**5. Design focused on applications. Feasibility**

This section will describe how to design the heat exchanger once an application is specified. Free-cooling and temperature maintenance in rooms with special requirements possess high potential for PCM application in different countries according to their climate. Until now, the low thermal conductivity of PCM and air hindered the development of suitable heat exchangers. This section has as the overall objective to apply methodologies to study PCM and PCM-air heat exchangers that allow the development of applications with technical and economical viability. Finally, using the combined technique of design of experiments (hereafter DOE) and simulations, the feasibility of the possible application of this type of equipment is studied for temperature maintenance in rooms. Because the simulation itself is

shows the overlap between the experimental curve (including the lower and upper limits associated with its uncertainty) and the simulation (including the uncertainty of the response heat rate calculated applying the reported technique). The agreement is significant in most of the process, finding the more relevant discrepancies as the curve reaches the end

0.00 1.00 2.00 3.00 4.00

**time (s)** Experimental upper limit Simulation upper limit Experimental lower limit Simulation lower limit Experimental Simulation

5.00 6.00 7.00 8.00 9.00

**time (s)** Experimental upper limit Simulation upper limit Experimental lower limit Simulation lower limit Experimental Simulation Fig. 12. Comparison of experimental and simulated results (including their corresponding uncertainty bands) for the melting (up) and solidification (down) of a thermal cycle.

This section will describe how to design the heat exchanger once an application is specified. Free-cooling and temperature maintenance in rooms with special requirements possess high potential for PCM application in different countries according to their climate. Until now, the low thermal conductivity of PCM and air hindered the development of suitable heat exchangers. This section has as the overall objective to apply methodologies to study PCM and PCM-air heat exchangers that allow the development of applications with technical and economical viability. Finally, using the combined technique of design of experiments (hereafter DOE) and simulations, the feasibility of the possible application of this type of equipment is studied for temperature maintenance in rooms. Because the simulation itself is

of the corresponding stage of the cycle (i.e. as the heat rate values are smaller).


**5. Design focused on applications. Feasibility** 

**Heat transfer rate (W)**

**Heat transfer rate (W)**

not a design tool, this methodology is proposed to size the equipment. This technique greatly reduces the time spent in performing the simulations required to find the optimal equipment (Del Coz Díaz et al., 2010) as well as and a potential cost saving on the experimental (Del Coz Díaz et al., 2010; Gunasegaram et al., 2009) if the prototype-model similarity relations are met. Moreover, contrary to a sequential analysis, it is reasonable to use a mathematical and statistical methodology that allows planning the sequence of experiments on the philosophy of maximum information with minimum effort.

#### **5.1 Empirical model: simulations of a case study and modular design**

An empirical model was built from the experimental results described in the previous section. The aim was to simulate the thermal behaviour of the tested heat exchanger in different cases. These simulations were used to evaluate the technical viability of application. The model describes the temperature evolution of a room with an internal cooling demand ( Q *demand*), where the PCM-air heat exchanger is operating and there is a ventilation system. The enclosure temperature was considered to be the average between the outside temperature and the room temperature. A diagram of the room is shown in figure 13. Expression D in figure 9 is equivalent to equation 9, expressing the energy balance applied to the air inside the room.

Fig. 13. Schematic diagram of the room in which the temperature is evaluated.

$$\begin{aligned} & \mathbf{m} \cdot \mathbf{c}\_{\mathrm{p,enclosed}} \cdot \left[ \left( \frac{\mathbf{T}\_{\mathrm{room}}^{i} + \mathbf{T}\_{\mathrm{outside}}}{2} \right) \cdot \left( \frac{\mathbf{T}\_{\mathrm{room}}^{i \cdot 1} + \mathbf{T}\_{\mathrm{outside}}}{2} \right) \right] = \mathbf{p}\_{\mathrm{air}} \cdot \mathbf{V} \cdot \mathbf{c}\_{\mathrm{p,air}} \cdot \left( \mathbf{T}\_{\mathrm{room}}^{i} \cdot \mathbf{T}\_{\mathrm{room}}^{i \cdot 1} \right) \\ &= \left[ \dot{\mathbf{m}}\_{\mathrm{ventilation}} \cdot \mathbf{c}\_{\mathrm{p,air}} \cdot \left( \mathbf{T}\_{\mathrm{outside}} \cdot \mathbf{T}\_{\mathrm{room}}^{i} \right) + \dot{\mathbf{Q}}\_{\mathrm{demand}} \cdot \dot{\mathbf{m}}\_{\mathrm{air}} \cdot \mathbf{r}\_{\mathrm{p,air}} \cdot \Delta \mathbf{T}^{i \cdot 1} \right] \cdot \Delta \mathbf{t} \left( \text{i.i-1} \right) \end{aligned} \tag{9}$$

where *ΔT* is obtained at each instant as a function of surface T and the inlet air temperature, *Tinletair* (at instant *i* equal to *Troomi* ); and the surface T at instant *i* is obtained from the stored energy evolution.

The real-scale PCM-air heat exchanger tested was constituted of 18 parallel modules (*#modules* denotes de number of PCM modules in the heat exchanger). A module is constituted by a

PCM-Air Heat Exchangers: Slab Geometry 449

the equipment when modifying any other parameter or variable, or if we need to

As a starting point we will continue using the case brought by Lazaro, 2009, which provides that, for proper running of the electronic equipment, the maximum air temperature in the room should be between 38 ºC and 48 °C, in particular we will establish it at 44 °C. The heat generation of the electronic equipment is 5 kW. For the evolution of temperature inside the room, an energy balance was stated with the following simplifications: 1) the cooling effect of the terrain was not considered. The ground floor area is supposed to be occupied by the equipment; 2) exterior ventilation is introduced only when it is favourable, and considering

The idea behind this system is that after a failure of the conventional cooling system, the TES unit is intended to smooth the evolution of the temperature of the room so that it extends the time to reach a certain threshold temperature value. The aim is this period to be about two hours, so technicians have sufficient time to reach the place where the room is located and to repair the damage of the cooling system without having to stop the electronic

 Dimensions limitation due to the telecommunications shelter: the maximum length of the system is limited to 2.5 m (height of the shelter) which limits the section of the PCM

> MPCM [kg] *V* [m3/h] eplate [mm] eair [mm] Finishing 132 1340 6.5 12 3

The operating conditions are shown in table 9 and the simulation results with the theoretical

01234

**time (h)** TPCM in TPCM mid TPCM out Tair out Troom w TES Troom w/o TES

**Heat rate (W)**

to 1.25 m. Likewise, the width of the unit is also limited to 5 m due to the wall; Electrical power consumption limitation of the fan, so it can be supplied by batteries without being essential a connection to the grid. Pressure drop should be less than 30

improve/optimize the design, we have to move to the numerical model.

that the environment outside the house is 40 ° C (worst case).

equipment. A series of restrictions put on the TES system follow:

model of the unit proposed by Lazaro, 2009, are shown in figure 14.

Pa.

Table 9. Operating conditions.

Heat rate

Fig. 14. Theoretical model simulated results of Lazaro's case (2009).

**Temperature (ºC)**

metallic PCM container between two air channels. The pressure drop is the same for each module, and the air distribution through the air channels can be considered uniform. The unitary air flow through a module is the mass air flow ( mair HX ) divided by 18. Since the geometry and the air flow were maintained identical, the total stored energy for one module (*Et mod*) between two temperatures is the stored energy for the real-scale PCM-air heat exchanger between the two temperatures divided by 18 (equation 10). The total melting time depends on *Et mod* and on the cooling power demand (equation 11).

$$\text{Stored energy} = \#\_{\text{modules}} \mathbb{E}\_{\text{t}}^{\text{mod}} \tag{10}$$

$$\text{At}\_{\text{melt}} = \text{Stored energy} / \dot{\mathbf{Q}}\_{\text{demand}} = \left( \#\_{\text{modules}} \cdot \text{E}\_{\text{t}}^{\text{mod}} \right) / \dot{\mathbf{Q}}\_{\text{demand}} \tag{11}$$

$$\mathbf{\overline{T}}\_{\text{plateau}} = \mathbf{T}\_{\text{melt}} + \mathbf{1.58} \cdot \mathbf{\dot{Q}}\_{\text{resistance}} = \mathbf{T}\_{\text{melt}} + \mathbf{1.58} \cdot \mathbf{\dot{Q}}\_{\text{demand}} \cdot \mathbf{18}/\mathbf{\dot{\pi}}\_{\text{modules}} \tag{12}$$

The 1.58 value in equation 13 comes from the linear correlation between the average plateau temperatures and the heating power ( Q *resistances*) data obtained experimentally. The origin ordinate is the average phase change temperature of the PCM used. The relationship between the average phase change temperature (*Tmelt*) and the cooling power demand (expression E in figure 9) is described in equation 12. Assuming that the origin ordinate in the adjustment equation 13 is *Tmelt* , it is possible to define the number of modules and the *Tmelt* needed for a given cooling power demand, as well as the *Tob* and *Δtob* to maintain such a level (equations 14 and 15).

$$
\Delta\text{T[K]=-1.4683-1.10943 }\overleftarrow{\text{T}}^{\text{surface}}\text{[}^{\text{o}}\text{C]}+1.10706 \cdot \text{T}^{\text{air}}\_{\text{inlet}}\text{[}^{\text{o}}\text{C]}\tag{13}
$$

$$\mathbf{T}\_{\rm melt} = \mathbf{T}\_{\rm ob} \cdot \mathbf{1}.58 \; \dot{\mathbf{Q}}\_{\rm demand} \cdot \mathbf{18}/\#\_{\rm modules} \tag{14}$$

$$\#\_{\text{modulus}} = \dot{\mathbf{Q}}\_{\text{demand}} \cdot \Delta \mathbf{t}\_{\text{ob}} \Big/ \mathbf{E}\_{\text{t}}^{\text{mod}} \tag{15}$$

For example, in the case where a 2 kW cooling power demand is required and a temperature level of 25 ºC maintained during 2 h using a TES system, then 18 heat exchanger modules filled with a PCM of the same thermal properties of the one used in prototype 2 but with a *Tmelt* of 21.8 ºC would be needed. The same case with a cooling power of 4 kW would require a *Tmelt* of 18.7 ºC (see table 8).


Table 8. Design conclusions for different cooling demands.

#### **5.2 Theoretical model: DOE applied to simulations, improving design**

The empirical model can give a very fast approach of relevant design parameters such as the PCM average phase change temperature. However, if we want to analyze the behaviour of

metallic PCM container between two air channels. The pressure drop is the same for each module, and the air distribution through the air channels can be considered uniform. The unitary air flow through a module is the mass air flow ( mair HX ) divided by 18. Since the geometry and the air flow were maintained identical, the total stored energy for one module

*mod*) between two temperatures is the stored energy for the real-scale PCM-air heat exchanger between the two temperatures divided by 18 (equation 10). The total melting time

The 1.58 value in equation 13 comes from the linear correlation between the average plateau temperatures and the heating power ( Q *resistances*) data obtained experimentally. The origin ordinate is the average phase change temperature of the PCM used. The relationship between the average phase change temperature (*Tmelt*) and the cooling power demand (expression E in figure 9) is described in equation 12. Assuming that the origin ordinate in the adjustment equation 13 is *Tmelt* , it is possible to define the number of modules and the *Tmelt* needed for a given cooling power demand, as well as the *Tob* and *Δtob* to maintain such a

For example, in the case where a 2 kW cooling power demand is required and a temperature level of 25 ºC maintained during 2 h using a TES system, then 18 heat exchanger modules filled with a PCM of the same thermal properties of the one used in prototype 2 but with a *Tmelt* of 21.8 ºC would be needed. The same case with a cooling power of 4 kW would require

The empirical model can give a very fast approach of relevant design parameters such as the PCM average phase change temperature. However, if we want to analyze the behaviour of

<sup>Q</sup>*demand* [kW] Tob [ºC] tob [s] Tmelt [ºC] #modules

2 25 7200 21.8 18 4 25 7200 18.7 18

**5.2 Theoretical model: DOE applied to simulations, improving design** 

Table 8. Design conclusions for different cooling demands.

mod modules t Stored energy=# ·E (10)

 mod melt demand modules t demand t =Stored energy Q = # ·E Q (11)

T =T +1.58·Q =T +1.58·Q · 18 # plateau melt resistances melt demand modules (12)

surface air ΔT K =-1.4683-1.10943·T ºC +1.10706·T ºC inlet (13)

T =T -1.58·Q · 18 # melt ob demand modules (14)

mod # =Q · modules demand ob t <sup>Δ</sup>t E (15)

*mod* and on the cooling power demand (equation 11).

(*Et*

depends on *Et*

level (equations 14 and 15).

a *Tmelt* of 18.7 ºC (see table 8).

the equipment when modifying any other parameter or variable, or if we need to improve/optimize the design, we have to move to the numerical model.

As a starting point we will continue using the case brought by Lazaro, 2009, which provides that, for proper running of the electronic equipment, the maximum air temperature in the room should be between 38 ºC and 48 °C, in particular we will establish it at 44 °C. The heat generation of the electronic equipment is 5 kW. For the evolution of temperature inside the room, an energy balance was stated with the following simplifications: 1) the cooling effect of the terrain was not considered. The ground floor area is supposed to be occupied by the equipment; 2) exterior ventilation is introduced only when it is favourable, and considering that the environment outside the house is 40 ° C (worst case).

The idea behind this system is that after a failure of the conventional cooling system, the TES unit is intended to smooth the evolution of the temperature of the room so that it extends the time to reach a certain threshold temperature value. The aim is this period to be about two hours, so technicians have sufficient time to reach the place where the room is located and to repair the damage of the cooling system without having to stop the electronic equipment. A series of restrictions put on the TES system follow:



Table 9. Operating conditions.

The operating conditions are shown in table 9 and the simulation results with the theoretical model of the unit proposed by Lazaro, 2009, are shown in figure 14.

Fig. 14. Theoretical model simulated results of Lazaro's case (2009).

PCM-Air Heat Exchangers: Slab Geometry 451

respectively. Once the objectives are defined, each variable is assigned a weight (between 0.1

In this approach to the optimization, each of the values of the responses is transformed using a desirability function. The weight defines the shape of this function for each response

After calculating the desirability for each response, the desirability composite is calculated (weighted geometric mean of the single ones) that allows to obtain the optimal solution.

In this case, the same weight is set to each of the answers assuming a unit value. This will set the target as important as any value within the limits for the corresponding answer.

On the other hand, assigning a value to the importance of each answer is related to the importance given to each of the answers, and if any of these responses is more important than the others (the most important is a 10, the less important is a 0.1). The optimization

> variable Objective Weight Importance taditional, T=44ºC Maximize 1 10 Δp minimize 1 5 taditional, T=38ºC Maximize 1 5 Investment minimize 1 1 %Melt Maximize 1 1

What is interesting of the optimized results is the value of composite desirability as well as its trend according to each of the factors considered. The composite desirability obtained in this case (0.919) indicates that the values determined by the optimization nearly fulfil the requirements of the response variables. The trends of composite desirability for each factor allow to adjust their value (usually due to physical or technological constraints) while keeping high desirability values. However, at least there are two drawbacks to use this configuration: first, it does not respect the width limitation (this unit has a width of more than 10 meters), and secondly, when manufacturing the TES unit it will be more feasible to use a PCM thickness higher than 0.5 mm (proposed in the optimization). Thus, moving in the optimization plot to a greater value of PCM thickness without reducing too much the composed desirability and rounding parameters, a value of 2.5 mm in thickness is selected (which also meets the width restriction). Table 13 shows the results of the corresponding simulation. The results of the last proposed unit are somewhat unfavourable compared to the optimized unit, but the proposed thickness of PCM is much more realistic than the optimized one. Yet the responses provided by the proposed unit represent a storage that improves the very first one. The comparison of these results against the ones of the initial



and 10) and an importance (also between 0.1 and 10).

and is related to the emphasis on achieving the target:


results are shown in figure 15.

Table 12. Optimization parameters.

Response

As it can be seen in the results of the simulation the contribution of the storage equipment is remarkable: the time spent to reach the room 38 ºC is 1h 40min (determined by the red dotted line), extending almost 40 minutes than if there was no storage system (red line). Table 10 compiles the main results.


Table 10. Main results of the simulation with Lazaro's case (2009).


Table 11. List of factors and their corresponding domain.

For the implementation of DOE the following factors and responses were considered:


#### **5.2.1 Response optimization**

Given that the main objective of the TES unit is to extend the time period during which the room temperature is below a certain temperature limit (in order to safeguard electronic equipment), the highest importance has set to that response. Table 12 lists the input parameters in the optimization. It has been considered that the most important requirement is to get the unit to extend as much as possible the time to reach the temperature limit of the air in the room, assigning the greatest importance to the maximum temperature limit (44 ºC), *taditional, T=44ºC*, and considering also important, but lesser, the time to reach the first temperature limit (38 ºC), *taditional, T=38ºC*, as well as the pressure drop, *Δp* (in order to be as lower as possible so that the electrical power consumption of the corresponding fan will be reduced). Also the investment and the melting ratio, *%Melt*, are interesting responses considered in the study, as they are related to economical and technical feasibility

As it can be seen in the results of the simulation the contribution of the storage equipment is remarkable: the time spent to reach the room 38 ºC is 1h 40min (determined by the red dotted line), extending almost 40 minutes than if there was no storage system (red line).

%Melt Investment [€] taditional, T=38ºC [min] taditional, T=44ºC [min] Δp [Pa] 69.47 3924 36 61 36

Factors Domain

MPCM [kg] 100 200 *V* [m3/h] 1000 2000 eplate [mm] 6 14 eair [mm] 10 20 Finish 1.5 2

For the implementation of DOE the following factors and responses were considered:

 Factors (listed in table 11 along with their domain): mass of PCM, air flow, air channel width, thickness of the PCM plate, finishing of the plates (related to rugosity or to the

 Responses: melting ratio in 3 hours, additional time for the air to reach a temperature of 38 º C (compared with the evolution of temperature without unit TES) in the room, additional time for the air to reach a temperature of 44 º C (compared with the evolution of temperature without TES unit) in the room, pressure drop, initial investment (mainly depending on the amount of PCM, the installed fan, the casing, and

Given that the main objective of the TES unit is to extend the time period during which the room temperature is below a certain temperature limit (in order to safeguard electronic equipment), the highest importance has set to that response. Table 12 lists the input parameters in the optimization. It has been considered that the most important requirement is to get the unit to extend as much as possible the time to reach the temperature limit of the air in the room, assigning the greatest importance to the maximum temperature limit (44 ºC), *taditional, T=44ºC*, and considering also important, but lesser, the time to reach the first temperature limit (38 ºC), *taditional, T=38ºC*, as well as the pressure drop, *Δp* (in order to be as lower as possible so that the electrical power consumption of the corresponding fan will be reduced). Also the investment and the melting ratio, *%Melt*, are interesting responses considered in the study, as they are related to economical and technical feasibility

Level (-) Level (+)

Table 10. Main results of the simulation with Lazaro's case (2009).

Table 11. List of factors and their corresponding domain.

presence of bulges in the surface of the plates).

whether or not the plates have bulges on its surface).

**5.2.1 Response optimization** 

Table 10 compiles the main results.

respectively. Once the objectives are defined, each variable is assigned a weight (between 0.1 and 10) and an importance (also between 0.1 and 10).

In this approach to the optimization, each of the values of the responses is transformed using a desirability function. The weight defines the shape of this function for each response and is related to the emphasis on achieving the target:


After calculating the desirability for each response, the desirability composite is calculated (weighted geometric mean of the single ones) that allows to obtain the optimal solution.

In this case, the same weight is set to each of the answers assuming a unit value. This will set the target as important as any value within the limits for the corresponding answer.

On the other hand, assigning a value to the importance of each answer is related to the importance given to each of the answers, and if any of these responses is more important than the others (the most important is a 10, the less important is a 0.1). The optimization results are shown in figure 15.


Table 12. Optimization parameters.

What is interesting of the optimized results is the value of composite desirability as well as its trend according to each of the factors considered. The composite desirability obtained in this case (0.919) indicates that the values determined by the optimization nearly fulfil the requirements of the response variables. The trends of composite desirability for each factor allow to adjust their value (usually due to physical or technological constraints) while keeping high desirability values. However, at least there are two drawbacks to use this configuration: first, it does not respect the width limitation (this unit has a width of more than 10 meters), and secondly, when manufacturing the TES unit it will be more feasible to use a PCM thickness higher than 0.5 mm (proposed in the optimization). Thus, moving in the optimization plot to a greater value of PCM thickness without reducing too much the composed desirability and rounding parameters, a value of 2.5 mm in thickness is selected (which also meets the width restriction). Table 13 shows the results of the corresponding simulation. The results of the last proposed unit are somewhat unfavourable compared to the optimized unit, but the proposed thickness of PCM is much more realistic than the optimized one. Yet the responses provided by the proposed unit represent a storage that improves the very first one. The comparison of these results against the ones of the initial

PCM-Air Heat Exchangers: Slab Geometry 453

In any case, the DOE methodology proposed above could be followed to design a proper

Methods to obtain enthalpy as well as the curves of thermal conductivity in the solid and liquid phases vs. temperature were proposed as a result of a critical analysis of the existing methods. A setup based on the T-history method was designed and built with significant improvements: 1) The possibility of measuring, for both organic and inorganic materials, cooling processes, therefore hysteresis and sub-cooling can also be studied; 2) The horizontal position decreases the error on enthalpy values since the liquid phase movements are minimized; 3) A Labview application allows the h-T curves to be directly obtained.

Results show that a heat exchanger using a PCM with lower thermal conductivity and lower total stored energy, but adequately designed, has higher cooling power and can be applied for free-cooling. Pressure drop is a key factor when designing any type of heat exchanger as it will determine the electrical energy consumption of the device. In the PCM-air heat exchangers with plates studied here, the pressure drop is ranged from 5 to 25 Pa. The analysis of the experimental data gathered accomplishes two aims: to develop empirical models of the TES unit and to come to a series of rules of thumb. Both are useful tools to design such kind of heat exchangers. For total energy storage strategy, the duration time of the cooling capacity of PCM heat exchanger depends on the cooling power demand. To validate the theoretical model developed, an uncertainties propagation analysis is proposed; here, the difference between the experimental and the simulation is less than 10% in terms of heat rate. The combined methodology of Design of Experiments applied to the numerical simulations seems to be a valid tool for design this kind of heat exchangers. When applied to the case study of temperature maintenance in a room, time to reach the maximum air temperature in the room was increased (19.7%), the initial investment was reduced by 11% and the PCM melting ratio was improved by 23.2%, as a drawback, the volume occupied by

The authors would like to thank the Spanish Government for the partial funding of this work within the framework of research projects ENE2005-08256-C02-02 and ENE2008- 06687-C02-02. Pablo Dolado would specially like to thank the former Spanish Ministry of Education and Science for his FPI grant associated with the research project. The authors also wish to thank the company CIAT for the support given in the early stages of the experimental work. Special thanks are extended to Mr. Miguel Zamora, CIAT R&D

TES unit to the corresponding application (Dolado, 2011).

the unit was increased around 3 times.

**7. Acknowledgment** 

Manager, for his collaboration.

A [m2] heat exchange area At [m2] tube lateral area

Ai [m2] area under the T-t curve, for the PCM Ai' [m2] area under the T-t curve, for water

b [J/(g·K)] parameter associated with the slope of the curve in all liquid phase and all-solid phase, sensible heat, heat capacity

**8. Nomenclature** 

**6. Conclusion** 

unit reflected that: a) Time to reach the target temperature of 44 °C increases: from 61 minutes it extends to 73 (19.7% improvement), being this a fundamental aspect of the application; b) The initial investment is reduced by 11%: from 3924 € to 3489 €; c) The PCM melting ratio is improved 23.2%; d) However, the volume occupied by the unit increments from 1.2 m3 to 3.8 m3.


Table 13. Main results of the proposed and optimized units.

Fig. 15. Optimization plot results.

## **5.2.2 Model-prototype similarity**

Dimensional analysis of these units show that the natural convection within the PCM is not going to be significant in any of the 2 units, being the heat transfer process by pure conduction for the second unit, and the ratio *λeff/λ* within the range of experimental validity for the other one (Dolado, 2011).Furthermore, since both Re and Bi numbers and NTU are within the range of experimental validity, the units can be used for design purposes.

#### **5.3 Other applications**

Keeping the temperature range, this type of heat exchanger can be applied in other different situations such as free-cooling, heat pumps, absorption solar cooling systems, greenhouses. In any case, the DOE methodology proposed above could be followed to design a proper TES unit to the corresponding application (Dolado, 2011).
