Flow Boiling of Water in a Rectangular Metallic Microchannel

Figures & data

Figure 1. (a) Schematic diagram of the experimental facility, (b) Top view of the test section (TS3). Dimensions in mm.

Table 1. Dimensions of the microchannels in the current study.

Test section	H, mm	W, mm	L, mm	Dh, mm	β	Ac, mm^2	Dpi/Dpo
TS1	0.84	0.42	62.0	0.56	0.5	0.35	1.9
TS2	0.39	1.0	62.0	0.56	2.56	0.39	2.0
TS3	0.34	1.68	62.0	0.56	4.94	0.57	2.4

Figure 2. Three-dimensional model of the test section.

Figure 3. Single-phase validation of experimental procedure and measurements.

Table 2. Single-phase pressure drop and heat transfer correlations, range and MAE reported by the corresponding authors based on their data.

Reference	Correlation	Range	MAE
Shah and London [24]	$f_{FD}=\frac{24}{\mathrm{Re}}(1-1.3553\beta +1.9467{\beta }^2$ $-1.7012{\beta }^3+0.9654{\beta }^4-0.2537{\beta }^5)$	Laminar Developed flow Analytical Correlation	0.5%
Shah and London [24]	$f_{\mathit{app}}=\frac{3.44}{\mathrm{Re}\sqrt{L*}}+\frac{f_{FD}\mathrm{Re}+\frac{K(\infty )}{4L*}-\frac{3.44}{\sqrt{L*}}}{\mathrm{Re}\left[1+\frac{C}{L{*}^{{}^2}}\right]}$ $L*=\frac{L}{D_h\mathrm{Re}}$	Laminar Developing flow Analytical Correlation	2.4%
Shah and London [24]	$f_{\mathit{appturb}}=\left(0.0929+\frac{1.01612D_h}{L}\right)\mathrm{Re}{*}^{(-0.268\frac{0.3293D_h}{L})}$ $\mathrm{Re}*=\mathrm{Re}(2/3+\frac{11}{24}\beta (2-\beta ))$	Turbulent Developing flow Analytical Correlation	4%
Blasius [28]	$f=0.079{\mathrm{Re}}^{-0.25}$	Turbulent Developed flow Re: 2300–10^5	–
Shah and London [24]	$N{u}_{av}=8.235(1-10.6044\beta +61.1755{\beta }^2$ $-155.1803{\beta }^3+176.9203{\beta }^4-72.9236{\beta }^5)$	Laminar Developed flow Analytical Correlation	0.3%
Shah and London [24]	$N{u}_{av}=0.775L{*}^{-1/3}{15}^{1/3},$ $L*=\frac{L}{\mathrm{Re}\mathrm{Pr}{D}_h}$	Laminar Developing flow Analytical Correlation	3%
Dittus-Boelter [29]	$N{u}_{av}=0.026{\mathrm{Re}}^{0.8}{\mathrm{Pr}}^{0.3}$	Turbulent Developed flow Re: 2300–10^4 Pr: 0.7–160	–
Petukhov [30]	$N{u}_{av}=\frac{\frac{fp}{2}\mathrm{Re}\mathrm{Pr}}{C+12.7{\left[\frac{fp}{2}\right]}^{0.5}({\mathrm{Pr}}^{2/3}-1)}$ $fp=0.00128+0.1143{\mathrm{Re}}^{-0.311}$ $C=1.07+\frac{900}{\mathrm{Re}}-\left[\frac{0.63}{1+10\mathrm{Pr}}\right]$	Turbulent Developing flow Re: 10^4–5 × 10^6 Pr: 0.5–2000	5-6%
Mirmanto et al. [27]	$N{u}_{av}={\mathrm{Re}}^{0.283}{\mathrm{Pr}}^{-0.513}L{*}^{-0.309}$	Laminar Developing flow De-ionized water Re: 244–1998 Pr: 3–5 Dh: 0.44–0.64 mm	7.8%
Mirmanto et al. [27]	$N{u}_{av}=0.032{\mathrm{Re}}^{0.841}{\mathrm{Pr}}^{-0.51}L{*}^{-0.153}$	Turbulent Developing flow De-ionized water Re: 2000–4100 Pr: 4–5 Dh: 0.44–0.64 mm	5.8%

Figure 4. Definition of the observed flow patterns in the current study. (a) Bubbly flow, (b) Slug flow, (c) Churn flow, and (d) Annular flow.

Figure 5. Fluctuations in fluid inlet and outlet temperature and pressure drop at G = 400 kg/(m²s) for TS2: (a) single phase flow with q” = 0 kW/m², (b) During periodic flow, q” = 99.1 kW/m².

Figure 6. Sequence of flow images at the middle of the channel for periodic flow regime in the microchannel TS2 (β = 2.56) at q” = 99.15 kW/m² and G = 400 kg/(m²s).

Table 3. The ratio of the evaporation momentum force and the inertia force for TS2 at boiling incipience.

G (kg/(m^2s))	Fevap/Finertia	Q (W)	Ac (m^2)	ilg (J/kg)	ρl (kg/m^3)	ρg (kg/m^3)
200	1.91	5.9	3.9 × 10^−7	2.26 × 10^6	958.3	0.598
400	1.06	8.8	3.9 × 10^−7	2.25 × 10^6	959.1	0.578
600	0.5	9.1	3.9 × 10^−7	2.26 × 10^6	959.4	0.568
800	0.3	9.4	3.9 × 10^−7	2.26 × 10^6	959.6	0.563

Figure 7. Effect of channel aspect ratio on bubbly flow.

Figure 8. Effect of channel aspect ratio on slug flow.

Figure 9. Effect of channel aspect ratio on churn flow.

Figure 10. Effect of channel aspect ratio on annular flow.

Figure 11. Boiling curve for TS1 (β = 0.5) at z/L = 0.6.

Figure 12. Wall and saturation temperature versus dimensionless axial distance for (a) G = 200 kg/(m²s) and (b) G = 800 kg/(m²s).

Figure 13. Effect of aspect ratio on boiling curve for G = 800 kg/(m²s) at z/L = 0.6.

Figure 14. Effect of low and moderate heat flux input and local quality on the local heat transfer coefficient at 200 kg/(m²s) for TS1.

Figure 15. Effect of high heat flux input on the local heat transfer coefficient for the TS1 at 200 kg/(m²s); (a) versus local vapor quality and (b) versus axial distance.

Figure 16. Saturation temperature variation (24 K) and wall temperature variation (12 K) along the channel axial distance for the TS1 at 800 kg/(m²s) at two different heat fluxes.

Figure 18. Effect of aspect ratio and heat flux on the average heat transfer coefficient for the three test sections; (a) at G = 200 (kg/m²s) and (b) at G = 600 (kg/m²s).

Table 4. MAE and the percentage of data within ± 30% error bands for conventional scale correlations.

Correlation	β = 0.5 (TS1)		β = 2.56 (TS2)		β = 4.94 (TS3)
	MAE %	α %	MAE %	α %	MAE %	α %
Shah [47]	49.8	34.8	45.9	36	41.9	37.9
Gungor and Winterton [48]	56.4	31.8	46.6	38.8	50.5	38.1
Kandlikar [49]	66.8	24.8	58.2	36.2	65	46.4
Liu and Winterton [50]	35.3	44.7	33.9	46.6	28.6	56.9

Table 5. MAE and the percentage of data within ± 30% error bands for micro-scale correlations.

Correlation	β = 0.5 (TS1)		β = 2.56 (TS2)		β = 4.94 (TS3)
	MAE %	α %	MAE %	α %	MAE %	α %
Lazarek and Black [55]	30.6	51.2	32.5	48.7	26.6	61.1
Yu et al. [46]	26.5	59.2	37.5	33.7	30.5	45.1
Kandlikar and Balasubramanian [51]	35.2	43.3	38.6	39.3	55.3	40.5
Lee and Mudawar [52]	41.8	23.9	50.6	19.2	38.7	35.4
Sun and Mishima [53]	25.2	62.7	29.3	50.3	24.2	64.5
Li and Wu [54]	15.8	89.5	27.1	60.8	19.3	97.4
Mahmoud and Karayiannis [56] (correlation 1)	21.6	73.6	31	56.9	22.6	72.7
Mahmoud and Karayiannis [56] (correlation 2)	23.3	69.1	35.3	51.8	30.8	49.3
Lim et al. [22]	58.9	1.4	65.8	2.1	64.1	1.2

Table 6. Conventional-scale and micro-scale boiling heat transfer correlations, range and MAE reported by the corresponding authors based on their data.

Reference	Applicability	MAE
Shah [47]	Based on 780 data points	4–11%
Gungor and Winterton [48]	Based on 3600 data points Water, R-11, R-12, R-22, R-113, R-114 D: 2.95–32 mm p: 8–20260 kPa	21.4–25%
Kandlikar [49]	Water, R-11, R-12, R-22, R-113, R-134a, R-152a G: 13–8179 kg/m^2s q”: 0.3–228 kW/m^2 p: 40–6420 kPa	15.9–18.8%
Liu and Winterton [50]	G: 12.4–8179.3 kg/m^2s D: 2.95–32 mm q”: 0.35–2620 kW/m^2 xlocal: 0–0.948	12.6–20.5%
Lazarek and Black [55]	Based on 728 data points R-113, D: 3.1 mm G: 125–750 kg/m^2s Re: 860–5500 p: 130–410 kPa q”: 14–380 kW/m^2	15%
Yu et al. [46]	Water, D: 2.98 mm, p: 200 kPa G: 50–200 kg/m^2s, xlocal: 0.15–1	2%
Kandlikar and Balasubramanian [51]	Range of the data in the Kandlikar correlation [49] above.	20%
Lee and Mudawar [52]	Water, R-134a, Dh: 0.35 mm	11.6–16.1%
Sun and Mishima [53]	Based on 2505 data points 10 fluids and water D: 0.21–6.05	30.8%
Li and Wu [54]	Based on 3744 data points 11 fluids and water D: 0.148–3.25	26.13%
Mahmoud and Karayiannis [56] (correlation 1)	Based on 8561 data points R-134a, D: 0.52–4.26 mm G: 100–500 kg/m^2s p: 600–1400 kPa	14–17.1%
Mahmoud and Karayiannis [56] (correlation 2)	Range of the data same as in the Mahmoud and Karayiannis [56] (correlation 1) given above.	14–17.9%
Lim et al. [22]	Water, Dh: 0.5 mm G: 200–600 kg/m^2s p: 110–170 kPa q”: 100–400 kW/m^2 xlocal: 0–0.2	7.2%

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