**4. Data Reduction**

The average heat transfer coefficient for the considered heated tube with various working fluids is calculated using Equation (17) [12].

$$h = \frac{\mathcal{Q}}{A\left(T\_{\rm s} - T\_{f,\rm ave}\right)}\tag{17}$$

The heat absorbed by working fluid is calculated using Equation (18) [41,42].

$$Q = m\_f c\_p \left( T\_{f,o} - T\_{f,i} \right) \tag{18}$$

The average Nusselt number considering calculated average heat transfer coefficient, hydraulic diameter of tube and thermal conductivity of working fluid is evaluated using Equation (19) [23].

$$Nu = \frac{hD}{k} \tag{19}$$

Here, *T<sup>s</sup>* (K) presents average temperature of wall surface, *T<sup>f</sup>* ,*<sup>o</sup>* (K) presents outlet fluid temperature, *T<sup>f</sup>* ,*<sup>i</sup>* (K) presents inlet fluid temperature, *T<sup>f</sup>* ,*ave* (K) presents average fluid temperature, *D* (mm) presents hydraulic diameter, *k* (W/m·K) presents thermal conductivity of working fluid, *m<sup>f</sup>* (kg/s) presents mass flow rate of fluid and *c<sup>p</sup>* (J/kg·K) presents specific heat of fluid.

The pressure drop of working fluid across the tube is calculated using Equation (20) [43].

$$
\Delta P = P\_{f,i} - P\_{f,o} \tag{20}
$$

The friction factor for a tube with various working fluids is evaluated using pressure drop, length of tube, hydraulic diameter, density and average velocity as presented by Equation (21) [21,23].

$$f = \frac{\Delta P}{\frac{L}{D} \times \frac{\rho U^2}{2}}\tag{21}$$

Here, ∆*P* (Pa) is pressure drop, *P<sup>f</sup>* ,*<sup>i</sup>* (Pa) is inlet fluid pressure, *P<sup>f</sup>* ,*<sup>o</sup>* (Pa) is outlet fluid pressure, *f* is friction factor, *L* (mm) is length of tube, *ρ* (kg/m<sup>3</sup> ) is density of fluid and *U* (m/s) is the average velocity.

Considering the Nusselt numbers and friction factors of base fluid and nanofluids, the performance evaluation criteria is defined as presented by Equation (22) [44].

$$PEC = \frac{\left(\frac{Nu\_{nf}}{Nu\_{bf}}\right)}{\left(\frac{f\_{nf}}{f\_{bf}}\right)^{\frac{1}{3}}}\tag{22}$$

where *Nun f* is Nusselt number of nanofluid, *Nub f* is Nusselt number of basefluid, *fn f* is friction factor of nanofluid and *fn f* is friction factor of nanofluid.
