2.3. Data Reduction

The local-heat transfer coefficient h(Z) was predicted using the measurements of inlet and outlet temperatures and wall temperature at different axial locations (Z = 20, 60, 110, 160, and 250 mm) [33], as in Equation (6):

where q, Tf(Z), and Twi(Z) are the actual heat flux gained by working fluids, mean fluid temperature, and inner wall temperature at specific distance Z, respectively, which can be calculated using the following equations:

where Two(Z), ks, and l are the surface wall temperature, thermal conductivity of the brass material, and length of minitube, respectively. In addition, u is the bulk velocity, which can be computed from the flow rate Q and microtube cross-section area A as u=Q/A.

The Nusselt number (Nu) was estimated using Equation (10):

The percentage of the enhancement heat transfer coefficient was calculated using Equation (11):

The thermal entropy generation rate (S˙th) was defined as:

This can also be introduced in terms of heat transfer coefficients as follows:

where Tav=Tin−Toutln(TinTout).

The friction entropy generation rate (S˙fr) can be determined as follows [23]:

The uncertainty analysis for all measurements was performed by the Taylor method [38], which is based on the deviations of repeated measurements from the mean and the number of iterated values. The maximum uncertainties of all the derived experimental parameters are <5.5%. In addition, the average data of three runs were used to perform all experiments for distilled water, MWCNTs, and MWCNTs/GNPs hybrid nanofluids. Table 4 shows the precision values of the used apparatus in the present experiments.

Uncertainties of the experimental apparatus.