**5. Method of Determining HTC on the Individual Row Based on CFD Simulations**

A method for determining HTCs for the individual rows is illustrated with an example of four-row PFTHE (Figure 4). The HTC is appointed, factoring constant fin and tube temperatures, which are equal to 70 ◦C Further simulations have also been performed for two different temperatures: 60 ◦C and 80 ◦C. It has been shown that, for three different surface temperatures of the tubes and fins, the determined HTCs do not differ more than 1.5% (Figure 5), and that proposed procedure for determining the air-side HTC can be successfully used in practice. The method consists of the following steps.


$$
\Delta T\_{m,a}^{i} = \frac{\left(T\_{w} - \overline{T}\_{a}^{i+1}\right)\left(T\_{w} - \overline{T}\_{a}^{i}\right)}{\ln\left(\frac{T\_{w} - \overline{T}\_{a}^{i+1}}{T\_{w} - \overline{T}\_{a}^{i}}\right)}\tag{3}
$$

**Figure 4.** Graphical representation of determining HTC on the individual row based on a CFD simulation. The numbers on the picture show the order of calculation to determine HTC in the case of PFTHE.

**Figure 5.** Relative differences of Nusselt numbers for each row of PFTHE for different air wall temperatures (constant temperature of fin and tube wall), where reference temperature is 70 ◦C: (**a**) 70 ◦C and 80 ◦C; (**b**) 70 ◦C and 60 ◦C.

The symbol *Tw* denotes a constant fin and tube surface temperature. The symbols *<sup>T</sup><sup>i</sup> a* and *<sup>T</sup>i*+<sup>1</sup> *<sup>a</sup>* designate the inlet and outlet mass average air temperature for the *i*-th row of PFTHE. Then:


$$\alpha\_a^i = Q\_i / \left( A\_w \Delta \mathbf{T}\_{m,a}^i \right) \tag{4}$$

.

The following designations are used in Equation (4): *Q <sup>i</sup>* the total heat flow rate for the entire row of the repetitive fragment of PFTHE; *α<sup>i</sup> <sup>a</sup>* the air-side HTC in a particular row.

• Calculate Nusselt number *Nu<sup>i</sup> <sup>a</sup>* = (*α<sup>i</sup> <sup>a</sup> dh*)/*λ<sup>a</sup>* and Colburn factor *j i <sup>a</sup>* = *Nu<sup>i</sup> a*/ *Re<sup>i</sup> <sup>a</sup> Pr<sup>i</sup> a* 1/3
