Figure 7: Nanofluid samples after one month of preparation

3.2. Uncertainty Analysis

In this experimental study, the measured values’ uncertainty was achieved by focusing on errors that resulted from parameter measurements. The parameters on focus included weight, temperature, viscosity, and thermal conductivity. Regarding the examination of the thermal conductivity parameter, the study relied on a KD2 thermal properties analyzer. On the other hand, the MCR 302 Rheometer aided in assessing the nanofluids’ viscosity. It is also worth noting that the Analytical Balance weighing scale was used to determine the nano particles’ weight, with a resistance temperature detector utilized towards the measurement of the parameter of temperature. To determine the uncertainty, the expression that was used was [57]:
\(u_{m}=\sqrt{\left(\frac{k}{k}\right)^{2}+\left(\frac{T}{T}\right)^{2}+\left(\frac{w}{w}\right)^{2}}\)(3)
The accuracy of the RTD was 0.5oC. The accuracy of the Analytical Balance was 0.0001g. Hence the total uncertainty of thermal conductivity experiment was observed to be less than ±2.1%. The uncertainty of viscosity can be calculated using the Equation (3) by replacing thermal conductivity, k with viscosity, μ and the uncertainty was observed to be ±4.1%.

Regression Analysis of Thermo-Physical Properties

The experimental data that was obtained aided in conducting a theoretical analysis relative to the thermo-physical properties of interest. From the literature [21,35,38,58], some experimental data exists. This data was incorporated into this study, especially for regression. Some of the parameters to which the regression analysis, which partially relied on the data obtained from the previous studies, included thermal conductivity, viscosity, specific heat, and density. For both nanofluids and other fluids, correlations were implemented in relation to different thermo-physical properties. It is also worth acknowledging that the nanofluids and base fluids’ equations in the literature were applied towards successful regression analysis for the target physical properties (4)-(15).

4.1. Base Fluid Properties for 60EGW

In the 60EGW mixture, the parameter or thermo-physical properties of thermal conductivity, viscosity, specific heat, and density were determined via the use of correlations accruing from the regression analysis. Also, some of the experimental data in the previous literature [41] was incorporated into the analysis. The correlations below summarize the base fluid properties of the investigation:
\(\rho_{\text{bf}}=1090.6-0.32857T-0.00286T^{2}+5.421{\times 10}^{-19}T^{3}\)(4)
\(C_{\text{pbf}}=3044.135+4.2808T-0.00186T^{2}+0.0000155759T^{3}\)(5)
\(\mu_{\text{bf}}=0.0087-0.000245439T+0.00000282043T^{2}-0.00000001178T^{3}\)(6)
\(k_{\text{bf}}=0.33944+0.00111T-0.0000100528T^{2}+0.0000000377393T^{3}\)(7)

4.2. Base Fluid Properties for 40EGW

The EG-W base fluid properties were obtained from regression correlations using ASHRAE data [41],
\(\rho_{\text{bf}}\ =\ 1066.79734\ -0.3071T\ \ -0.00243T^{2}\) (8)
\(C_{\text{pbf}}\ =\ 3401.21248+3.3443T+9.04977E-5T^{2}\) (9)
\(\mu_{\text{bf}}=0.00492-1.24056E-4T{+1.35632E-6T}^{2}{-5.56393E-9T}^{3}\)(10)
\(k_{\text{bf}}=0.39441+0.00112T-5.00323E-6T^{2}\) (11)

4.3. Nanofluid Properties with Base Fluid 60EGW

Indeed, the nanofluids’ properties determine the assessment of the friction factor and the heat transfer coefficients. For the EG-water based nanofluids that included SiO2,Al2O3 and CuO, the viscosity and thermal conductivity were established based on varying parameters. These parameters included material concentration, temperature, and particle size; with the data in the previous literature playing a crucial role at this stage [21,35,38,58]. The correlations below illustrate how thermal conductivity and viscosity parameters were assessed via regression analysis, which also dependent on a numerical program.
\(\frac{\mu_{\text{nf}}}{\mu_{\text{bf}}}=4.589\left(1+\frac{\varnothing}{100}\right)^{0.2963}\left(1+\frac{T_{\text{nf}}}{97}\right)^{0.1398}\left(1+\frac{d_{p}}{53}\right)^{-0.4531}\)(12)
\(\frac{k_{\text{nf}}}{k_{\text{bf}}}=0.852\left(1+\frac{\varnothing}{100}\right)^{2.608}\left(1+\frac{T_{\text{nf}}}{97}\right)^{0.3889}\left(1+\frac{d_{p}}{77}\right)^{-0.08427}\left(\frac{\alpha_{p}}{\alpha_{\text{bf}}}\right)^{0.04192}\)(13)
The correlations (12) and (13) are valid in the range of\(\ 0\ \leq\ \varnothing\ \leq 4\%\ \); 20\(\leq\ T_{\text{nf}}\ \leq\) 90oC; 20\(\leq\ d_{p}\ \leq\) 50nm with a maximum deviation of 10

4.4. Nanofluid Properties with Base Fluid 40EGW

Given the SiO2/40EGW nanofluids’ experimental results gained from the previous literature and this study’s experimental results for the Al2O3/40EGW nanofluids, the outcomes that were gained aided in conducting the regression correlations. These correlations would, in turn, give crucial insight into the aspects of thermal conductivity and viscosity evaluations; having targeted variables such as particle size, temperature, and volume concentration. The correlations below were used to evaluate the aforementioned parameters of thermal conductivity and viscosity.
\(\frac{\mu_{\text{nf}}}{\mu_{\text{bf}}}=1.389\left(1+\frac{\varnothing}{100}\right)^{60.68}\left(1+\frac{T_{\text{nf}}}{70}\right)^{-0.669}\left(1+\frac{d_{p}}{50}\right)^{-0.1573}\)(14)
In this case, the standard deviation and average deviation were estimated and found to be 8.5% and 6.9% respectively\y.
Equation (15) shows the thermal conductivity state achieved. Particularly, the standard deviation and average deviation obtained after implementing the correlations were 2.8% and 1.9% respectively.
\(\frac{k_{\text{nf}}}{k_{\text{bf}}}=0.9431\left(1+\frac{\varnothing}{100}\right)^{0.1612}\left(1+\frac{T_{\text{nf}}}{70}\right)^{0.1115}\left(1+\frac{d_{p}}{50}\right)^{-0.003986}\left(\frac{\alpha_{p}}{\alpha_{\text{bf}}}\right)^{0.006978}\)(15)
The correlations (14) and (15) are deemed or perceived as valid; given of \(0\ \leq\ \varnothing\ \leq 1.5\%\ \); 20\(\leq\ T_{\text{nf}}\ \leq\) 70oC; 13\(\leq\ d_{p}\ \leq\) 50nm.

Experimental Results of Nanofluid Thermal conductivity and Viscosity

In this chapter, the main objective is to discuss the theoretical and experimental results that were reported in the previous literature and this study respectively. From the literature [21,35,38,58], thermo-physical values were obtained based on the formulated correlations. The results were compared with those that were obtained by this investigation, especially due to the need to make valid and informed conclusions and inferences about relations among the parameters or variables that were being investigated. Some of the crucial data that aided in making inferences included the viscosity and thermal conductivity values. Indeed, there was less than 20-percent deviation in relation to a comparison that was made between the experimental results and the theoretical outcomes reported in the previous literature.
The experimental thermal conductivity values are compared with correlations of 60EGW base fluid (7) and with 40EGW base fluid (11) and are shown in Figure 8 . The experimental data was taken in the temperature range of 25oC-60oC for a particle size of 20nm. A deviation less than 7% was observed with correlation (7) and a deviation less than 3% with correlation (11). And the same data was compared with ASHRAE data as well and a maximum deviation of 8% was observed.