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.