*2.1. Thermal Conductivity*

In this study, the thermal conductivity of the Al2O<sup>3</sup> and TiO<sup>2</sup> NFs was tested at room temperature (20 ◦C) by the transient hot-wire technique which showed good reliability for NFs measurements [37]. Several tests were performed for each NF with an interval time of 20 min. The resulted thermal conductivity' values of the Al2O<sup>3</sup> and TiO<sup>2</sup> NFs are given in Figure 1 for several particles' concentrations, and they show good enhancements up to 4.25% and 7.34% for TiO<sup>2</sup> NF and Al2O<sup>3</sup> NF at 0.2% particles' concentration, respectively, compared to the BF. Moreover, Al2O<sup>3</sup> NFs reported higher enhancement in the thermal conductivity values compared to TiO<sup>2</sup> NFs at several values of *ϕ*. This is understandable as the thermal conductivity of Al2O<sup>3</sup> has several times (~5 times) larger than that of the TiO2.

**Figure 1.** The enhancements of thermal conductivity of NFs as a function of volumetric concentrations of Al2O3 and TiO2 nanoparticles. **Figure 1.** The enhancements of thermal conductivity of NFs as a function of volumetric concentrations of Al2O<sup>3</sup> and TiO<sup>2</sup> nanoparticles. **Figure 1.** The enhancements of thermal conductivity of NFs as a function of volumetric concentrations of Al2O3 and TiO2 nanoparticles.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 4 of 15

#### *2.2. Viscosity 2.2. Viscosity*

*2.2. Viscosity* 

The rheology of NFs is considered a unique parameter for understanding their hydraulic and thermal behavior in the flows through heat exchanges. Therefore, the viscosity and rheology of the NFs and BFs are determined using a rheometer (from Brookfield) with a thermostatic bath for several temperatures and shear rates. However, the viscosity values did not change with shear rate values for all the types of particles and their amounts into the BF, which indicates a Newtonian behavior for those NFs. The latter (Newtonian The rheology of NFs is considered a unique parameter for understanding their hydraulic and thermal behavior in the flows through heat exchanges. Therefore, the viscosity and rheology of the NFs and BFs are determined using a rheometer (from Brookfield) with a thermostatic bath for several temperatures and shear rates. However, the viscosity values did not change with shear rate values for all the types of particles and their amounts into the BF, which indicates a Newtonian behavior for those NFs. The latter (Newtonian behavior) was also reported in the literature for similar NF samples [38,39]. The rheology of NFs is considered a unique parameter for understanding their hydraulic and thermal behavior in the flows through heat exchanges. Therefore, the viscosity and rheology of the NFs and BFs are determined using a rheometer (from Brookfield) with a thermostatic bath for several temperatures and shear rates. However, the viscosity values did not change with shear rate values for all the types of particles and their amounts into the BF, which indicates a Newtonian behavior for those NFs. The latter (Newtonian behavior) was also reported in the literature for similar NF samples [38,39].

behavior) was also reported in the literature for similar NF samples [38,39]. On the other hand, the viscosity' values of Al2O3 and TiO2 NFs are tested for several temperatures' values and . The resulted values are presented in Figure 2 show that the level of viscosity decreased by increasing the temperature value and raised by the increase in the particles' volume fraction for both types of NFs (Al2O3 and TiO2 NFs), in similar behavior to most results in the literature [11,38]. On the other hand, the viscosity' values of Al2O<sup>3</sup> and TiO<sup>2</sup> NFs are tested for several temperatures' values and *ϕ*. The resulted values are presented in Figure 2 show that the level of viscosity decreased by increasing the temperature value and raised by the increase in the particles' volume fraction for both types of NFs (Al2O<sup>3</sup> and TiO<sup>2</sup> NFs), in similar behavior to most results in the literature [11,38]. On the other hand, the viscosity' values of Al2O3 and TiO2 NFs are tested for several temperatures' values and . The resulted values are presented in Figure 2 show that the level of viscosity decreased by increasing the temperature value and raised by the increase in the particles' volume fraction for both types of NFs (Al2O3 and TiO2 NFs), in similar behavior to most results in the literature [11,38].

**Figure 2.** Viscosity of NFs as a function of temperature for two types of nanoparticles: (**a**) Al2O3, and (**b**) TiO2. **Figure 2.** Viscosity of NFs as a function of temperature for two types of nanoparticles: (**a**) Al2O<sup>3</sup> , and (**b**) TiO<sup>2</sup> .

**Figure 2.** Viscosity of NFs as a function of temperature for two types of nanoparticles: (**a**) Al2O3, and

(**b**) TiO2. It can be noticed a close values of viscosity for TiO2 and Al2O3 at the same particles' concentrations and an increase of about 2.15% for 0.01 vol.% and of about 6.54% for 0.2 vol.% in comparison with the BF. Moreover, the decrease in the viscosity' value due to the rise in the temperature is significant: up to around 33.6% for 0.2 vol.% when the temperature was increased from the lowest value of 21 °C to the highest value of 40 °C. The latter It can be noticed a close values of viscosity for TiO2 and Al2O3 at the same particles' concentrations and an increase of about 2.15% for 0.01 vol.% and of about 6.54% for 0.2 vol.% in comparison with the BF. Moreover, the decrease in the viscosity' value due to the rise in the temperature is significant: up to around 33.6% for 0.2 vol.% when the temperature was increased from the lowest value of 21 °C to the highest value of 40 °C. The latter findings (viscosity results) were anticipated and agreed with the data in the literature for similar NFs [11,38]. It can be noticed a close values of viscosity for TiO<sup>2</sup> and Al2O<sup>3</sup> at the same particles' concentrations and an increase of about 2.15% for 0.01 vol.% and of about 6.54% for 0.2 vol.% in comparison with the BF. Moreover, the decrease in the viscosity' value due to the rise in the temperature is significant: up to around 33.6% for 0.2 vol.% when the temperature was increased from the lowest value of 21 ◦C to the highest value of 40 ◦C. The latter findings (viscosity results) were anticipated and agreed with the data in the literature for similar NFs [11,38].

findings (viscosity results) were anticipated and agreed with the data in the literature for

similar NFs [11,38].

### **3. Experimental Heat Exchanger System and Methods 3. Experimental Heat Exchanger System and Methods**

The experimental rig of the CPHE was established for the fluid flow and heat transfer of nanofluids as presented in Figure 3. The CPHE system contains an open loop for the cold fluid (using only water that goes to the drain after passing the CPHE) and a hot fluid loop for the NF flow, which includes a tank with heater, pump, 2 flow meters, differential pressure sensor, 4 thermocouples for temperature measurements, and DAQ linked to PC for collecting data. Details about this investigational setup and working principle can be found in an earlier study [40]. The components' accuracy of the investigational setup was firstly checked with DW as a well-known fluid and calibration procedure for the CPHE system was conducted [40]. A temperature of 40 ◦C was set for the NF at the inlet of the CPHE. The stabilization of the set flows and temperature were insured before recording the data by the data acquisition system considering 2 s interval time. In short, the fluids and NFs samples are heated in a tank then they flow into the hot loop passing the flowmeter and the CPHE to return to the tank. The temperatures of the fluid at the inlets and outlets of the CPHE are determined through four thermocouples and used to calculate the convection heat transfer coefficient (CHTC) for each sample at each flow rate. The experimental rig of the CPHE was established for the fluid flow and heat transfer of nanofluids as presented in Figure 3. The CPHE system contains an open loop for the cold fluid (using only water that goes to the drain after passing the CPHE) and a hot fluid loop for the NF flow, which includes a tank with heater, pump, 2 flow meters, differential pressure sensor, 4 thermocouples for temperature measurements, and DAQ linked to PC for collecting data. Details about this investigational setup and working principle can be found in an earlier study [40]. The components' accuracy of the investigational setup was firstly checked with DW as a well-known fluid and calibration procedure for the CPHE system was conducted [40]. A temperature of 40 °C was set for the NF at the inlet of the CPHE. The stabilization of the set flows and temperature were insured before recording the data by the data acquisition system considering 2 s interval time. In short, the fluids and NFs samples are heated in a tank then they flow into the hot loop passing the flowmeter and the CPHE to return to the tank. The temperatures of the fluid at the inlets and outlets of the CPHE are determined through four thermocouples and used to calculate the convection heat transfer coefficient (CHTC) for each sample at each flow rate.

**Figure 3.** A flow diagram of the setup used for the experimental investigation. **Figure 3.** A flow diagram of the setup used for the experimental investigation.

The heat absorbed from the hot loop (*Qh*) and moved to the cold loop (*Qc*) is determined by Equations (3) and (4), and the average heat *Q* is assessed by Equation (5). The heat absorbed from the hot loop (*Q<sup>h</sup>* ) and moved to the cold loop (*Qc*) is determined by Equations (3) and (4), and the average heat *Q* is assessed by Equation (5).

$$\mathbf{Q}\_{\rm h} = \dot{m}\_{\rm h} \mathbf{C}\_{p,h} (T\_{\rm hi} - T\_{\rm ho}) \tag{3}$$

$$Q\_{\mathcal{L}} = \dot{m}\_{\mathcal{c}} \mathbb{C}\_{p,\mathcal{c}} (T\_{\dot{c}i} - T\_{\text{co}}) \tag{4}$$

$$Q = (Q\_{\mathbb{H}} + Q\_{\mathbb{C}}) / 2 \tag{5}$$

 and represent the temperatures values at the inlet and outlet of the hot loop of the PHE, respectively. In addition, and represent the temperatures values at the inlet and outlet of the cold loop of the PHE, respectively. Moreover, the overall convection heat transfer coefficient (*U*) is found by Equations (6) and (7). *Thi* and *Tho* represent the temperatures values at the inlet and outlet of the hot loop of the PHE, respectively. In addition, *Tci* and *Tco* represent the temperatures values at the inlet and outlet of the cold loop of the PHE, respectively. Moreover, the overall convection heat transfer coefficient (*U*) is found by Equations (6) and (7).

$$
\mathcal{U} = \frac{\mathcal{Q}}{A \cdot LMTD} \tag{6}
$$

*A* is the convection heat transfer area and *LMTD* is the log mean temperature difference. *A* is the convection heat transfer area and *LMTD* is the log mean temperature difference.

$$LMTD = \frac{(T\_{ho} - T\_{ci}) - (T\_{hi} - T\_{co})}{\ln\frac{(T\_{ho} - T\_{ci})}{(T\_{hi} - T\_{co})}} \tag{7}$$

( − )

Then, the convection heat transfer coefficient (CHTC) for NFs in the hot loop (*h<sup>h</sup>* ) is defined by Equation (8):

$$
\mathcal{U} = \frac{1}{h\_h} + \frac{\delta}{k\_{pl}} + \frac{1}{h\_c} \tag{8}
$$

where *δ* is the thickness of the plate of the heat exchanger, *kpl* represents the thermal conductivity of the plate's material. Furthermore, *h<sup>c</sup>* is the CHTC for the water in the cold loop and it is theoretically predicted based on the heat exchanger design by Equation (9) [41] that has been used and validated in previous studies [42,43] for similar conditions.

$$Nu = 0.348 Re^{0.663} pr^{0.33} \tag{9}$$

Then *h<sup>c</sup>* is determined from the definition of *Nu* as given by Equation (10),

$$h\_{\mathfrak{c}} = k \times \text{Nu} / D\_{\mathfrak{h}} \tag{10}$$

*D<sup>h</sup>* is the hydraulic diameter of the channel in the CPHE (*D<sup>h</sup>* = 2*b*).
