**4. Discussion**

The present work was aimed at the parametric design of HPHE aided by the computational model. The model was validated against the experiment on a nine-row prototype HPHE. There was a good agreement between the model and measured heat transfer rates of the prototype HPHE. Process and design specifications were made for HPHE utilized as an air-to-air recuperator for air conditioning systems. This HEX type implies the following design parameters:

The HP container is a 1 mm thick 20 mm outer diameter copper tube, and the finned surface is made of aluminum. Finned tubes are manufactured by cold rolling technology. Aluminum was chosen because of its lower weight than copper, and considerably lower price.

The computational model was used to obtain the heat transfer rates, effectiveness, and pressure drop for varying parameters. The first set of calculations with assumed constant inlet and outlet air temperatures was analyzed to choose a number of rows that fulfills the 60% thermal efficiency goal: 20 rows were chosen (including three extra HPS as a safety factor in calculations). In this arrangement (for 300 m3/h volumetric flow of hot and cold airstreams), the pressure drop does not exceed 100 Pa, increasing the maximal temperature difference of HPHE decreases in Δ*P*, with a relatively slight increase in effectiveness. The penalty for a reduction in temperature difference is not great as effectiveness drops by 4% over a 20 ◦C decrease. To sum up, a 20-rows HPHE exhibits stable effectiveness over a broad temperature range with an acceptable pressure drop for small air conditioning applications.

Further parametric computations were made to choose the optimal spacing between the HPs—3D plots show the dependence of efficiency and pressure drop on *Xl* and *Xt*. Traversal heat pipes spacing has the greatest influence on heat transfer rate; upon reduction in traversal spacing there is a steep increase in heat transfer rate and effectiveness for *Xt* ≈ 61 mm caused by the increase in the number of HPs in rows. Four and three pipe arrangement can be used (70 HPs total) instead of three and two (50 HPs total). *Xt* = 50 was chosen as the most effective transverse spacing between HPs, which corresponds to the physical contact of HPs. Smaller *Xl* means a shorter heat exchanger but also a higher pressure drop (Figure 23). To minimize the pumping power of the fan longitudinal spacing *Xl* = 61 mm was chosen. It corresponds to the total length of the heat exchanger, *L*<sup>2</sup> = 1.22 m.

The final dimensions of the designed heat pipe heat exchanger are:

$$\text{Length } L\_2 = 1.22 \text{ m}; \text{Height } L\_1 = 0.245 \text{ m}, \text{Width } L\_3 = 0.245 \text{ m}.$$

The final finned heat pipe arrangement is shown in Figure 25. Tables 4 and 5 summarize HPHE working parameters for typical winter and summer conditions. The present best HPHE geometrical parameters choice is supported by the optimization of the overall cost function, which could be simplified to:

$$\text{overall cost} = \text{HP cost} \cdot \text{N} + \text{cost of fan operation} - \text{savings due to heat evaporation} \tag{27}$$

where *N*—a number of HPs in an HPHE. The cost of the manufacture of one heat pipe was estimated as USD 21, and the value of the working fluid inside one HP is approx. USD 1.5. The cost of the fan operation is estimated, assuming a fixed price of 1 kWh of electricity (0.2 USD/kWh). The first two terms in Equation (27) generate cost—initial cost of manufacture of HPHE plus the consumed electric energy for the fans' operation. The savings come from the last term which takes into account the heat recuperation—in the cold months, the recuperated amount of thermal energy is priced as electrical energy (use of electrical heater), whereas in hot months, recuperated energy is divided by the Coefficient of Performance of the refrigeration device hypothetically used for airstream cooling. Based on the heat transfer rates, pressure drops, and air volumetric flow rate from the numerical model, the overall cost of HPHE in operation for 4 years is plotted in Figure 26. The chosen independent parameters were number of rows and traversal spacing *Xt*. The longitudinal spacing does not affect heat transfer or pressure drop significantly, so it was excluded from the analysis. The optimization method used to minimize the overall cost function is the so-called "brute force" method. The function's value is computed at each point of a multidimensional grid of points, to find the global minimum. An obvious disadvantage of this approach is the high computing power requirements, but the advantage is a certainty of obtaining the minimum in the range of the specified parameters. The minimum is marked in Figure 26, being USD −4218 (a negative value means that the savings are greater than the cost of the investment) for 18 rows HPHE, and optimal spacing *Xt* = 0.051 m. It is very similar to the final dimensions of the HPHE chosen according to previous engineering analysis.

**Figure 25.** Final heat pipe heat exchanger arrangement.

**Table 4.** Final HPHE working parameters for typical summer conditions.


**Table 5.** Final HPHE working parameters for typical winter conditions.


**Figure 26.** The overall cost of 4 years of operation of HPHE as a function of number of rows and traversal HPs spacing.
