudawar [21] conducted CHF experiments using saturated water in a copper microchannel heat sink comprising 21 rectangular channels. Their results revealed that the backflow effect among channels renders the inlet subcooling negligible with respect to the heat transfer coefficient. Based on these findings, the Katto–Ohno model was modified to improve its applicability to multi-channel systems. Li et al. [22] systematically investigated CHF characteristics of flow boiling in silicon-based parallel microchannels with an aspect ratio of 0.8. The study demonstrated that high-frequency two-phase oscillations (10–100 Hz), triggered by microscale bubble activity, significantly influence CHF. By incorporating auxiliary channel structures to stabilize the vapor column-extending over 60–80% of the channel length-the CHF was enhanced by 25%. Building on this foundation, a semi-theoretical CHF model incorporating both Helmholtz and Rayleigh-Taylor instability mechanisms was developed, achieving prediction errors within ±15%. Agostini et al. [23] investigated the CHF characteristics of R236fa in a microchannel heat sink comprising 67 parallel channels. The results showed that increasing the mass flux from 200 to 800 kg/(m²·s) led to a 40–60% enhancement in CHF. Conventional prediction correlations exhibited substantial inaccuracies: rectangular channel models (e.g., Katto–Ohno) overestimated CHF by approximately 30%, while circular tube models (e.g., Bowring correlation) underestimated it by about 25%. These findings underscore the critical role of microchannel geometry in determining CHF behavior. In their review, Bergles and Kandlikar [24] noted that approximately 60% of existing CHF data for parallel microchannels are influenced by Ledinegg instability, leading to a 10–30% reduction in experimentally measured CHF values. Kuan and Kandlikar [25] experimentally demonstrated that integrating pressure-drop elements into the inlet manifold effectively suppresses flow instabilities, resulting in an 18–22% increase in CHF. These results provide critical design guidelines for optimizing microchannel thermal management systems. Singh et al. [26] performed groundbreaking research on flow boiling characteristics in microchannels with a constant hydraulic diameter and a gradient of aspect ratios (1.24 ≤ AR ≤ 3.75), employing water as the working fluid. The study combined flow pattern visualization and theoretical modeling to gain deeper insights. Traditional annular flow models exhibited good predictive accuracy for nearly square microchannels (AR ≈ 1); however, their accuracy deteriorated significantly as AR increased beyond 2. In light of these findings, the authors recommend incorporating a channel cross-sectional shape factor or developing multi-parameter correlations using machine learning techniques. Zhang et al. [27] systematically assessed the predictive capability of existing CHF correlations for water flow boiling in microchannels. CHF data for small-diameter channels (0.33 to 6.22 mm) were compiled from the literature. The dataset was categorized into subcooled and saturated CHF, revealing that existing CHF correlations within the 0.33–6.22 mm range exhibit discontinuities at regime boundaries. Therefore, a unified predictive correlation is required to eliminate the discontinuities frequently encountered in existing models. Pan et al. [28] systematically studied flow boiling characteristics of HFE-7100 in microchannels with aspect ratios ranging from 0.83 to 6.06. Results showed that CHF reached its maximum at AR = 0.99 and gradually decreased as AR increased further. By comparing liquid film distributions across different aspect ratios, the decrease in CHF was attributed to the diminished and increasingly non-uniform liquid film at higher ARs. Kumar et al. [29] proposed a novel semi-empirical CHF correlation based on the Buckingham π theorem and an energy-based bubble growth model, which explicitly considered the influence of bubble growth and channel blockage on early CHF onset. While the correlation performed well for refrigerants, its predictive accuracy was limited for water-based systems.

Considerable progress has been made in understanding CHF in flow boiling heat transfer, and numerous models have been proposed to elucidate its underlying mechanisms. However, the inherent complexities of flow boiling-including significant phase property disparities (e.g., viscosity, density, and specific heat capacity) between vapor and liquid, coupled with violent bubble expansion from stochastic nucleation and rapid pressure/temperature fluctuations-often induce chaotic bubble dynamics and pronounced flow instabilities [30]. These phenomena limit the generalizability of existing CHF prediction correlations, which are often derived from narrowly defined experimental conditions. Furthermore, most current CHF correlations are developed for rod bundles and circular tubes, rendering them unsuitable for rectangular microchannels due to distinct geometrical and thermal characteristics. In addition, certain models involve complex and computationally intensive iterative procedures, which hinder their practical applicability. While existing correlations can often predict the saturated CHF with reasonable accuracy, they typically rely on numerous empirical constants, multiple equations, and intricate conditional criteria to determine appropriate expression. However, none of these specialized formulations have demonstrated consistent accuracy across a broad range of experimental datasets. Therefore, additional investigations are essential to consolidate existing data and formulate simple, computationally efficient CHF prediction models tailored to rectangular microchannels.

The field of thermal system analysis has undergone transformative developments in predictive capabilities, particularly through the adoption of machine learning and surrogate-based modeling techniques [31,32]. These methodological innovations aim to overcome the inherent limitations of conventional analytical techniques and offer more generalizable and reliable predictive tools for thermal systems. Notably, the application of machine learning techniques in thermal system analysis and prediction has experienced rapid growth and gained widespread recognition within the academic community [33,34]. Among various machine learning techniques, artificial neural networks (ANNs) exhibit particular advantages in thermal management system modeling owing to their superior nonlinear mapping capabilities [35,36,37]. Numerous studies have demonstrated that ANNs can accurately predict CHF [38,39,40]. In contrast to prior studies that predominantly utilized flow parameters—such as mass flow rate and pressure—our work innovatively integrates key geometric characteristics, including hydraulic diameter, aspect ratio, and contact angle, as critical input variables. Therefore, the synergistic integration of artificial neural networks and parameter trend analysis holds great promise for advancing the CHF prediction in microchannel flow boiling and facilitating the development of more accurate and computationally efficient predictive correlations.

Overall, although various prediction models for critical heat flux have been developed using traditional empirical correlations, machine learning, and deep learning techniques, the inherently complex physical mechanisms underlying CHF continue to present major challenges in developing a unified, accurate, and robust predictive framework. This challenge is further exacerbated by the diversity and inconsistency of experimental datasets accumulated over decades of CHF research. To address these issues, this study experimentally investigates flow boiling CHF behavior in minichannels under a wide range of heat and mass flux conditions, performing a parametric analysis to evaluate the influence of heat flux, hydraulic diameter, and mass flux on CHF. The analysis reveals the governing influence of these parameters on CHF in microchannels and enhances understanding of the dominant boiling heat transfer mechanisms operating within the studied heat flux and mass flux ranges. Ultimately, a more accurate and computationally efficient CHF prediction method is proposed for estimating CHF in microchannels, providing valuable guidance for the safe implementation of microchannel-based thermal management systems in high heat flux applications.

2. Experimental Setup and Method

2.1. Experimental Setup

The experimental setup is illustrated in Figure 1. It consists of a closed-loop system comprising a working fluid circulation loop, a liquid injection and storage unit, a microchannel test section, a data acquisition module, and a high-speed visualization subsystem.

Ethanol, used as the working fluid, is introduced into the system through the liquid injection device and stored in the reservoir tank. The fluid is then driven by a high-temperature magnetic pump (20CQG-12, Cijiu, Guangzhou, China) through a preheating tank, where it is conditioned to the target inlet temperature before entering the microchannel test section. A high-speed camera is synchronized with the test system to capture the two-phase flow characteristics within the rectangular microchannels. The high-speed camera operated at 4261 fps with a 1280 × 128 pixel resolution. After passing through the test section, the fluid is cooled sequentially in a brazed plate heat exchanger and a cooling water tank before re-entering the circulation loop. Deionized water and fluorinated refrigerants are less ideal for microchannel CHF studies than ethanol, which balances boiling point and safety. Industrial ethanol is thus adopted here to examine parametric effects on flow boiling CHF. The thermophysical properties of ethanol at standard atmospheric pressure, obtained from Refprop software (V9.1), are summarized in

Table 1. Physical properties of ethanol at standard atmospheric pressure.

Properties	Value
Fluid Density, kg/m3	736
Gas Density, kg/m3	1.63
Viscosity, Pa·s	4.42 × 10−4
Fluid Specific heat, J/(kg·K)	2930
Fluid Thermal conductivity, W/(m·K)	0.15
Latent heat of vaporization, KJ/kg	850.1
Surface tension, N/m	0.0174

.

2.2. Test Section

Figure 2 illustrates a schematic diagram of the test section. The test section consists of an upper cover plate, a quartz-glass visualization window, a polytetrafluoroethylene (PTFE) insulation chamber, an aluminum alloy microchannel heat sink, an oxygen-free copper heating block, electric heating rods, and a lower cover plate. To ensure uniform fluid distribution, inlet and outlet stabilizing chambers (23 × 20 × 30 mm) were incorporated into the test section, following the design proposed by Qu et al. [41]. The test section was oriented vertically to simulate practical operating conditions and ensure the stability of two-phase flow patterns. Five microchannels with hydraulic diameters ranging from 0.5 to 2.0 mm and a uniform length of 237 mm were fabricated using computer numerical control (CNC) machining. The geometric parameters of the heat sinks—including channel width (W_ch), channel height (H_ch), number of channels (N_ch), and rib width (W_w)—are summarized in

Table 2. Geometric parameters of microchannel heat sinks.

Items	De	Wch/mm	Hch/mm	β	A/mm2	Nch	Ww/mm
HD1#	2.0	2.0	2.0	1	4	7	2
HD2#	1.3	1.0	2.0	2	2	8	2
HD3#	1.0	1.0	1.0	1	1	14	1
HD4#	0.7	0.5	1.0	2	0.5	17	0.6
HD5#	0.5	0.5	0.5	1	0.25	28	0.6

.

2.3. Experimental Process

The following are the experimental procedures: (a) Degassing: The working fluid was degassed under boiling conditions for 0.5 h in an external separate setup prior to being injected into the cleaned and dried test loop. The degassed fluid was then cooled to room temperature before testing; (b) vacuum and filling: following evacuation with a vacuum pump (FY-1H-N, Feiyue, Suzhou, China) for 60 min to a stable reading of −99 kPa (though not an absolute vacuum), the test loop was filled with the degassed liquid; (c) fluid circulation: the liquid was pumped into the flow loop using a magnetic pump; (d) flow regulation: the outlet pressure and flow rate were controlled by a calibrated flow meter (LZB-4B, Yuyao, Jinan, China) and the adjustable valve-4, 5 and 6; (e) inlet subcooling control: the inlet temperature (subcooling degree) of the working fluid was maintained using a preheater; (f) heat flux adjustment and data acquisition: the heat flux was incrementally increased via an adjustable DC power supply (TDGC2-3KVA, Ruiling, Suzhou, China). Once all temperature readings stabilized (within ±0.3 °C) for at least 5 min, experimental data (including temperature and pressure) were recorded using a data acquisition system (Agilent 34972A, Shenzhen, China); (g) CHF determination: the critical heat flux (CHF) was assumed to be reached when further increasing the heat flux led to an unstable thermal state, accompanied by visual observation of local dryout in the microchannel. The CHF value was then determined based on the last stable heat flux condition.

2.4. Heat Loss Estimation

To quantify heat dissipation, the test section-excluding the visualization window-was wrapped in thermal insulation cotton (λ < 0.040 W/(m·K)). A dry-burning test was performed under no-flow conditions, following the methodologies described in Refs. [16,42]. The heater power was modulated to stabilize the system at target temperatures, and heat loss was estimated from the temperature differential between the test section wall and the ambient surroundings. Experimental data fitted with a linear model (Figure 3) exhibited an almost perfect correlation (R² ≈ 1). During the experiments, the average wall temperature ranged from 80 °C to 120 °C, corresponding to heat losses between 42.37 W and 67.27 W.

2.5. Data Acquisition and Uncertainties

In our experiment, the input power of the heater is regulated by a power controller to control the heat flux of the test section. The effective heat flux (q_eff) is expressed by the following:

$$q_{\mathrm{eff}}={\displaystyle \frac{Q-Q_{\mathit{loss}}}{S}}$$

(1)

where S denotes the longitudinal cross-sectional area of the microchannel heat sink. CHF was identified by abrupt increases in wall temperature and severe pressure drop fluctuations at the channel outlet.

The mass flux (G) at the channel inlet was derived from the following:

$$G={\displaystyle \frac{M}{N_{ch}{W_{\mathrm{c}\mathrm{h}}H}_{c\mathrm{h}}}}$$

(2)

The heating surfaces of the microchannel consist of the bottom, the left wall, and the right wall of the channel. Therefore, the influence of channel fins on heat transfer must be taken into account. The energy balance during the flow boiling process in a rectangular channel is described by the following [43]:

$$q_{\mathrm{eff}}\left(W_w+W_{\mathrm{ch}}\right)=h_i\left(T_{\mathrm{w},i}-T_f\right)\left(W_{\mathrm{ch}}+2\eta H_{\mathrm{ch}}\right)$$

(3)

The local heat transfer coefficient (h) can be derived from the following:

$$h_i={\displaystyle \frac{q_{\mathrm{eff}}\left(W_{\mathrm{ch}}+W_w\right)}{(T_{\mathrm{w},i}-T_f)(W_{\mathrm{ch}}+2\eta H_{\mathrm{ch}})}}$$

(4)

$$\eta ={\displaystyle \frac{t{anh}_i\left(m{H}_{\mathrm{ch}}\right)}{m{H}_{\mathrm{ch}}}}$$

(5)

$$m=\sqrt{{\displaystyle \frac{2h_i}{k_{\mathrm{st}}{W}_w}}}$$

(6)

where η is fin efficiency, T_w,i is the bottom wall temperature, T_f is the fluid temperature at measurement point.

The wall temperature (T_w,i) was calculated based on one-dimensional steady-state heat conduction, as follows:

$$T_{w,i}=T_i-{\displaystyle \frac{q_{\mathrm{eff}}{d}_{\mathrm{ch}}}{{\lambda }_a}}$$

(7)

where d_ch is the distance from the microchannel base to the thermocouple, and λ_a is the thermal conductivity of 6061 aluminum alloy.

Local fluid temperature T_f,n is [44] as follows:

$$T_{\mathrm{f},n}=\left\{\begin{array}{c}{T}_{\mathrm{i}\mathrm{n}}+{\displaystyle \frac{q_{\mathrm{e}\mathrm{f}\mathrm{f}}{W}_{\mathrm{t}}{z}_n}{\dot{m}{c}_{p,\mathrm{f}}}}\\ T_{\mathrm{s}\mathrm{a}\mathrm{t},n}\end{array}\right.\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{o}\mathrm{n}$$

(8)

where T_in denotes fluid temperature at the inlet, c_p,f denotes the specific heat capacity, T_sat,n denotes local saturation temperature.

The wall superheat (∆T_oh) was defined as follows:

$$\Delta T_{\mathrm{oh}}=T_{\mathrm{w},i}-T_{\mathrm{sat}}$$

(9)

The thermodynamic equilibrium quality and the length of subcooled region were determined using the following interpolative methods:

$$L_{\mathrm{tp}}=L-L_{\mathrm{sp}}$$

(10)

$$L_{\mathrm{sp}}={\displaystyle \frac{M{c}_{p,1}△T_{\mathrm{sub},\mathrm{in}}}{q_{\mathrm{eff}}{N}_{\mathrm{ch}}(W_w+W_{\mathrm{ch}})}}$$

(11)

$$△T_{\mathrm{sub},\mathrm{in}}=T_{\mathrm{sat}}-T_{\mathrm{in}}$$

(12)

$$x_e=-{\displaystyle \frac{c_{p,l}\left(T_{\mathrm{sat}}-T_f\right)}{H_{\mathrm{fg}}}},x_e<0$$

(13)

$$x_e={\displaystyle \frac{q_{\mathrm{eff}}(W_{ch}+2H_{\mathrm{ch}})\left(Z_i-L_{\mathrm{sp}}\right)}{H_{\mathrm{fg}}M}},0\le x_e\le 1,i=\mathrm{1,2},\mathrm{3,4}$$

(14)

where H_fg is the latent heat of vaporization, Z_i is the distance between the temperature test points and inlet.

The total pressure drop (∆P_tot) and its standard deviation (σ(∆P_tot)) were measured to evaluate flow stability, as defined by the following:

$$\Delta P_{\mathrm{tot}}=P_{\mathrm{in}}-P_{\mathrm{out}}$$

(15)

$$\sigma (\Delta P_{\mathrm{tot}})=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^{n\sum }(\Delta p_i-{\displaystyle \frac{1}{n}}\sum _{i=1}^{n{\sum }^2}\Delta p_i)}$$

(16)

Additionally, the Mean Absolute Error (MAE), a statistical metric used to quantify the deviation between predicted and actual values of CHF, is defined by the following:

$$\mathit{MAE}={\displaystyle \frac{1}{N}}\sum _1^N{\displaystyle \frac{\left|q_{\mathrm{CHF},\mathrm{pred}}-q_{\mathrm{CHF},\exp }\right|}{q_{\mathrm{CHF},\exp }}}\times 100\%$$

(17)

Measurement uncertainties were systematically evaluated based on error propagation analysis as proposed by Moffat et al. [45]. The relative uncertainties of directly and deduced variables are listed in

Table 3. List of the relative uncertainties of major variables.

Variable	Uncertainties
Temperature	±0.1 °C
Pressure	±0.5 Pa
Mass Flow Rate	±1.5%
Mass Flux	±1.6%
Heat Flux	±4.82%
Thermodynamic Equilibrium Quality	±2.41%
Heat Transfer Coefficient	±7.53%

.

3. Results and Discussion

3.1. CHF Identification and Characterization

The onset of CHF was identified through abrupt increases in wall superheat (∆T_oh), defined as the temperature difference between the heated wall (T_w,4) and the fluid saturation temperature (T_sat). As shown in Figure 4, when the heat flux increased from 100.33 to 122.67 kW/m², ∆T_oh increased gradually from 1.2 °C to 3.5 °C, corresponding to bubbly and slug flow regimes. Beyond 122.67 kW/m², ∆T_oh increases sharply, reaching 15.06 °C at 157.33 kW/m². High-speed visualization confirms a transition to churn flow and the onset of partial dryout, indicating the occurrence of CHF. This behavior is consistent with the liquid sublayer dryout model, wherein insufficient liquid replenishment results in wall overheating [46].

Pressure drop fluctuations (σ(∆P_tot)) served as additional indicators for the onset of CHF. Figure 5 illustrates the temporal evolution of pressure drop fluctuations under various heat flux conditions. At heat fluxes below 145.67 kW/m², σ(∆P_tot) remains stable within the range of 0.29–0.39 kPa, indicative of periodic bubble growth and detachment, as shown in Figure 5. By changing the heating power, when the effective heat flux density increased from 122.67 kW/m² to 157.33 kW/m², the standard deviation of the system pressure drop fluctuation increased from 0.29 to 0.58, indicating a significant increase in gas phase in the channel. Small bubbles gradually grew and coalesced with adjacent bubbles, causing a change in fluid flow pattern. The working fluid changed from bubbly to slug flow, and the intermittent appearance of bubbly bubbles also intensified the pressure drop fluctuation inside the channel. This abrupt instability highlights strong coupling between hydrodynamic disturbances and thermal runaway during CHF [47].

3.2. CHF Trends Under Varied Conditions

3.2.1. Effect of Mass Flux (G)

Figure 6 illustrates the variation in the local heat transfer coefficient above the T₄ measurement point location as a function of mass flux. As shown in Figure 6, under varying mass flux conditions, the heat transfer coefficient increases with rising heat flux until the onset of CHF. Beyond CHF, further increases in heat flux result in a rapid deterioration of heat transfer performance. Notably, the CHF value increases significantly with increasing mass flux (G = 57.24–155.38 kg/m²·s). This enhancement is primarily attributed to the direct influence of mass flux on fluid velocity within the channel. Higher mass flux increases inertial forces, enhances turbulence, and promotes the early detachment of bubbles from the heated surface. The detached bubbles are carried into the core flow, effectively delaying the onset of localized dryout and thus increasing CHF [48,49].

3.2.2. Effect of Channel Hydraulic Diameter (De)

Figure 7 depicts the variation in CHF with hydraulic diameter. For the same mass flux, the critical heat flux (CHF) increases with channel size. Under identical mass flux conditions, the average CHF values of the larger channels HD1# (De = 2.0 mm), HD2# (De = 1.3 mm), HD3# (De = 1.0 mm), and HD4# (De = 0.7 mm) were 80.2%, 62.7%, 40.7%, and 16.4% higher than that of HD5# (De = 0.5 mm), respectively. This enhanced performance is attributed to reduced flow restriction and increased liquid replenishment capacity in larger channels, which mitigates bubble crowding and dryout [50]. Conversely, smaller channels (D_e < 1.0 mm) exhibited intensified bubble confinement effects, exacerbating flow instabilities.

3.2.3. Effect of System Pressure (P)

Figure 8 depicts the variation in CHF with mass flow under different system pressures. The experimental results indicate that, for the same microchannel plate, increasing system pressure leads to higher CHF values, assuming other experimental conditions remain constant. Additionally, the relationship between CHF and mass flow rate becomes more linear at elevated system pressures. This behavior is attributed to the direct influence of system pressure on the physical properties of the vapor-liquid two-phase working fluid: higher pressure raises the saturation temperature, increases the energy required for vaporization, reduces bubble nucleation frequency, and stabilizes the liquid film [49]. These findings are consistent with the interfacial lift-off model, which predicts that vapor momentum thresholds scale with pressure.

3.2.4. Effect of Inlet Subcooling (∆T_sub,in)

Figure 9 depicts the variation in CHF with mass flow under different inlet subcooling. Increased inlet subcooling significantly enhances CHF in microchannels. At identical mass flow rates, increasing inlet subcooling from 12.5–13.4 °C to 17.5–18.4 °C and 22.5–23.4 °C resulted in average CHF increases of 9.6% and 16.7%, respectively. Higher inlet subcooling requires the fluid to absorb more heat before reaching saturation and initiating boiling, thereby delaying boiling onset. This stabilizes fluid flow, reduces vapor bubble generation and coalescence, and slows the formation of vapor films and dryout phenomena [51]. Moreover, increased subcooling reduces vapor bubble growth rates, consistent with the delayed dryout mechanism [52].

3.3. CHF Predictive Model Study

3.3.1. Validation of Existing Models

Four classical CHF prediction models—Sudo [51,53], Katto–Ohno [54], Qu–Mudawar [21], and Zhang–Hibiki [27]—were evaluated against experimental data to assess their applicability to rectangular microchannels. Originally developed for rod bundles or circular tubes, these models are based on empirical correlations derived from macroscale flow boiling studies. Figure 10 depicts the comparison between experimental and predicted CHF values obtained from four existing models.

Table 4. MAE comparison of four CHF prediction models.

Models	Year	Predictive Correlations	MAE
			De ≥ 1.0 mm	De < 1.0 mm	All
Sudo [53]	1993	$q_{\mathrm{CHF}}=\mathit{max}\left(q_1,q_3\right)\left[0.2388h_{\mathrm{fg}}\sqrt{\lambda {\rho }_g\left({\rho }_l-{\rho }_g\right)g}\right]$ $q_1=0.005{\left[{\displaystyle \frac{G}{\lambda {\rho }_g\left({\rho }_l-{\rho }_g\right)g}}\right]}^{0.611}$ $q_3=0.7{\displaystyle \frac{A_{\mathrm{c}\mathrm{h}}\sqrt{\raisebox{1ex}{$W_{\mathrm{c}\mathrm{h}}$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}}{S{\left[1+{\left({\rho }_g/{\rho }_l\right)}^{1/4}\right]}^2}}\lambda =\sqrt{{\displaystyle \frac{\sigma }{g\left({\rho }_l-{\rho }_g\right)}}}$	41.73%	136.39%	58.94%
Katto–Ohno [54]	1984	${\displaystyle \frac{q_{\mathrm{CHF}}}{G{h}_{\mathrm{fg}}}}=0.175{\left({\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{0.467}{\left(1+{\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{1/3}{\left({\displaystyle \frac{\sigma {\rho }_l}{G^{2}L}}\right)}^{1/3}$	19.28%	87.01%	31.60%
Qu–Mudawar [21]	2004	${\displaystyle \frac{q_{\mathrm{CHF}}}{G{h}_{\mathrm{fg}}}}=33.43{\left({\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{1.11}{W}_{\mathrm{eD}}^{-0.21}(L/D_e{)}^{-0.36}$ $W_{eD}={\displaystyle \frac{G^2{D}_{\mathrm{e}}}{\sigma {\rho }_l}}$	72.96%	148.69%	86.73%
Zhang–Hibiki [27]	2006	${\displaystyle \frac{q_{\mathrm{CHF}}}{G{h}_{\mathrm{fg}}}}=0.0352{\left[W_{\mathrm{eD}}+0.0119{\left({\displaystyle \frac{L}{D_e}}\right)}^{2.31}{\left({\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{0.361}\right]}^{-0.205}$$\times {\left({\displaystyle \frac{L}{D_e}}\right)}^{-0.311}\left[2.05{\left({\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{0.17}-x_{\mathrm{in}}\right]$ $W_{\mathit{eD}}={\displaystyle \frac{G^2{D}_{\mathrm{e}}}{\sigma {\rho }_l}}$	88.23%	45.45%	80.45%

summarizes the mean absolute error (MAE) comparisons for these CHF prediction models.

As shown in Figure 10 and Table 4, all models systematically overpredict CHF values across the tested hydraulic diameters (D_e = 0.5–2.0 mm), with maximum mean absolute errors (MAE) reaching 148.69% for D_e < 1.0 mm. The Zhang–Hibiki model yielded the lowest mean absolute error (MAE) of 45.45% for D_e < 1.0 mm, whereas the Katto–Ohno model showed superior performance for D_e ≥ 1.0 mm with an MAE of 19.28%. This discrepancy stems from fundamental differences in flow dynamics between rectangular microchannels and conventional geometries. For example, the sharp corners and shallow aspect ratios of rectangular channels intensify bubble confinement effects, resulting in chaotic interfacial interactions and accelerated liquid film depletion-phenomena unaccounted for in existing models [32]. Furthermore, the assumption of uniform bubble distribution inherent in rod-bundle-based models fails to represent the localized vapor accumulation characteristic of microchannels [33]. These limitations underscore the necessity for developing geometry-specific correlations.

3.3.2. Development of Modified CHF Model

An artificial neural network (ANN) is a machine learning architecture inspired by the information processing mechanisms of biological neural systems. By mimicking inter-neuronal connections and signal transmission, ANNs can autonomously learn complex nonlinear relationships from data. A typical ANN consists of an input layer, one or more hidden layers, and an output layer, with weighted inter-layer connections forming a feedforward network. During training, the network iteratively updates the connection weights using the backpropagation algorithm to minimize prediction error. Owing to its strong feature extraction capabilities, ANN has demonstrated exceptional performance in fields such as image recognition, natural language processing, and predictive modeling. In this study, an ANN model was employed to predict the critical heat flux (CHF) in microchannels. The implementation procedure is detailed as follows:

• Data Preprocessing

The experimental dataset comprises four critical input features: mass flux (kg/(m²·s)), hydraulic diameter of the channel (mm), system pressure (kPa), and inlet subcooling (°C), with the critical heat flux (CHF, kW/m²) as the output variable.

The data preprocessing procedure includes the following steps:

a. Data splitting: The dataset was partitioned into training (80%) and testing (20%) subsets using a stratified random sampling approach to preserve the representativeness of the data distribution across both sets.

b. Data normalization: Z-score standardization was applied to remove dimensional discrepancies among features, thereby enhancing the stability and convergence speed of model training.

2.

Network Architecture Design

The architecture of the multilayer feedforward neural network (as depicted in Figure 11) is designed as follows:

(1) Input layer: The input layer serves as the entry point for raw data and consists of four neurons, each representing one of the input features: mass flux (kg/(m²·s)), hydraulic diameter (mm), system pressure (kPa), and inlet subcooling (°C).

(2) Hidden layers: These intermediate layers perform nonlinear transformations to extract high-level features from the input data. A fully connected architecture is employed. To investigate the effect of network depth on model performance, three architectures with varying hidden layer depths were designed (see Section 4 for details).

(3) Output layer: A linear activation function is applied to generate the final prediction of critical heat flux (CHF).

3.

Training Strategy

The model is trained using the Adaptive Moment Estimation (Adam) optimizer with an initial learning rate of 0.001. Mean Squared Error (MSE) is employed as the loss function. The training process is conducted over 300 epochs with a batch size of 32 (configurable). To mitigate overfitting and enhance generalization, L2 regularization (λ = 0.01) is incorporated into the loss function.

4.

Implementation Details

The model was implemented using TensorFlow 2.x and Scikit-learn. To prevent overfitting, early stopping was enabled with a patience value of 100 epochs, and L2 regularization was applied. For reproducibility, the NumPy random seed was fixed at 42.

3.3.3. Model Performance Evaluation and Comparative Analysis

Three artificial neural network (ANN) models with different hidden layer configurations were developed: a baseline model [4,100,50,1], a medium-depth model [4,100,50,25,25,1], and a deep model [4,100,50,25,12,6,3,1]. These models were designed to systematically investigate the influence of network depth on predictive performance, with the goal of identifying the most suitable structure for CHF prediction. Figure 12 illustrates the comparison between predicted and experimental CHF values obtained from the three ANN architectures.

Table 5. Comparison between the most tuned ANNs by using deep learning regarding computational cost.

ANN Cascade Structure	MAE			R2 Score
	Training	Testing	Total
ANN [4,100,50,1]	13.98%	18.1%	13.30%	0.85
ANN [4,100,50,25,25,1]	10.15%	14.43%	9.36%	0.85
ANN [4,100,50,25,12,6,3,1]	9.24%	12.88%	8.93%	0.87

summarizes the comparative performance of these models in terms of computational efficiency and prediction accuracy. All three ANN architectures exhibited robust predictive capabilities. Compared to traditional empirical models such as Sudo and Katto–Ohno, the ANN models demonstrated substantially improved accuracy and successfully mitigated the systematic overestimation commonly observed in conventional CHF correlations. The predicted CHF values were largely symmetrically distributed around the zero-error line, with 93% of predictions falling within ±15% of the experimental data. The best-performing model achieved a mean absolute error (MAE) as low as 8.93%. Although deeper models generally yielded better predictive accuracy, the performance gap between the four-layer and six-layer models was marginal, with both achieving test-set MAEs around 10%. Overall, the ANN models developed in this study significantly outperformed the four classical CHF correlations and demonstrated high predictive accuracy for flow boiling CHF in rectangular microchannels. This work confirms that deep learning techniques offer a powerful alternative to empirical correlations by overcoming their inherent limitations in CHF prediction for microchannels, establishing a new paradigm for high-precision thermal-hydraulic analysis.

4. Conclusions

This study systematically investigated the critical heat flux characteristics in rectangular microchannels under flow boiling conditions through experimental and theoretical analyses. The key findings are summarized as follows:

(1)

Based on mechanistic models such as the theory of liquid sublayer drying and interfacial detachment, the occurrence of CHF can be determined by monitoring sudden increases in wall superheat (∆T_oh), severe pressure drop fluctuations, and visual observations of localized drying.

(2)

CHF increases with higher G, but the growth rate diminishes due to enhanced liquid entrainment into the vapor core, which accelerates thin-film dryout. Larger channels (D_e ≥ 1.0 mm) exhibit significantly higher CHF (up to 78% improvement) by mitigating bubble confinement and enhancing liquid replenishment. Elevated pressure stabilizes the liquid film by suppressing bubble nucleation frequency, leading to an increase in CHF with G. Higher subcooling (∆T_sub,in) delays boiling inception and reduces vapor generation, improving CHF by up to 16.7%.

(3)

Existing CHF models (Sudo, Katto–Ohno, Qu–Mudawar, and Zhang–Hibiki) overpredicted experimental values, especially for D_e < 1.0 mm (MAE up to 148.69%). ANN deep learning models have an overall MAE of 8.93%, and 93% of the predictions are within ±15%, providing a reliable tool for designing high heat flow microchannel cooling systems in applications.