Boiling local heat transfer enhancement in minichannels using nanofluids
 Ali Ahmad Chehade^{1},
 Hasna Louahlia Gualous^{1}Email author,
 Stephane Le Masson^{2},
 Farouk Fardoun^{3} and
 Anthony Besq^{1}
DOI: 10.1186/1556276X8130
© Chehade et al.; licensee Springer. 2013
Received: 30 September 2012
Accepted: 17 February 2013
Published: 18 March 2013
Abstract
This paper reports an experimental study on nanofluid convective boiling heat transfer in parallel rectangular minichannels of 800 μm hydraulic diameter. Experiments are conducted with pure water and silver nanoparticles suspended in water base fluid. Two small volume fractions of silver nanoparticles suspended in water are tested: 0.000237% and 0.000475%. The experimental results show that the local heat transfer coefficient, local heat flux, and local wall temperature are affected by silver nanoparticle concentration in water base fluid. In addition, different correlations established for boiling flow heat transfer in minichannels or macrochannels are evaluated. It is found that the correlation of Kandlikar and Balasubramanian is the closest to the water boiling heat transfer results. The boiling local heat transfer enhancement by adding silver nanoparticles in base fluid is not uniform along the channel flow. Better performances and highest effect of nanoparticle concentration on the heat transfer are obtained at the minichannels entrance.
Keywords
Minichannels Nanofluid Convective boilingReview
Introduction
The rapid improvement in the microelectronic devices is accompanied by a high increase in the heat generation, which would decrease its efficiency and lifetime. Nanofluid flow boiling in microchannels and minichannels came up to be a novel solution to withstand high heat fluxes with low working mass flow rates and more uniform temperature. Thus, the combination of nanofluid and small channel’s dimensions in heat exchangers constitutes an innovating method providing effectiveness, compactness, low thermal resistance, and, simultaneously, environmental protection by the reduction of working fluid inventory.
Several studies were carried out to better understand the boiling phenomena in microchannels with different working fluids [1, 2]. Bowers and Mudawar [3] conducted experiments in circular minichannels and microchannels heat sinks by using R113 as a working fluid. They found that minichannels and microchannels in heat exchangers are capable of achieving heat fluxes in excess of 200 W/cm^{2}. Moreover, Qu and Mudawar [4] investigated convective boiling heat transfer, flow patterns, and pressure drop of water in parallel microchannels. They showed that the flow pattern was strongly affected by the heat flux and it is difficult to withstand bubbly flow regimes using water as working fluid due to its high surface tension and large contact angle. Liu and Garimella [5] conducted experiments on boiling heat transfer of deionized water in copper microchannels. They found that Shah correlation [6] predicts well the heat transfer coefficient in the subcooled boiling regimes. Chen and Garimella [7] investigated physical characteristics of boiling FC77 flow in parallel silicon minichannels. They studied bubbly and sluggish flow pattern at low heat flux and thin annular and churn flows at high heat flux using three different mass fluxes. Fang et al. [8] conducted a comparative study of existing correlations for flow boiling heat transfer in microchannels. They collected 1158 data points of flow boiling heat transfer of R134a in minichannels and reviewed 18 flow boiling heat transfer correlations. They found that no correlation has satisfactory accuracy and that more efforts should be made to develop better correlations for boiling in minichannels.
In addition, the recent development of nanotechnology materiel led to intensify the heat transfer coefficient in microscale devices by using suspended metallic nanoparticles in conventional working fluids. Most studies published in the literature on nanofluids heat transfer have reported that using nanoparticles with average sizes below than 100 nm in traditional working fluids increases the thermal conductivity of fluids and enhances heat transfer coefficient [9, 10]. Mohammed et al. [11] reported that there are few studies on convective heat transfer compared to those on nanofluid properties because forced convective flows are affected by nanofluids thermal properties in addition to the Reynolds and Prandtl numbers. Consequently, there are many experimental studies, which focused on nanofluids thermal conductivities since it is the most important parameter to enhance convective heat transfer. Among many experimental methods reported in the literature to measure the nanofluids thermal conductivity, the transient hot wire method has been used extensively. Various correlations and models were proposed for the calculation of the thermal conductivity of nanofluids [12, 13].
In contrast, nanofluids in microchannels have received little attention. Few numerical and experimental studies have been conducted on convection nanofluid heat transfer in microchannels for single phase and boiling flows [14, 15]. Various sizes and types of nanoparticles have been tested such as Al_{2}O_{3}, CuO, diamond, SiO2, Ag, and TiO2 s. These studies have revealed that the heat transfer performance and pressure drop increase with increasing nanoparticle volume concentration in base fluid and decrease with increasing nanoparticle size.
Regarding boiling heat transfer using nanofluids as working fluids, it can be seen that there are several published researches on pool boiling [16, 17]. However, few studies on convective boiling heat transfer of nanofluid in microchannels or minichannels have been conducted in the past 3 years [18–20]. Boudouh et al. [21] conducted experiments on heat transfer of nanofluid with three different volume fractions of nanoparticles in the base fluid 0.00056%, 0.0011%, and 0.0056%. They showed that the local heat flux, local vapor quality, and local heat transfer coefficient increase with copper nanoparticle volume fraction. Henderson et al. [22] found that the heat transfer coefficients of the R134a/POE/CuO nanofluid could be increased by 52% and 76% for volume fractions of 0.04% and 0.08% respectively. Kim et al. [23] studied Al_{2}O_{3}water nanofluid at low volume concentration and observed an enhancement of the boiling critical heat flux up to 70% at nanoparticle concentrations lower than 0.01%. They attributed this enhancement to the nanoparticle deposition on the heat exchanger surface. On the other hand, Lee and Mudawar [24] tested two volume fractions of Al_{2}O_{3}water nanofluid (1% and 2%) with diameter of 36 nm. They noted that the boiling of nanofluid could fail since large clusters are formed near the channel exit due to localized evaporation once boiling was started. More recently, Xu and Xu [25] investigated flow boiling heat transfer in a single microchannel using 40 nm Al_{2}O_{3} nanoparticles with low volume fraction (0.2%). They showed that nanofluids stabilize the boiling flow and inhibit the dry patch development between the heater surface and vapor phase. They also observed an enhancement of the heat transfer using nanofluid without particle deposition on the heater surface.
From this literature review, it is clear that there are only limited studies on nanofluid boiling heat transfer in microchannels with low volume concentration. Most of the studies are focused on pool boiling and singlephase heat transfer in microchannels. Additionally, the encouraging results of a few research works on boiling heat transfer in microchannels at very low nanoparticle volume fractions show the possibility of employing boiling nanofluid in micro heat sinks. Therefore, more efforts must be made in this field to improve effectiveness in engineering designs and applications.
The objective of this study is to investigate the boiling thermal performance of waterbased silver nanoparticles in rectangular minichannels. Experiments were conducted with pure water and nanofluids having low nanoparticle concentrations. The results of local heat transfer coefficients for both water and nanofluids were compared under steady state. Effects of the suspended silver nanoparticles in water on the local surface temperature, local heat flux, and local heat transfer coefficient are also analyzed.
Experimental setup
Flow loop
Test section
Instrumentation
Experimental procedure, data reduction, and uncertainties
For all tests, the heat exchange surface was oriented vertically. The liquid in the tank was first preheated to the required temperature. The liquid flow rate was adjusted with a regulating valve at the desired value. All temperatures were recorded during time. The total power supplied to the heater source was set at the maximum value. When the boiling phenomenon had occurred and the temperatures have reached almost a steady state, the values of the liquid flow rate or the heat flux of the power source were varied and the same procedure was repeated. For each fixed experimental condition, the test section was heated and the temperatures were monitored continually. Experiments were performed with deionized water and silverwater nanofluids.
where q_{channel, x} is the local heat flux estimated by taking into account the local heat loss, T_{s,x} is the local surface temperature, T_{f} is the fluid bulk mean temperature, and x is the axial coordinate parallel to the flow's direction.
where λ_{w}(=389 W/mK) is the thermal conductivity of the copper wall, T_{1,x} and T_{2,x} are the temperatures measured inside the copper plate, Δy is the space between thermocouples locations inside the wall (see Figure 4b).
where G is the total mass flux measured during experiments, H_{channel} is the channel height, W_{channel} is the channel width, and N_{channel} is the number of channels.
Uncertainties for different parameters involved in the experimental tests
Parameter  Uncertainty 

Temperature, T (°C)  ±0.1°C 
Mass flow rate, $\dot{m}$ (kg/s)  ±1.3% 
Mass flux, G (kg/m^{2}s)  ±1.35% 
Position of thermocouples, y (m)  ±0.1 mm 
Power input, (W)  1% 
Heat flux, q (W/m^{2})  8% 
Heat transfer coefficient, h (W/m^{2}k)  ±12% 
Results and discussion
Experiments are performed in parallel rectangular minichannels using pure water and silverwater nanofluid with two small volume fractions (0.000237% and 0.000475%) as working fluids in a compact heat exchanger. A comparison between proposed correlations in the literature and experimental data is carried out initially to verify the present measurements and then to evaluate correlations defined for flow boiling heat transfer in minichannel or macrochannel. Experiments are conducted with various values of mass flux and heat flux.
Water boiling heat transfer in minichannels: measurement results and predictions
Transient state: temperature measurements and instability
Steady state: temperature and heat transfer coefficient measurements
Comparison of experimental data with the existing correlations for flow boiling heat transfer
Correlations for boiling flow heat transfer coefficient
Reference  Fluid composition  Description  Correlation  

Geometry  Comment  Parameter range  
Warrier et al. [27]  FC84  Small rectangular parallel channels of D_{h} = 0.75mm  Singlephase forced convection and subcooled and saturated nucleate boiling  3 < x <55%  ${h}_{\mathrm{tp}}={h}_{\mathrm{sp}}\left(1+6{\mathrm{Bo}}^{\frac{1}{16}}5.3\left(1855\mathrm{Bo}\right){\chi}_{\mathrm{v},x}^{0.65}\right)\phantom{\rule{2em}{0ex}}\left(6\right)$ ${h}_{\mathrm{sp}}=0.023R{e}_{\mathrm{l}}^{0.8}P{r}_{\mathrm{l}}^{0.4}{\lambda}_{\mathrm{l}}/{D}_{\mathrm{h}}\phantom{\rule{2em}{0ex}}\left(7\right)$ 
Kandlikar and Balasubramanian [28]  Water, refrigerants, and cryogenic fluids  Minichannels and microchannels  Flow boiling  x <0.7 ~ 0.8  $\mathrm{Co}<0.65,{h}_{\mathrm{tp}}={h}_{\mathrm{sp}}\left[1.136{\mathrm{Co}}^{0.9}{\left(25F{r}_{\mathrm{lo}}\right)}^{c}+667.2{\mathrm{Bo}}_{\mathrm{lo}}^{0.7}\right]\phantom{\rule{2em}{0ex}}\left(8\right)$ $\mathrm{Co}>0.65,{h}_{\mathrm{tp}}={h}_{\mathrm{sp}}\left[0.6683{\mathrm{Co}}^{0.2}{\left(25F{r}_{\mathrm{lo}}\right)}^{c}+1058{\mathrm{Bo}}_{\mathrm{lo}}^{0.7}\right]\phantom{\rule{2em}{0ex}}\left(9\right)$ h_{sp} is calculated Equation 7 
Sun and Mishima [29]  Water, refrigerants (R11, R12, R123, R134a, R141b, R22, R404a, R407c, R410a) and CO2  Minichannel diameters from 0.21 to 6.05 mm  Flow boiling laminar flow region  Re_{ L } < 2,000 and Re_{ G } < 2,000  ${h}_{\mathrm{tp}}=\frac{6R{e}_{\mathrm{lo}}^{1.05}{\mathrm{Bo}}^{0.54}{\lambda}_{\mathrm{l}}}{{\mathrm{We}}_{\mathrm{l}}^{0.191}{\left({\rho}_{\mathrm{l}}/{\rho}_{g}\right)}^{0.142}{D}_{\mathrm{h}}}\phantom{\rule{2em}{0ex}}\left(10\right)$ 
Bertsch et al. [30]  Hydraulic diameters ranging from 0.16 to 2.92 mm  Minichannels  Flow boiling and vapor quality  0 to 1  ${h}_{\mathrm{tp}}=\left(1{\chi}_{\mathrm{v},x}\right){h}_{\mathrm{nb}}+\left[1+80\left({\chi}_{\mathrm{v},x}^{2}{\chi}_{\mathrm{v},x}^{6}\right){e}^{0.6{\mathrm{Co}}_{\mathrm{f}}}\right]{h}_{\mathrm{sp}}\phantom{\rule{2em}{0ex}}\left(11\right)$ h_{nb} is calculated by Cooper [35]:${h}_{\mathrm{nb}}=55{P}_{\mathrm{R}}^{0.120.087ln\xi}{\left(0.4343ln{P}_{\mathrm{R}}\right)}^{0.55}{M}^{0.5}{q}^{0.67}\phantom{\rule{2em}{0ex}}\left(12\right)$ h_{sp} = χ_{v,x}h_{sp,go} + (1 − χ_{v,x})h_{sp,lo} (13)${h}_{\mathrm{sp},\mathrm{ko}}=\left[3.66+\frac{0.0668R{e}_{\mathrm{ko}}P{r}_{k}{D}_{\mathrm{h}}/L}{1+0.04{\left(R{e}_{\mathrm{ko}}P{r}_{k}{D}_{\mathrm{h}}/L\right)}^{2/3}}\right]\frac{\lambda}{{D}_{\mathrm{h}}}\phantom{\rule{1em}{0ex}}\left(14\right)$${\mathrm{Co}}_{\mathrm{f}}=\sqrt{\frac{\sigma}{g\left({\rho}_{\mathrm{l}}{\rho}_{\mathrm{g}}\right){D}_{\mathrm{h}}^{2}}}\phantom{\rule{2em}{0ex}}\left(15\right)$ 
Temperature  −194°C to 97°C  
Heat flux  4–1,150 kW/m^{2}  
Mass flux  20–3,000 kg/m^{2}s  
Lazarek and Black [31]  R113  Macrochannels 3.15 mm inner diameter tube  Saturated flow boiling    $N{u}_{x}=30R{e}_{\mathrm{lo}}^{0.857}{\mathrm{Bo}}^{0.714}\phantom{\rule{2em}{0ex}}\left(16\right)\phantom{\rule{0.25em}{0ex}}$ 
Gungor and Winterton [32]  Water and refrigerants (R11, R12, R22, R113, and R114)  Horizontal and vertical flows in tubes and annuli D = 3 to 32 mm  Saturated and subcooled boiling flow  0.008 < p_{sat} < 203 bar; 12 < G < 61.518 kg/m^{2}s; 0 < x < 173%; 1 < q < 91.534 kW/m^{2}  h_{tp} = (SS_{2} + FF_{2})h_{sp} (17) h_{sp} is calculated Equation 6 S = 1 + 3, 000Bo^{0.86} (18)$F=1.12{\left(\frac{{\chi}_{\mathrm{v},x}}{1{\chi}_{\mathrm{v},x}}\right)}^{0.75}{\left(\frac{{\rho}_{\mathrm{l}}}{{\rho}_{\mathrm{g}}}\right)}^{0.41}\phantom{\rule{2em}{0ex}}\left(19\right)$${S}_{2}=\left\{\begin{array}{l}F{r}_{\mathrm{lo}}^{(0.12\mathrm{Fr}{}_{\mathrm{lo}})}\phantom{\rule{0.25em}{0ex}}\mathrm{if}\phantom{\rule{0.25em}{0ex}}\mathrm{horizontal}\phantom{\rule{0.25em}{0ex}}\mathrm{with}\phantom{\rule{0.25em}{0ex}}F{r}_{\mathrm{lo}}<0.05\\ 1\phantom{\rule{0.25em}{0ex}}\mathit{otherwise}\end{array}\right.\phantom{\rule{2em}{0ex}}\left(20\right)$${F}_{2}=\left\{\begin{array}{l}F{r}_{\mathrm{lo}}^{\left(0.5\right)}\phantom{\rule{0.25em}{0ex}}\mathrm{if}\phantom{\rule{0.25em}{0ex}}\mathrm{horizontal}\phantom{\rule{0.25em}{0ex}}\mathrm{with}\phantom{\rule{0.25em}{0ex}}F{r}_{\mathrm{lo}}<0.05\\ 1\phantom{\rule{0.25em}{0ex}}o\mathrm{therwise}\end{array}\right.\phantom{\rule{2em}{0ex}}\left(21\right)$ 
Liu and Witerton [36]  Water, refrigerants and ethylene glycol  Vertical and horizontal tubes, and annuli  Subcooled and saturated flow boiling    ${h}_{\mathrm{tp}}=\sqrt{{\left(F{h}_{\mathrm{lo}}\right)}^{2}+{\left(S{h}_{\mathrm{nb}}\right)}^{2}}\phantom{\rule{2em}{0ex}}\left(22\right)\phantom{\rule{0.5em}{0ex}}$ h_{nb} is calculated by Cooper [35] (Equation 11)$F=0.35\left[1+{\chi}_{\mathrm{v},x}\frac{{\mu}_{\mathrm{l}}{C}_{\mathrm{p},\mathrm{l}}}{{\lambda}_{\mathrm{l}}}\left(\frac{{\rho}_{\mathrm{l}}}{{\rho}_{\mathrm{v}}}1\right)\right]\phantom{\rule{2em}{0ex}}\left(23\right)$$S=\left[1+0.055{F}^{0.5}R{e}_{\mathrm{lo}}^{0.16}\right]\phantom{\rule{2em}{0ex}}\left(24\right)$ 
Kew and Cornwell [33]  R141b  Single tubes of 1.39–3.69 mm inner diameter  Nucleate boiling, confined bubble boiling, convective boiling, partial dry out    ${h}_{\mathrm{tp}}=30R{e}_{\mathrm{lo}}^{0.857}{\mathrm{Bo}}^{0.714}\frac{{\lambda}_{\mathrm{l}}}{{D}_{\mathrm{h}}}{\left(\frac{1}{1{\chi}_{\mathrm{v},x}}\right)}^{0.143}\phantom{\rule{2em}{0ex}}\left(25\right)$ 
Yan and Lin [34]  R134a  28 parallel tubes 2 mm  Convective boiling  G = 50 to 200 kg/m^{2}s; q = 0.5 to 2 W/cm^{2}  ${h}_{\mathrm{tp}}=\left({C}_{1}{\mathrm{Co}}^{{C}_{2}}+{C}_{3}{\mathrm{Bo}}^{{C}_{4}}F{r}_{\mathrm{lo}}\right){\left(1{\chi}_{\mathrm{v},\mathrm{m}}\right)}^{0.8}{h}_{\mathrm{l}}\phantom{\rule{2em}{0ex}}\left(26\right)$ h_{l} = 4.364λ_{l}/D_{h} (27)${C}_{m}={C}_{m,1}{\mathrm{Re}}_{\mathrm{lo}}^{{C}_{m,2}}{T}_{\mathrm{R}}^{{C}_{m,3}}\phantom{\rule{2em}{0ex}}\left(28\right)$ The best fitting values for the constants C_{m,1}, C_{m,2}, and C_{m,3} are listed in Table 3 
Values of the constants in Yan and Lin[34] correlation
Average  Co > 0.5  0.15<Co ≤ 0.5  Co ≤ 0.15  

C _{m,1}  C _{m,2}  C _{m,3}  C _{m,1}  C _{m,2}  C _{m,3}  C _{m,1}  C _{m,2}  C _{m,3}  
1  933.6  0.07575  26.19  47.3  0.3784  14.67  356600  −0.6043  18.59 
2  −0.2  0  0  2612.8  0  37.27  1409.1  −0.5506  16.303 
3  21700  0.5731  34.98  100150  0  24.371  12.651  0.3257  10.118 
4  14.84  −0.0224  13.22  3.99  −0.1937  4.794  0.15  0  0 
Standard deviation of the various correlations with respect to experimental results
G value (kg/m^{2})  Measurement results  Warrier et al.[27] (%)  Kandlikar and Balasubramanian[28] (%)  Sun and Mishima[29] (%)  Bertsch et al.[30] (%)  Lazarek and Black[31] (%)  Gungor and Winterton[32] (%)  Liu and Witerton[36] (%)  Kew and Cornwell[33] (%)  Yan and Lin[34] (%) 

130.59  0.92  −27.89  41.6  133.99  166.33  65.87  188.31  −32.68  16.22  −19.64 
174.12  1.24  −31.37  30.34  97.03  130.45  60.27  93.15  −60.02  33.67  −8.55 
217.65  1.63  −34.92  20.25  80.65  100.28  45.09  67.84  −43.69  −1.22  −6.23 
261.18  2.12  −38.41  10.32  48.89  44.37  25.75  16.35  −58.02  −18.09  −26.22 
304.71  2.37  −36.85  10.14  50.32  53.31  29.29  8.49  −56.62  −20.13  −22.64 
348.24  2.96  −40.13  0.84  25.01  30.2  11.31  −10.39  −59.7  −25.52  −25.17 
391.77  3.2  −38.46  1.54  28.33  60.69  14.79  2.17  −47.7  −17.36  −5.16 
435.3  3.39  −33.23  6.6  26.66  69.24  27.36  4.72  −42.28  −14.41  11.49 
478.83  3.95  −35.52  −0.32  13.33  60.17  3.62  −3.11  −43.35  −20.11  14.45 
522.36  4.2  −31.93  2.24  6.52  38.53  17.09  −19.72  −52.51  −26.04  4.7 
565.89  4.48  −29.01  2.21  3.02  47.22  −0.97  −16.04  −47.65  −25.47  22.78 
609.42  5.06  −29.69  −0.56  −5.43  41.32  5.61  −19.94  −48.04  −29.81  25.42 
652.95  5.55  −29.21  −7.08  −10.67  53.45  12.48  5.53  −36.92  −28.05  29.41 
Nanofluids boiling heat transfer in minichannels
Effect of silver nanoparticles on the local heat transfer
where λ is the thermal conductivity, ϕ is the nanoparticle volume fraction, μ_{b} is the viscosity of the base fluid, ρ is the density, and C_{p} is the specific heat capacity.
Pure water and nanofluid properties at 100 kPa and 60°C
Water  Silver nanoparticles  Silver nanofluid (C= 25 mg/L)  Silver nanofluid (C= 50 mg/L)  

Effective thermal conductivity λ (mw/mK)  603  429  603.427  603.856 
Density ρ (kg/m^{3})  996  10490  998.25  1000.51 
Dynamic viscosity μ (kg/ms)  7.977 × 10^{−4}    0.000798  0.0008 
Specific heat, C_{p} (J/kgK)  4,182  233  4181.064  4180.124 
Effect of silver nanoparticles on the average heat transfer
In general, heat transfer enhancement using nanofluid has being investigated by many researchers, and several mechanisms leading to this enhancement are presented, such as nanoparticle interactions with bubbles [38], nanoparticle porous deposition on the surface [20], reduction of the thermal boundary layer thickness due to nonuniform distribution of the thermal conductivity and viscosity [39], increase in the viscosity and decrease in the thermal capacity [40], chaotic movement, and dispersion and fluctuation of nanoparticles [41]. Also, as explained by Wen and Ding [37], nanofluid improves the convection heat transfer coefficient because of nanoparticle rotation and the associated microconvection. However, Xu and Xu [25] attributed enhancement of nanofluid heat transfer to the increase of the thin liquid film evaporation. It has been found by several researchers [42, 43] that bubble diameters increase using nanofluids boiling, but the nucleation site density decreases. In the boiling field, further studies on bubble dynamics and on the heat transfer of nanofluid microlayer evaporation will provide valuable information about the physical mechanisms controlling heat transfer enhancement when adding nanoparticles to the base fluid.
Conclusions
 1.
Among all correlations employed in the present work, only Kandlikar and Balasubramanian [28] correlation best predicts the heat transfer coefficients for convective boiling in minichannels. Those of Lazarek and Black [31] and Yan and Lin [34] established for macrochannels give satisfactory estimation of boiling heat transfer coefficient with the standard deviation of 29%. However, Sun and Mashima [29] correlation gives the best predictions with standard deviation of 13% for high mass flux only, but it over predicts measurements for low mass fluxes.
 2.
Adding silver nanoparticles in the water base fluid enhances the boiling local heat transfer coefficient, local heat flux, and local vapor quality, and reduces the surface temperature compared to pure water.
 3.
The boiling local heat transfer enhancement with silverwater nanofluid is highest in the minichannel entrance region where the vapor quality is low, and it decreases along the flow direction. The enhancement of the local heat transfer coefficient can reach 86% and 200% for 25 mg/L and 50 mg/L silver concentrations in waterbased fluid, respectively.
 4.
At high vapor quality, the presence of silver nanoparticles in water base fluid has no effect on the boiling local heat transfer coefficient, which decreases dramatically.
 5.
Suspension of silver metallic nanoparticles in water base fluid at very low concentration can significantly increase the heat transfer performance of the miniature systems. The maximum enhancement of the average heat transfer coefficient is about 132% and 162% for 25 mg/L and 50 mg/L silver concentrations nanofluid respectively. Using nanofluids, at low nanoparticle concentrations, in minichannels or microchannels can be considered as the potential revolution in heat transfer enhancement processes for many industries' applications.
Abbreviations
 Bo:

boiling number, q_{channel,x} / (Gh_{ fg })
 Co:

convection number, (1/χ_{v,x} − 1)^{0.8}(ρ_{g} / ρ_{l})^{0.5}
 C:

concentration
 Cp:

specific heat capacity (J/kgK)
 Dh:

hydraulic diameter (m) 2H_{channel}W_{channel} / (H_{channel} + W_{channel})
 e:

channel thickness (m)
 F:

forced convection enhancement factor
 Fr:

Froude number, G^{2}/(ρ^{2}gD_{h})
 g:

gravity (m/s^{2})
 G:

mass flux (kg/m^{2}s)
 h:

heat transfer coefficient (W/m^{2}K)
 hfg:

latent heat of vaporization (J/kg)
 Hchannel:

channel height (m)
 L:

channel length (m)
 $\stackrel{\xb7}{m}$ :

mass flow rate (kg/s)
 M:

molar mass (kg/kmol)
 Nchannel:

number of channels
 Nu:

Nusselt number
 PR:

reduced pressure, P/P_{crit}
 Pr:

Prandtl number
 q:

heat flux (W/m^{2})
 Re:

Reynolds number, GD_{h}/μ
 S:

nucleate boiling suppression factor
 T:

temperature (K)
 TR:

reduced temperature, T/T_{crit}
 Wchannel:

channel width (m)
 We:

Weber number, G^{2}D_{h}/(σρ_{l})
 χ:

vapor quality
 x:

axial coordinate (m)
 y:

axial coordinate (m). Greek letters: Δ, increment, standard deviation
 λ:

thermal conductivity (W/m K)
 ξ:

channel surface roughness (μm)
 μ:

dynamic viscosity (kg/ms)
 ρ:

density (kg/m^{3})
 σ:

surface tension (N/m)
 φ:

volume fraction. Subscripted letters: bf, base fluid
 crit:

critical point
 eff:

effective
 g:

gas
 go:

gas only
 f:

fluid
 k:

index, gas or liquid: l, liquid
 lo:

liquid only
 m:

average
 nb:

nucleate boiling
 nf:

nanofluid
 p:

solid nanoparticles
 s:

surface
 sat:

saturation
 sp:

single phase
 tp:

two phase
 v:

vapor
 w:

wall
 x:

local value.
Declarations
Acknowledgment
The authors of this article would like to thank the French Ministry of Industry and Commerce (DGCIS) for the funding of this work, which is integrated in the European project OPERANET2 labeled by CelticPlus.
Authors’ Affiliations
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