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here. The dashed lines to either side of the mean represent the lower and upper 95 % simultaneous (multiple-use) confidence intervals for the mean. From the confidence intervals, the expanded uncertainty of the estimated mean viscosity for the 95 % confidence level was shown to increase with respect to the mass fraction of the CuO nanoparticles being ± 0.5 mm2·s-1, ± 3.9 mm2·s-1, ± 6.7 mm2·s-1, and ± 10.2 mm2·s-1 for the 0 %, 2.9 %, 5.6 %, and the 39.2 % mass fraction nanolubricants, respectively. The residuals for the fits given in Table 3 are within ± 15 % for all of the fluids. Although the relative percent residuals did not increase with respect to mass fraction, the absolute residuals did. Table 3. Viscosity fit with respect to temperature: v = exp ⎛ A + A1 + A ln T ⎞ v⎜0T2r⎟ o⎝r⎠ Paper No. IIR-177 Fitting Constant A0 A1 A2 RL68H -52.1976 58.8482 36.8224 xm =2.9% -103.767 110.709 82.9465 xm =5.6% -11.7911 18.2429 0 xm =39.2% -10.1572 18.0583 0 5. DATA CORRELATION WITH RESPECT TO MASS FRACTION The following section presents the correlation of the density with respect to CuO mass fraction (xm). The viscosity was correlated with respect to the density. 5.1 Density The resulting correlation of the liquid density of the base lubricant and the CuO nanolubricants to the CuO mass fraction at atmospheric pressure was: 1 ρ[kgim]=(7.627×10 -6.729×10xm)T[K]+7.984×10 -6.672×10xm (3) where the density (ρ) has units of kg·m-3 while the input temperature (T) has units of kelvin. Equation (3) faithfully reproduced the individual fits giving the same residuals with respect to the measurements as shown in Fig. 3. More specifically, the residuals between the measure kinematic viscosity and the single correlation with respect to CuO mass fraction were ± 0.02 %, ±0.03%, ±0.04%, and ±0.6% for the 0%, 2.9%, 5.6%, and 39.2% mass fractions, respectively. Consistent with Eq. (1), Eq. (3) shows that the liquid density of the nanolubricant increases linearly with increasing CuO mass fraction. 5.2 Viscosity The necessity of a fluid-specific correlation for the nanolubricants’ viscosity was verified by comparing the measurements to the Stokes-Einstein equation (Einstein, 1956) for a dilute (φ < 0.6) nanofluid with spherical nanoparticles: -13 -7 -7 -4 -4 vρ =1+(5/2)φ vLρL (4) where φ is the volume fraction of the CuO nanoparticles. The viscosity measurements for the 0.45 % and the 0.9 % volume fractions (0.029 and 0.056 mass fractions, respectively) were centered about Eq. (4) and within ± 9 %. However, the 9 % volume fraction (39.2 % mass fraction) viscosity measurements were approximately six times the value given by Eq. (4).PDF Image | VISCOSITY AND DENSITY OF CUO NANOLUBRICANT
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