*2.5. Viscosity*

Calibration of the vibro-viscometer was carried out prior to viscosity measurement of the DIW and MWCNT-Fe2O3/DIW nanofluids at temperatures of 15 ◦C to 55 ◦C. A percent error of 1.6% was estimated when the measured viscosity of DIW was compared to the standard viscosity of water. The uncertainty of the viscosity measurement was 7.02%. Relative viscosity and improvement of the viscosity of MWCNT-Fe2O3/DIW nanofluids compared with DIW were evaluated using Equations (4) and (5), respectively.

$$
\mu\_{rel} = \frac{\mu\_{\text{hf}f}}{\mu\_{bf}} \tag{4}
$$

$$
\mu\_{enhan}(\text{\textquotedblleft}\_{\text{\textquotedblleft}f} = \left(\frac{\mu\_{\text{\textquotedblleft}f} - \mu\_{bf}}{\mu\_{bf}}\right) \times 100\tag{5}
$$

where

*µhnf* = measured viscosity of hybrid nanofluids and *µbf* = measured viscosity of DIW.

The expression in Equation (6) was used to evaluate the margin of deviation (MOD) of the thermal properties of MWCNT-Fe2O3/DIW nanofluids.

$$MOD(\%) = \left(\frac{V\_{Exp.} - V\_{Pred.}}{V\_{Exp.}} \times 100\right) \tag{6}$$

where

*VExp.* = experimental data and *VPred.* = predicted data.

It is worth stating that the measured variable (Z), temperature (*T*), weight of hybrid nanoparticles (*m*), and volume of DIW were sources of error associated with the measurement of pH, µ, and σ. The errors were propagated using Equation (7) to estimate the uncertainty related to pH, µ, and σ.

$$\mathcal{U}(\%) = \pm \sqrt{\left(\frac{\Delta Z}{Z}\right)^2 + \left(\frac{\Delta T}{T}\right)^2 + \left(\frac{\Delta m}{m}\right)^2 + \left(\frac{\Delta V}{V}\right)^2} \tag{7}$$
