**1.2 Ethanol/polyalphaolefin nanoemulsion: a novel heat transfer fluid**

A variety of industries and military sectors have faced the challenge of finding effective and efficient thermal management solutions as the electronic systems used can output heat flux as high as 100 W/cm<sup>2</sup> [7–11]. While many advanced works have been performed to develop high performance heat exchangers with varieties of shape, size and tube surface augmentation, the bottleneck of improvement has fall into how to develop efficient heat transfer fluids with significantly improved thermal properties over those currently available. To date, several heat transfer fluid candidates have been reported, which include, but not limited to, nanofluids [12–34], dilute emulsion [35, 36], and emulsion [37–41]: Nanofluid has been intensively studied since it was proposed in 1995 by Choi [42]. It is consisted of a mixture of solid nanoparticles and base fluid, and it has been reported to be potentially useful in applications such as nuclear power system, solar collector, and compact high power density electronics system. Emulsion and dilute emulsion fluid are essentially similar systems made of a mixture of two immiscible liquids, while the "dilute emulsion" has 5 vol% or less dispersed component. Using emulsion to enhance heat transfer can be dated back to 1959 by Moore [43], and it has attracted interests of researchers [35–45]. One of the most detailed descriptions of how emulsions boil is the work of Bulanov and Gasanov [38–41, 44, 45], in which they proposed chain-reaction boiling of the droplets as an explanation for the observed superheated droplets and bubble dynamics on the heat surface. In addition, Rosele [46] et al. carried out an experimental study of boiling heat transfer from a horizontal heated wire, including visual observations in which the heat transfer could be enhanced in dilute emulsions compared to that of water as a base fluid.

Recently, the authors have proposed a new type of heat transfer fluid called "nanoemulsion" [47]. Nanoemulsion is a suspension of liquid nanodroplets formed by self-assembly inside another immiscible fluid, as part of a broad class of multiphase colloidal dispersions [48]. The nanoemulsion eliminates the presence of solid particles, which usually cause abrasion and erosion issues even with extremely fine particles such as nanoparticles [49–53], and instead, uses liquid nanostructures [54–63]. The droplets typically have a length scale less or equal to 50 nm, which makes the nanoemulsion fluid thermodynamically stable and transparent to natural light. A comparison of nanoemulsion with emulsion (dilute emulsion) is represented in **Table 3** [47, 48].


#### **Table 3.**

*Comparison of Nanoemulsion and emulsion (dilute emulsion).*

conventional to micro dimensions. The channel classification suggested in [4] has categorized the range of 1–100 μm as the microchannels, 100 μm to 1 mm as the mesochannels, 1–6 mm as the compact passages, and the range above 6 mm as the

Kandlikar et al. [3] improved their channel classification reported earlier in [5], and then presented a more general classification according to the minimum channel dimension, shown in **Table 1**. In this table, D indicates the channel diameter. However, in case the channel is non-circular, the smallest channel dimension is recommended to be taken for D; for instance, in a rectangular channel the smaller side is considered for D. This channel classification may be used for either of single-

For the case of phase-change heat transfer in particular, the channels with various scales are classified according to the Bond number proposed by Cheng et al. [6] for expressing the transition from macroscale heat transfer to microscale heat transfer. Bond number takes into consideration the impacts of pressure, temperature, and some thermophysical properties of a fluid and is given as follows:

> *Bo* <sup>¼</sup> *Dh lC* � �<sup>2</sup>

where *Dh* stands for hydraulic diameter, and *lC* accounts for capillary length

For water at 373 K, the capillary length (*lC*) of water is practically 2.72 mm. Based on Cheng's et al. classification, the channels with the range of a hydraulic diameter (*Dh*) between 600 μm and 4,720 μm can be considered as minichannels for the applications using water as the base liquid. **Table 2** shows the channel

**Channel Classification Smallest Channel Dimension (D)**

**Channel Classification Bond Number (Bo) Hydraulic Diameter** Microchannels Bo <0.05 *Dh* < 600 μm Minichannels 0.05 < Bo <3 600 μm < *Dh* < 4720 μm Macrochannels Bo >3 *Dh* > 4720 μm

Conventional Channels D ˃ 3 mm Minichannels 3 mm ≥ D ˃ 200 μm Microchannels 200 μm ≥ D ˃ 10 μm Transitional Microchannels 10 μm ≥ D ˃ 1 μm Transitional Nanochannels 1 μm ≥ D ˃ 0.1 μm Nanochannels 0.1 μm ≥ D

r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *σ g* ð Þ *ρ*<sup>1</sup> � *ρ<sup>V</sup>*

*lC* ¼

classification based on Bond Number (Bo) for water at 373 K.

(1)

(2)

conventional channels.

expressed as:

**Table 1.**

**Table 2.**

**168**

*Channel classification based on dimensions.*

*Channel classification based on bond number for water at 373 K.*

phase or two-phase flow applications.

*Heat Transfer - Design, Experimentation and Applications*

Pool boiling heat transfer studies of nanoemulsion fluids have shown that: (i) the thermophysical properties of the nanoemulsion fluids are found to be better than that of the base fluid [54, 55]; and (ii) an appreciable increase in heat transfer coefficient (HTC) and critical heat flux (CHF) can be observed in nanoemulsion fluids when the phase-changeable nanodroplets formed inside undergo nucleation [57, 61, 62].

Convective heat transfer of conventional heat transfer fluids inside mini/ microchannel heat exchangers has been extensively studied due to its capability to remove high heat fluxes [33, 36, 64–66]. However, relatively few studies have been carried out to investigate the application of novel heat transfer fluids inside mini/ microchannels. The recent development of nanotechnology has led to the improvement of heat transfer coefficient using novel nanostructured working fluids. While there are some recent experimental studies addressing the possibility of using nanostructured heat transfer fluids inside micro/nanostructured surface to enhance heat transfer [26, 31, 34], other recent studies showed that the use of nanofluids and nanotube coating offers a lower heat transfer coefficient at the coated surface compared to the bare surface [67–70].

Despite the significant enhancement observed in pool boiling heat transfer of nanoemulsion fluids compared to the base fluids, it remains inconclusive whether the same optimistic outlook can be expected in the convective heat transfer of nanoemulsion fluids. The present study aims to numerically and experimentally investigate the flow and heat transfer characteristics of ethanol/PAO nanoemulsion inside a conventionally manufactured minichannel and compares them with those of a microchannel heat exchanger manufactured additively.

### **2. Experimental approach**

#### **2.1 Preparation of nanoemulsion**

To minimize the impact of the differences in thermophysical properties of the two constitutive fluids on the convective heat transfer experiments, ethanol and PAO fluids were used to prepare the nanoemulsion for this study since their thermal conductivity values are very similar. Dioctyl sulfosuccinate sodium salt (Sigma Aldrich) was used as a surfactant to form the nanoemulsion.

In the preparation process, the first step was to add the dioctyl sulfosuccinate sodium salt (Sigma Aldrich) into PAO fluid. The mixture was stirred until the dioctyl sulfosuccinate sodium salt was completely dissolved. The second step is to inject ethanol into the base fluid and mix them well until the mixture became transparent. In the present study, ethanol (4 or 8 percentage of ethanol by weight) is added into PAO to form 4 wt % or 8 wt % Ethanol/PAO nanoemulsion fluids respectively.

conductivities of the base PAO fluid and 8 wt % Ethanol/PAO nanoemulsion fluid and their dependence upon temperature. Thermal conductivity of the pure PAO and Ethanol/PAO nanoemulsion fluids was measured in the temperature range from 25–75°C using the 3ω-wire method [56]. As represented in **Figure 3**, the Ethanol/PAO nanoemulsion fluid experimented here exhibits a higher thermal conductivity compared to pure PAO: a 3.9% increase which agrees well with the earlier study [57]. In addition, the thermal conductivity decreases with higher temperature

*Thermal conductivity of the pure PAO and 8 wt % ethanol/PAO nanoemulsion at temperature range of*

*Small angle neutron scattering curves for 4 wt % and 8 wt % ethanol/PAO nanoemulsion heat transfer fluids.*

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini…*

*DOI: http://dx.doi.org/10.5772/intechopen.96015*

Similarly, the viscosity of the Ethanol/PAO nanoemulsions was measured using a commercial viscometer (Brookfield DV-I Prime) from 25–75°C. In general, the viscosity is found to decrease with increasing temperature in most heat transfer fluids, which is also observed in the proposed Ethanol/PAO nanoemulsion, that is, a decrease from 14.3 cP to 3.05 cP as illustrated in **Figure 4**, which agrees well with

The thermophysical properties considered in the present study for ethanol/PAO nanoemulsion and pure PAO fluids to conduct experimental heat transfer tests are

but at a substantially lower rate compared to pure PAO.

the authors' previous study [57].

summarized in **Table 4**.

**171**

**Figure 2.**

**Figure 3.**

*25 75°C.*

#### *2.1.1 Structural properties*

**Figure 2** shows the small angle neutron scattering (SANS) experimental results of ethanol nanodroplets measured by NG7 SANS beamline at NIST Center for Neutron Research (NCNR), and the data was reduced to extract the structural information following the protocol provided by NCNR [71, 72]. It was found that the ethanol nanodroplets formed inside the nanoemulsion fluids have a radius of less than 1 nm on average.

#### *2.1.2 Thermophysical properties*

Thermal conductivity and viscosity are macroscopically observable parameters that affect the thermal performance of the fluids. **Figure 3** shows the thermal

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini… DOI: http://dx.doi.org/10.5772/intechopen.96015*

#### **Figure 2.**

Pool boiling heat transfer studies of nanoemulsion fluids have shown that: (i) the thermophysical properties of the nanoemulsion fluids are found to be better than that of the base fluid [54, 55]; and (ii) an appreciable increase in heat transfer coefficient (HTC) and critical heat flux (CHF) can be observed in nanoemulsion fluids when the phase-changeable nanodroplets formed inside undergo nucleation [57, 61, 62]. Convective heat transfer of conventional heat transfer fluids inside mini/ microchannel heat exchangers has been extensively studied due to its capability to remove high heat fluxes [33, 36, 64–66]. However, relatively few studies have been carried out to investigate the application of novel heat transfer fluids inside mini/ microchannels. The recent development of nanotechnology has led to the improvement of heat transfer coefficient using novel nanostructured working fluids. While there are some recent experimental studies addressing the possibility of using nanostructured heat transfer fluids inside micro/nanostructured surface to enhance heat transfer [26, 31, 34], other recent studies showed that the use of nanofluids and nanotube coating offers a lower heat transfer coefficient at the coated surface

Despite the significant enhancement observed in pool boiling heat transfer of nanoemulsion fluids compared to the base fluids, it remains inconclusive whether the same optimistic outlook can be expected in the convective heat transfer of nanoemulsion fluids. The present study aims to numerically and experimentally investigate the flow and heat transfer characteristics of ethanol/PAO nanoemulsion inside a conventionally manufactured minichannel and compares them with those

To minimize the impact of the differences in thermophysical properties of the two constitutive fluids on the convective heat transfer experiments, ethanol and PAO fluids were used to prepare the nanoemulsion for this study since their thermal conductivity values are very similar. Dioctyl sulfosuccinate sodium salt (Sigma

In the preparation process, the first step was to add the dioctyl sulfosuccinate sodium salt (Sigma Aldrich) into PAO fluid. The mixture was stirred until the dioctyl sulfosuccinate sodium salt was completely dissolved. The second step is to inject ethanol into the base fluid and mix them well until the mixture became transparent. In the present study, ethanol (4 or 8 percentage of ethanol by weight) is added into PAO to form 4 wt % or 8 wt % Ethanol/PAO nanoemulsion fluids respectively.

**Figure 2** shows the small angle neutron scattering (SANS) experimental results

Thermal conductivity and viscosity are macroscopically observable parameters

that affect the thermal performance of the fluids. **Figure 3** shows the thermal

of ethanol nanodroplets measured by NG7 SANS beamline at NIST Center for Neutron Research (NCNR), and the data was reduced to extract the structural information following the protocol provided by NCNR [71, 72]. It was found that the ethanol nanodroplets formed inside the nanoemulsion fluids have a radius of

compared to the bare surface [67–70].

*Heat Transfer - Design, Experimentation and Applications*

**2. Experimental approach**

*2.1.1 Structural properties*

less than 1 nm on average.

**170**

*2.1.2 Thermophysical properties*

**2.1 Preparation of nanoemulsion**

of a microchannel heat exchanger manufactured additively.

Aldrich) was used as a surfactant to form the nanoemulsion.

*Small angle neutron scattering curves for 4 wt % and 8 wt % ethanol/PAO nanoemulsion heat transfer fluids.*

#### **Figure 3.**

*Thermal conductivity of the pure PAO and 8 wt % ethanol/PAO nanoemulsion at temperature range of 25 75°C.*

conductivities of the base PAO fluid and 8 wt % Ethanol/PAO nanoemulsion fluid and their dependence upon temperature. Thermal conductivity of the pure PAO and Ethanol/PAO nanoemulsion fluids was measured in the temperature range from 25–75°C using the 3ω-wire method [56]. As represented in **Figure 3**, the Ethanol/PAO nanoemulsion fluid experimented here exhibits a higher thermal conductivity compared to pure PAO: a 3.9% increase which agrees well with the earlier study [57]. In addition, the thermal conductivity decreases with higher temperature but at a substantially lower rate compared to pure PAO.

Similarly, the viscosity of the Ethanol/PAO nanoemulsions was measured using a commercial viscometer (Brookfield DV-I Prime) from 25–75°C. In general, the viscosity is found to decrease with increasing temperature in most heat transfer fluids, which is also observed in the proposed Ethanol/PAO nanoemulsion, that is, a decrease from 14.3 cP to 3.05 cP as illustrated in **Figure 4**, which agrees well with the authors' previous study [57].

The thermophysical properties considered in the present study for ethanol/PAO nanoemulsion and pure PAO fluids to conduct experimental heat transfer tests are summarized in **Table 4**.

#### **Figure 4.**

*Dynamic viscosity of the pure PAO and ethanol/PAO Nanoemulsion fluids at temperature range of 25* � *75°C.*

microchannel heat exchangers were placed horizontally to the ground. The liquid in the reservoir was first preheated to a preset temperature of 75°C. The liquid flow rate was adjusted to the desired value and monitored by a digital paddle wheel flow meter (Micro-Flow™). Within the experiments, the fluid temperature and surface temperature were automatically recorded by the data acquisition system. The test system reached steady-state conditions while the changing rates of all the set parameters mentioned above were less than 0.2%. The entire test rig was fully automated using the National Instrument LabVIEW software and data acquisition devices (National

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini…*

*DOI: http://dx.doi.org/10.5772/intechopen.96015*

**Figure 6(a)** and **(b)** depict the side-view and top-view of the test sections respectively, in which seven thermocouples were attached to the top surface of both minichannel and microchannel heat exchangers and were used to measure the local

*Schematic of the test sections (both mini- and microchannels): (a) side view, (b) top view with wall-mounted*

Instruments Corp., Austin, TX, USA).

**Figure 5.**

**Figure 6.**

**173**

*thermocouples.*

*Schematic of the test apparatus.*


#### **Table 4.**

*Thermophysical properties of ethanol/PAO Nanoemulsion and PAO at 25°C.*

## **2.2 Experimental apparatus**

The convective heat transfer tests of nanoemulsion fluids were carried out for two heat exchangers comprising a conventionally manufactured minichannel of 12 circular channels and an additively manufactured microchannel of 30 rectangular channels, both with the same exterior heat exchanger geometry. A schematic of the test loop setup built to conduct experiments is shown in **Figure 5**. The test apparatus consists mainly of a horizontal test section of either minichannel or microchannel heat exchanger, three gear pumps, a fluid reservoir, a flow sight glass, preheating section, condenser, and data acquisition system to measure and record the pressure, temperature, and mass flow rate. In the present study, the heat transfer tests were performed under a uniform wall heat flux applied on the top and bottom surfaces of the minichannel and microchannel heat exchangers. A programmable DC power supply with 0.05% power uncertainty was used to electrically heat up the test sections in order to obtain the constant wall heat flux. Furthermore, the preheating section was also electrically heated by a circulator, and the inlet fluid temperature is controlled at a desired value before entering the test sections. The inlet and outlet fluid temperatures were measured by two K-type thermocouples. The test section was carefully wrapped using an insulation material with a thermal conductivity of 0*:*043 *W=*ð Þ *m:K* . A layer of aluminum foil was then wrapped on the outside of thermal insulation layer. The heat losses through the insulation layer were estimated to be lower than 2% of total heat losses and it was neglected in thermal performance calculations in the present study. Pressure drops of the test section were measured by two GP-50 differential pressure transducers with a working range of 0–200 kPa and an uncertainty of 0.25%. For all the tests conducted, both minichannel and

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini… DOI: http://dx.doi.org/10.5772/intechopen.96015*

**Figure 5.** *Schematic of the test apparatus.*

microchannel heat exchangers were placed horizontally to the ground. The liquid in the reservoir was first preheated to a preset temperature of 75°C. The liquid flow rate was adjusted to the desired value and monitored by a digital paddle wheel flow meter (Micro-Flow™). Within the experiments, the fluid temperature and surface temperature were automatically recorded by the data acquisition system. The test system reached steady-state conditions while the changing rates of all the set parameters mentioned above were less than 0.2%. The entire test rig was fully automated using the National Instrument LabVIEW software and data acquisition devices (National Instruments Corp., Austin, TX, USA).

**Figure 6(a)** and **(b)** depict the side-view and top-view of the test sections respectively, in which seven thermocouples were attached to the top surface of both minichannel and microchannel heat exchangers and were used to measure the local

**Figure 6.**

*Schematic of the test sections (both mini- and microchannels): (a) side view, (b) top view with wall-mounted thermocouples.*

**2.2 Experimental apparatus**

**Figure 4.**

**Table 4.**

**172**

The convective heat transfer tests of nanoemulsion fluids were carried out for two heat exchangers comprising a conventionally manufactured minichannel of 12 circular channels and an additively manufactured microchannel of 30 rectangular channels, both with the same exterior heat exchanger geometry. A schematic of the test loop setup built to conduct experiments is shown in **Figure 5**. The test apparatus consists mainly of a horizontal test section of either minichannel or microchannel heat exchanger, three gear pumps, a fluid reservoir, a flow sight glass, preheating section, condenser, and data acquisition system to measure and record the pressure, temperature, and mass flow rate. In the present study, the heat transfer tests were performed under a uniform wall heat flux applied on the top and bottom surfaces of the minichannel and microchannel heat exchangers. A programmable DC power supply with 0.05% power uncertainty was used to electrically heat up the test sections in order to obtain the constant wall heat flux. Furthermore, the preheating section was also electrically heated by a circulator, and the inlet fluid temperature is controlled at a desired value before entering the test sections. The inlet and outlet fluid temperatures were measured by two K-type thermocouples. The test section was carefully wrapped using an insulation material with a thermal conductivity of 0*:*043 *W=*ð Þ *m:K* . A layer of aluminum foil was then wrapped on the outside of thermal insulation layer. The heat losses through the insulation layer were estimated to be lower than 2% of total heat losses and it was neglected in thermal performance calculations in the present study. Pressure drops of the test section were measured by two GP-50 differential pressure transducers with a working range of 0–200 kPa and

*Dynamic viscosity of the pure PAO and ethanol/PAO Nanoemulsion fluids at temperature range of 25* � *75°C.*

**Property 4 wt % Nanoemulsion 8 wt % Nanoemulsion PAO** Density (*kg=m*3) 794 792 798 Conductivity (W/m-K) 0.148 0.149 0.143 Viscosity (kg/m-s) 13.8 � <sup>10</sup>�<sup>3</sup> 14.3 � <sup>10</sup>�<sup>3</sup> 7.34 � <sup>10</sup>�<sup>3</sup> Nanodroplet radius (*nm*) 0.5 0.8 N/A

*Thermophysical properties of ethanol/PAO Nanoemulsion and PAO at 25°C.*

*Heat Transfer - Design, Experimentation and Applications*

an uncertainty of 0.25%. For all the tests conducted, both minichannel and


#### **Table 5.**

*Geometry of the test sections along with operating conditions used.*

wall temperatures as shown in **Figure 6(b)** where each red dot represents one wallmounted thermocouple.

**Table 5** summarizes geometry of both test sections (minichannel and microchannel) coupled with the operating conditions applied to conduct experimental tests for single-phase flow and two-phase flow as well as to conduct numerical analysis of heat transfer performance for comparison purposes.

#### *2.2.1 Data processing*

In the present study, the average heat transfer coefficient *h* is used and expressed as follows:

$$h = \frac{q\_{wall}}{T\_s - T\_f} \tag{3}$$

The Reynolds number of the flow can also be calculated as follows:

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini…*

Total pressure loss along the test sections is calculated by:

and the friction factor is calculated by:

*DOI: http://dx.doi.org/10.5772/intechopen.96015*

in which *ε* ¼ *H=W*.

listed in **Table 6**.

Heat flux (W/m<sup>2</sup>

*Uncertainties sources for the experimental tests.*

*Uncertainties for heat transfer performance parameters.*

**Table 6.**

**Table 7.**

**175**

*2.2.2 Uncertainty propagation*

*Re* <sup>¼</sup> *<sup>ρ</sup>VD μ*

*f* ¼ Δ*Pfriction*

number (Po) can be found to be only a function of microchannel's aspect ratio:

To take the shape of the channel's cross-section into consideration, the Poiseuille

*Po* <sup>¼</sup> *<sup>f</sup>* � *Re* <sup>¼</sup> <sup>4</sup>*π*<sup>2</sup> <sup>1</sup> <sup>þ</sup> *<sup>ε</sup>*<sup>2</sup> ð Þ

The uncertainties for different parameters involved in the experimental tests are

An uncertainty analysis is performed from the measurement uncertainties using calculus and the principle of superposition of errors. In general, for a variable F that

**Parameter Uncertainty** Temperature (°C) �0*:*1 Flow velocity (*m=s*) �6% Position of the thermocouples (m) �0*:*01 Dimensions of the minichannel (m) �0*:*002 Dimensions of the microchannel (m) �0*:*002 Power input (W) �0*:*5%

Pressure (Pascal) �0*:*25%

**Calculated Variable Uncertainty** Heat transfer coefficient, *h* �6% Nusselt number, *Nu* �8% Reynolds number, *Re* �6% Friction factor, *f* �10%

) �0*:*5%

is a function of several variables such as F ¼ Fð Þ *a*, *b*,*c*, … , the squares of the

3 ffiffi

2*D*

Δ*P* ¼ Δ*Pfriction* þ Δ*Pminor* (10)

*<sup>ρ</sup>LV*<sup>2</sup> (11)

*<sup>ε</sup>* <sup>p</sup> ð Þ <sup>1</sup> <sup>þ</sup> *<sup>ε</sup>* (12)

(9)

where *qwall* is the local heat flux estimated by considering the local heat loss as shown in Eqs. (4) and (5) for minichannel and microchannel respectively, *Ts* is the average local surface temperature measured by the wall-mounted thermocouples along the channel direction calculated by Eq. (6), *T <sup>f</sup>* is the fluid's bulk mean temperature calculated by Eq. (7).

$$q\_{wall} = \frac{Q}{n(\pi DL)}\tag{4}$$

$$q\_{wall} = \frac{Q}{n(2HL + 2WL)}\tag{5}$$

$$T\_s = \frac{1}{7} \sum\_{\mathbf{x}=1}^{\mathbf{x}=7} T\_\mathbf{x} \tag{6}$$

$$T\_f = \frac{1}{2} \left( T\_{\,f,in} + T\_{\,f,out} \right) \tag{7}$$

The average Nusselt number of nanoemulsion fluid can be expressed by:

$$Nu = \frac{h \ D\_h}{k\_f} \tag{8}$$

in which *Dh* is the hydrodynamic diameter for either of minichannel or microchannel.

*Convective Heat Transfer of Ethanol/Polyalphaolefin Nanoemulsion in Mini… DOI: http://dx.doi.org/10.5772/intechopen.96015*

The Reynolds number of the flow can also be calculated as follows:

$$Re = \frac{\rho \text{VD}}{\mu} \tag{9}$$

Total pressure loss along the test sections is calculated by:

$$
\Delta P = \Delta P\_{friction} + \Delta P\_{minor} \tag{10}
$$

and the friction factor is calculated by:

$$f = \Delta P\_{friction} \frac{2D}{\rho LV^2} \tag{11}$$

To take the shape of the channel's cross-section into consideration, the Poiseuille number (Po) can be found to be only a function of microchannel's aspect ratio:

$$P o = f \times Re = \frac{4\pi^2(1+\varepsilon^2)}{3\sqrt{\varepsilon}(1+\varepsilon)}\tag{12}$$

in which *ε* ¼ *H=W*.

wall temperatures as shown in **Figure 6(b)** where each red dot represents one wall-

**Test Section Material Cross Section Orientation Channel Diameter Length** Microchannel 316 L Steel Rectangular Horizontal 640*μm* � 760*μm* 120 mm Minichannel Aluminum Circular Horizontal 1 mm 120 mm

Loop Working Fluid *Tin Pin* Heat Flux Mass Flux Single-Phase Flow Nanoemulsion 75°C 159 kPa 13–44 kW/m<sup>2</sup> 1063–8504

Two-Phase Flow Nanoemulsion 75°C 159 kPa 13–44 kW/m2 630–5037

experimental tests for single-phase flow and two-phase flow as well as to conduct

**Table 5** summarizes geometry of both test sections (minichannel and microchannel) coupled with the operating conditions applied to conduct

numerical analysis of heat transfer performance for comparison purposes.

In the present study, the average heat transfer coefficient *h* is used and

*<sup>h</sup>* <sup>¼</sup> *qwall Ts* � *T <sup>f</sup>*

*qwall* <sup>¼</sup> *<sup>Q</sup>*

*qwall* <sup>¼</sup> *<sup>Q</sup>*

*Ts* <sup>¼</sup> <sup>1</sup> 7 X*x*¼7 *x*¼1

The average Nusselt number of nanoemulsion fluid can be expressed by:

in which *Dh* is the hydrodynamic diameter for either of minichannel or

*Nu* <sup>¼</sup> *h Dh k f*

*T <sup>f</sup>*,*in* þ *T <sup>f</sup>*,*out*

*<sup>T</sup> <sup>f</sup>* <sup>¼</sup> <sup>1</sup> 2 *<sup>n</sup>*ð Þ *<sup>π</sup>DL* (4)

*Tx* (6)

*<sup>n</sup>*ð Þ <sup>2</sup>*HL* <sup>þ</sup> <sup>2</sup>*WL* (5)

� � (7)

where *qwall* is the local heat flux estimated by considering the local heat loss as shown in Eqs. (4) and (5) for minichannel and microchannel respectively, *Ts* is the average local surface temperature measured by the wall-mounted thermocouples along the channel direction calculated by Eq. (6), *T <sup>f</sup>* is the fluid's bulk mean

(3)

Kg/m2 -s

Kg/m2 -s

(8)

mounted thermocouple.

**Table 5.**

Operating Conditions at Inlet of Test Sections

*Geometry of the test sections along with operating conditions used.*

*Heat Transfer - Design, Experimentation and Applications*

**Geometry**

*2.2.1 Data processing*

expressed as follows:

microchannel.

**174**

temperature calculated by Eq. (7).

#### *2.2.2 Uncertainty propagation*

The uncertainties for different parameters involved in the experimental tests are listed in **Table 6**.

An uncertainty analysis is performed from the measurement uncertainties using calculus and the principle of superposition of errors. In general, for a variable F that is a function of several variables such as F ¼ Fð Þ *a*, *b*,*c*, … , the squares of the


#### **Table 6.**

*Uncertainties sources for the experimental tests.*


#### **Table 7.**

*Uncertainties for heat transfer performance parameters.*

uncertainty in F is the sum of the square of the uncertainties due to each independent variable, *<sup>δ</sup><sup>F</sup>* <sup>¼</sup> *<sup>∂</sup><sup>F</sup> <sup>∂</sup><sup>a</sup> <sup>δ</sup><sup>a</sup>* � �<sup>2</sup> <sup>þ</sup> *<sup>∂</sup><sup>F</sup> <sup>∂</sup><sup>b</sup> <sup>δ</sup><sup>b</sup>* � �<sup>2</sup> <sup>þ</sup> *<sup>∂</sup><sup>F</sup> <sup>∂</sup><sup>c</sup> <sup>δ</sup><sup>c</sup>* � �<sup>2</sup> <sup>þ</sup> … h i0*:*<sup>5</sup> where *δa* stands for the uncertainty due to variable*a*. The uncertainties of the heat transfer performance parameters are calculated and represented in **Table 7**.
