*3.2. Data Processing Steps*

The experiment requires that we record the raw data and process them as follows.

The average temperature, feature size and feature velocity are calculated, and the corresponding physical parameters are obtained.

(1) The average temperature *t*<sup>0</sup> for convective heat transfer flowing in the channels of the electronic heat sink parts is as follows:

$$t\_0 = \left(t\_1 + t\_2 + t\_3 + \dots + t\_n\right) / n. \tag{12}$$

where *t*<sup>0</sup> is the average temperature of the radiator surface; *t*1, *t*<sup>2</sup> ... *tn* are the radiator surface temperature, ◦C.

(2) Feature dimensions refer to standard-like geometric dimensions. Convective heat transfer within the electronic heat sink is dimensioned as a microchannel. This experiment is a rectangular cross section, so the equivalent diameter *de* is as follows:

$$d\_e = 4\frac{S}{L} = 2\frac{ab}{a+b}.\tag{13}$$

where *de* is the equivalent diameter of the flow channel or the so-called hydraulic diameter; *S* is the effective cross-sectional area of the flow channel also known as the cross-flow cross-sectional area, m2; *U* is the electronic heat sink parts section perimeter, and fluid contact with the solid wall perimeter, *m* and *a*, *b* are the length and width of the micro-channel cross-section, m.

(3) The characteristic velocity in a heat exchanger can be obtained by taking the flow rate and the cross-flow area. The ratio between the two is the characteristic velocity.

In order to obtain the total convective heat transfer *Q* during the experiment, the heat transfer coefficient *h* needs to be determined. The total heat was obtained using Equation (2) and averaged when the heat absorbed by the cold fluid was in equilibrium with that of the hot fluid (Δ*Q* < 5%). The log-average temperature difference is calculated using Equation (3) and the total heat transfer coefficient *K* is calculated from Equation (4).

$$Q = qA = h\Delta TA = \rho v c\_p (t\_{out} - t\_{in}).\tag{14}$$

Known from fluid mechanics, the equation for the resistance coefficient of a medium flowing through a system is as follows:

$$f = \frac{\Delta p}{\frac{1}{2}\rho v^2} \cdot \frac{d\_c}{l} \tag{15}$$

where Δ*p* is the pressure drop in the experimental section measured by the differential pressure transmitter in the experiment; *v* is the average flow rate of the tube and *l* is the distance between the static pressure measurement in the experimental section (110 mm for this experiment).

The resistance coefficients for each group of experiments were fitted using the least squares method as shown in (18) as follows:

$$f = \mathbb{C}\_f \mathbb{R} \mathbf{e}^{\mathbf{x}} \tag{16}$$
