Heat and Mass Transfer

, Volume 54, Issue 9, pp 2871–2884 | Cite as

A comparative study on the modeling of a latent heat energy storage system and evaluating its thermal performance in a greenhouse

  • A. Mirahmad
  • S. M. Sadrameli


Thermal Energy Storage (TES) systems can be compared with batteries. As batteries can be charged when electricity is available for using during the power failure, TES systems can do the same for the thermal energy, i.e., they can absorb the available heat in one cycle, called charge cycle, and release it in a consecutive cycle, called discharge cycle. Among different kinds of TES systems, Phase Change Materials (PCM) have drawn considerable attention, since by changing from one phase to another, they can exchange a significant amount of energy in a small temperature difference. In this quest, a one dimensional mathematical model is solved using two different techniques and the results are compared together; one method is based on the enthalpy and the other is based on the effective heat capacity as well. Secondly, through eight experiments designed by using factorial approach, effects of inlet air velocity and temperature on the outlet stream has been investigated. The results proved that having a determined temperature difference between the inlet air and the PCM in both hot and cold cycles can enhance the efficiency. Finally, the feasible applications of a LHTES system for reducing the temperature swing in a greenhouse is studied numerically and the results are compared with experimental values. As a result, by using this passive coolant system diurnal internal temperature can be reduced for 10 °C.



Width of flat slabs [m]


Area of cross section of duct = ab [m2]


Area of each face of the greenhouse [m2]


Total area of the greenhouse faces [m2]


Air gap between parallel slabs [m]


Heat capacity of PCM [J/kg°C]


Heat capacity of air [J/kg°C]


Equivalent Diameter (m)


Spatial length [m]


Time step [sec]




Heat transfer coefficient between air and flat slabs [W/m2°C]


Spatial step counter


Time step counter


Thermal conduction of PCM [W/m2°C]


Length of the Bed [m]


Mass flow rate of air change [kg/s]


Mass flow rate of air which passes through LHTES [kg/s]


Mass of PCM [kg]




Perimeter [m]


Peclete number


Prantl number


Transferred heat [J]


Reynolds Number


Solar radiation [w/m2]


Time [sec]


Temperature of the inside air of the LHTES [°C]


Environmental temperature [°C]


Temperature of the inside air of the greenhouse [°C]


Initial temperature [°C]


PCM temperature [°C]


Dimensionless parameter of regenerator


Natural heat transfer coefficient between the greenhouse and outlet environment [W/m2°C]


Overall heat transfer coefficient [W/m2°C]


Total volume of the greenhouse [m3]


Length variable [m]


Process termination [s]


Transmittance of the greenhouse cover to the direct solar radiation


Density of air [kg/m3]


Thermal Expansion [K−1]


Thermal diffusivity [m2/s]


Air velocity [m/s]


Thickness of slabs [m]


Dimensionless parameter of regenerator


Dimensionless parameter of regenerator


Constant of the proportion of solar radiation entering the greenhouse

1 Introduction

The ever-increasing trend of global warming and greenhouse gas emissions, combined with pollution and limited energy resources are the main reasons behind the attempts devoted to improve the use of various energy sources. The other solution which must be taken into account is to improve the energy efficiency. With regard to this solution, latent heat thermal energy storage (LHTES) systems are interesting candidates for reduction of mismatch between energy supply and demand.

Since energy is produced and transferred in the form of heat in many countries, thermal energy storage (TES) deserves to be studied in detail. One of the oldest usages of TES goes back to the time when ice was provided from frozen lakes and rivers in the winter. The collected ice was then kept in well insulated warehouses in order to satisfy the needs for food conservation and air conditioning through the year. The air conditioning of Hungarian Parliament Building in Budapest is still done by ice harvested from Lake Balaton in the winter [1].

Storing of thermal energy takes place by using a change in the internal energy like: sensible heat, latent heat or thermochemical [2]. Among these methods, LHTES systems have drawn considerable attention due to their high storage capacity and also their near isothermal operation [1, 2]. PCMs can absorb or release a high amount of energy in a small temperature difference via phase change from solid to liquid or vice versa, respectively.

So many studies have been performed for the modeling of LHTES systems and so many methods have been illustrated. One of the major techniques is related to the moving boundary problems. Unknown interface of phase change and its nonlinear movements have made the moving boundary problems so complex [3, 4]. Furthermore, this formulation can produce acceptable results mostly for PCMs with single temperature of phase change. However, most of the materials are not pure and their phase change occurs in a temperature range instead of a single point. Another approach, as suggested by Regin [5], is called “Enthalpy Formulation”. This formulation does not require knowing where phase change takes place. The other method (which can also be categorized as a subset of enthalpy formulation) is “Effective Heat Capacity”. In this method, the correlation between the heat capacity and temperature in the phase change transition range can be obtained by using differential scanning calorimetry (DSC) analysis. Therefore the formulation can be derived without considering the phase change [6].

30-40% of energy consumption is related to the buildings [7] and the significant portion of this amount is used in hot summer days by cooling systems having compressor. Consequently many studies have focused on the usage of LHTES systems in cooling applications which is called free cooling. In order to condition the indoors air by changing the material phase, PCM can be embedded in a heat exchanger. During the night, PCM solidifies and the energy can be released (discharge cycle) and subsequently during the hot day, via a move through the heat exchanger, air is cooled and PCM melts (charge cycle) [8, 9].

The results of the simulations using the empirical model presented by Lazaro et al. [10] showed that the capability of the same PCM to maintain temperature levels below a certain temperature depends upon the heating power. Therefore, for any application where an almost constant temperature is required, the power demand must be taken into account. To maintain a specific temperature level when the cooling demand is high, the PCM phase change temperature should be lower. On the other hand, for very low cooling demands, the phase change temperature should be close to the objective temperature level.

Greenhouses are enveloped places in which temperature of the air must be kept in a certain limitation due to agricultural requirements. Providing this temperature limitation for crop thermal comfort is a major challenge, since the coverings need to allow light into the structure, they conversely cannot insulate very well and consequently unwanted heat loss/gain occurs. Lazaar et al. [11] conducted an experimental study to evaluate the performance of a LES unit inside a tunnel greenhouse. A shell and tube heat exchanger containing 10 kg of CaCl2.6H2O as PCM was used in this work. They proved that by using the built LHTES system, the air temperature inside the greenhouse can be reduced by a difference of 5 °C to 8 °C in comparison to a greenhouse without the storage system.

Bouadila et al. [12] made an experimental study to evaluate the nighttime recovered heat of the solar air heater with latent heat storage collector (SAHLSC) in an east-west oriented greenhouse. It was shown that by using this passive heating system, 31% of the total heating requirements can be provided. Furthermore, they concluded that the payback period of the proposed system is approximately 5 years, if the passive heater be used only three months a year.

In the present research work, a one-dimensional model for a LHTES system containing flat slabs of PCM is solved through two different methods; in one method Effective Heat Capacity is used to reckon the latent heat during phase transition, while in the later one which is called Enthalpy approach, phase change temperature is assumed to be constant. Afterwards a detailed study is performed on a small scale LHTES system by using numerical and experimental data. Finally, temperature changes of a greenhouse located in Tunisia, with and without using LHTES system, are calculated theoretically and the results are compared with experimental values.

2 Mathematical model

A greenhouse with LHTES integrated into its inside air circulating system is illustrated in Fig. 1. The mathematical model used for this greenhouse contains two parts, one for the LHTES system and the other one for the air temperature inside the greenhouse.
Fig. 1

The schematic diagram of the greenhouse

2.1 LHTES system

For this part two approaches are used. In both approaches, assumptions and equations are quite the same. The only division lies in the calculation of the latent heat. The first method uses effective heat capacity (Cp = Cp(T)), while the later one separates the phase change process into three sections; one in the solid phase, second during the phase change and third, the liquid phase.

2.1.1 First approach-effective heat capacity

The mathematical model used for the LHTES system is based on the following assumptions:
  1. 1-

    Axial conduction in the air is neglected in the direction of the flow. This assumption is verified by the fact that the Peclet number is greater than 100 as recommended by [13] (Pe > 225).

  2. 2-

    Temperature variations of the air normal to the flow are not considered.

  3. 3-

    No super cooling happens in the PCM.

  4. 4-

    Thermophysical properties of the PCM are constant and are the same for both phases, except the heat capacity in case of “Effective Heat Capacity”, which is a function of temperature. This is due to the fact that temperature variations in the system are limited.

  5. 5-

    Thermophysical properties of air are constant. This assumption is valid because temperature variations in the process are limited.

  6. 6-

    Heat transfer coefficient is the same for all the slabs.

  7. 7-

    Heat loss to the surrounding is negligible.

  8. 8-

    Air residence time in the bed is small in comparison with the period duration.

  9. 9-

    Heat transfer by radiation is neglected.

  10. 10-

    Heat capacity and thermal resistance of PCM containers are not considered.

  11. 11-

    Due to the low thickness of slabs containing PCM (3 mm), natural convection in the melted parts of the PCM is neglected.

Based on the foregoing assumptions and a system shown in Fig. 2, the heat balance equation for the passing air through the bed of PCM is:
Fig. 2

Configuration of the PCM slabs for establishing the energy balance equation

$$ \frac{\partial T\left(x,t\right)}{\partial x}+\frac{PU_p}{\nu A\rho {c}_{pg}}T\left(x,t\right)-\frac{PU_p}{\nu A\rho {c}_{pg}}{T}_p\left(x,t\right)=0 $$
with the boundary condition T(0, t) = Tin(t), the solution is:
$$ T\left(x,t\right)={T}_p\left(x,t\right)+\left[{T}_{in}\left(x,t\right)-{T}_p\Big(x,t\Big)\right]\times {e}^{-\frac{PU_p\Delta x}{\nu A\rho {c}_{pg}}} $$
By replacing jΔt and iΔx instead of t and x respectively, numerical form of Eq. (2) can be obtained as:
$$ T\left(i+1,j\right)={T}_p\left(i,j\right)+\left[T\left(i,j\right)-{T}_p\Big(i,j\Big)\right]\times {e}^{-\frac{PU_p\Delta x}{\nu A\rho {c}_{pg}}} $$

In Eq. (3), a dimensionless parameter can be introduced:

$$ \Lambda =\frac{PU_p\Delta x}{\nu A\rho {c}_{pg}} $$

Λ represents the ratio of “regenerator length” to the "mass flow rate of the passing air". The transferred heat in each control volume is:

$$ Q\left(i,j\right)=\nu A\rho {c}_{pg}\left[T\left(i+1,j\right)-T\Big(i,j\Big)\right] $$

Substituting Eq. (3) into Eq. (5) gives:

$$ Q\left(i,j\right)=\nu A\rho {c}_{pg}\left(1-{e}^{-\Lambda}\right)\left[T\left(i,j\right)-{T}_p\Big(i,j\Big)\right] $$

Since all the heat transferred to the air is provided by the PCM, energy balance for each control volume of the PCM can be written as:

$$ {q}_x-{q}_{x+ dx}-Q={m}_p{c}_p\left({T}_p\right)\frac{dT_p}{dt} $$
$$ {k}_p a\delta \frac{\partial^2{T}_p}{\partial {x}^2} dx-Q={m}_p{c}_p\left({T}_p\right)\frac{dT_p}{dt} $$
$$ {\displaystyle \begin{array}{l}{T}_p\left(i,j+1\right)={T}_p\left(i,j\right)+\frac{\Delta t}{m_p{c}_p\left({T}_p\left(i,j\right)\right)}\left[\nu A\rho {c}_{pg}\left(1-{e}^{-\Lambda}\right)\right]\left[T\left(i,j\right)-{T}_p\Big(i,j\Big)\right]\\ {}\kern5em +\frac{k_p a\delta \Delta t}{m_p{c}_p\left({T}_p\left(i,j\right)\right)\Delta x}\left[{T}_p\left(i+1,j\right)-2{T}_p\Big(i,j\left)+{T}_p\right(i-1,j\Big)\right]\end{array}} $$
In the last equation a new dimensionless number can be introduced as:
$$ U\left({T}_p\left(i,j\right)\right)=\frac{\nu A\rho {c}_{pg}\Delta t}{m_p{c}_p\left({T}_p\left(i,j\right)\right)} $$

This dimensionless parameter is defined as the ratio of “mean bed temperature change” to the “mean air temperature change”. The dimensionless parameters in Eqs. (4) and (10) are the same as reduced length and utilization factor of sensible heat storage (SHS), respectively [14]. By using this similarity, another dimensionless parameter can be introduced, known as reduced period, which is a criterion of the bed heat capacity:

$$ \Pi =\Lambda U=\frac{PU_p\Delta x\Delta t}{m_p{c}_p\left({T}_p\left(i,j\right)\right)} $$

Finally by substituting Eqs. (4), (10) and (11) into Eq. (9), Eq. (12) can be developed as:

$$ {\displaystyle \begin{array}{l}{T}_p\left(i,j+1\right)={T}_p\left(i,j\right)+\frac{\Pi \left({T}_p\left(i,j\right)\right)}{\Lambda}\left(1-{e}^{-\Lambda}\right)\left[T\left(i,j\right)-{T}_p\Big(i,j\Big)\right]\\ {}\kern5em +\frac{k_p a\delta \Delta t}{m_p{c}_p\left({T}_p\left(i,j\right)\right)\Delta x}\left[{T}_p\left(i+1,j\right)-2{T}_p\Big(i,j\left)+{T}_p\right(i-1,j\Big)\right]\end{array}} $$
In the all forgoing equations Up is defined as:
$$ \frac{1}{U_p}=\frac{1}{\frac{1}{h}+\frac{\delta /2}{k_p}} $$

Generally, the introduced heat transfer correlations for the flow of air between the parallel plates are divided into two categories: constant and equal temperatures and constant and equal wall heat fluxes. However, since the problems associated with the phase change materials take place in a constant temperature or a limited temperature swing, the case of constant and equal temperatures is used [15].

$$ Nu=\left\{\begin{array}{cc}1.233{\left(\overline{x}\right)}^{\frac{-1}{3}}+0.4\kern6.25em & \mathrm{for}\ \overline{x}\le 0.001\\ {}7.541+6.874{\left(1000\overline{x}\right)}^{-0.488}{e}^{-245\overline{x}}& \mathrm{for}\ \overline{x}\ge 0.001\end{array}\right. $$
$$ \overline{x}=\frac{\frac{x}{De}}{\operatorname{Re}.\Pr } $$
where De is equivalent diameter of heat transfer fluid passage. Nu, Re and Pr stand for Nusselt number, Reynolds number and Prandtl number, respectively.

2.1.2 Second approach-enthalpy method

In this approach, the solution procedure of written equations has three stages: below melting temperature (T < Tm), during phase transition (T = Tm) and above melting temperature (T > Tm). In the first stage (solid state), Eqs. (3) and (9) are solved simultaneously in each segment. At initial stage, the temperature distribution in all the longitudinal points of PCM slabs are known from initial condition; so by successive horizontal calculations, the longitudinal distribution of air temperature can be found at t-0 (Eq. 3). Then, by successive vertical calculations, the temperature distribution in all the longitudinal points of PCM slabs can be reckoned for the next time interval as illustrated in Fig. 3. When the temperature of the PCM approaches Tm, the solution enters the second stage (phase transition). In this stage Eqs. (3) and (6) are solved as long as Q equals the latent heat, i.e. Q = ∆H. Finally in the last stage, like the first stage, Eqs. (3) and (9) are solved simultaneously for the liquid phase.
Fig. 3

Grid used for numerical solution

2.2 Air temperature inside the greenhouse

To calculate the variations of air temperature inside the greenhouse, these assumptions are employed:
  1. 1-

    Temperature gradient inside the greenhouse is ignored.

  2. 2-

    Internal air is completely dry and does not have any moisture.

  3. 3-

    Greenhouse is empty.

  4. 4-

    Solar radiation is the same for all the faces of the greenhouse.

In this model the enthalpy changes of the inside air is the outcome of solar radiation, heat exchange with the inlet air, heat exchange with environment through polyethylene cover and finally heat exchange with the LHTES system [16]:
$$ {\displaystyle \begin{array}{l}{Vc}_{pg}\rho \frac{dT_G}{dt}=\sum \limits_{n=1}^5{A}_n{\tau}_G{\gamma}_G{S}_n-{A}_G{U}_G\left({T}_G-{T}_E\right)\\ {}\kern5.25em -{m}_{ACH}{c}_{pg}\left({T}_G-{T}_E\right)-{m}_{LHTES}{c}_{pg}\left(T\left(0,t\right)-T\left(L,t\right)\right)\end{array}} $$
To obtain the temperature changes of the inside air, Eqs. (3), (12) and (16) must be solved simultaneously. To this end, the outlet air temperature of the LHTES system (T(L, t), t = (k − 1)Δt) is set equal to the inside air temperature of the greenhouse (\( {T}_G^{k-1} \)), then by considering solar radiation, heat exchange with inlet air, heat exchange with environment through polyethylene cover, and heat exchange with the LHTES system, \( {T}_G^k \) is obtained. At the end by putting\( {T}_G^k=T\left(0,k\Delta t\right) \), Eq. (16) changes to:
$$ {Vc}_{pg}\rho \frac{dT_G}{dt}=\sum \limits_{n=1}^5{A}_n{\tau}_G{\gamma}_G{S}_n-{A}_G{U}_G\left({T}_G-{T}_E\right)-{m}_{ACH}{c}_{pg}\left({T}_G-{T}_E\right)-{m}_{LHTES}{c}_{pg}\left({T}_G^k-{T}_G^{k-1}\right) $$
Chronological sequence, we know all temperatures for (k-1) temporal points, so by using backward difference in Eq. (17), required temperatures for (k) temporal points can be calculated:
$$ {\displaystyle \begin{array}{l}{T}_G^k=\frac{Vc_{pg}\rho +{m}_{LHTES}{c}_{pg}\Delta t}{Vc_{pg}\rho +{A}_G{U}_G\Delta t+{m}_{ACH}{c}_{pg}\Delta t+{m}_{LHTES}{c}_{pg}\Delta t}\times {T}_G^{k-1}\\ {}\kern2em +\frac{A_G{U}_G\Delta t+{m}_{ACH}{c}_{pg}\Delta t}{Vc_{pg}\rho +{A}_G{U}_G\Delta t+{m}_{ACH}{c}_{pg}\Delta t+{m}_{LHTES}{c}_{pg}\Delta t}\times {T}_E^{k-1}\\ {}\kern2em +\frac{\Delta t\sum \limits_{n=1}^5{A}_n{\tau}_G{\gamma}_G{S}_n}{Vc_{pg}\rho +{A}_G{U}_G\Delta t+{m}_{ACH}{c}_{pg}\Delta t+{m}_{LHTES}{c}_{pg}\Delta t}\end{array}} $$

3 Experimental setup

For the experimental analysis, a small-scale prototype regenerator, containing about 200 g of PCM packed in aluminum sheets (Fig. 4) was set up. The schematic diagram of the built LHTES system is shown in Fig. 5. The pouches made of aluminum coated with polyethylene films were embedded in bed parallel to each other with 13 mm gap between them. Because of the circular cross-section of the bed, which is shown in Fig. 6, several PCM containers with different dimensions were made. The specifications and numbers of the flat slabs are reported in the Table 1. The bed container was a PVC tube 85 mm in ID, 5 mm in wall thickness and 300 mm in length. Two K-type thermocouples were affixed to measure the inlet and outlet temperatures. In this prototype PEG1000 was used as the PCM. Fig. 7 depicts the result of the DSC analysis for PEG1000.
Fig. 4

The Aluminum Pouch

Fig. 5

The schematic diagram of the built LHTES system

Fig. 6

Circular cross section of the bed

Table 1

Specifications of the flat slabs

Dimensions of flat slabs [mm]

Mass of the injected PCM in each container [gr]

Numbers of each container

3 × 38 × 210



3 × 53 × 210



3 × 75 × 210



Fig. 7

DSC analysis of PEG1000

4 Results

4.1 Validation of the LHTES models

In order to validate the written correlations for the LHTES, results of two experiments which were performed with the built prototype have been compared with numerical results. These comparisons are shown in Fig. 8. As can be seen there is a good agreement between both theoretical methods and the experimental results. The existing discrepancies are mostly related to the non ideal distribution of PEG1000 in the aluminum pouches, existence of air in the pouches, non ideal insulation of the bed and also non ideal distribution of the air throughout the circular cross section of the bed.
Fig. 8

Comparison between theoretical and experimental results

As illustrated in foregoing plots, the accuracy of the two solutions is almost equal for the same equations. These models are quite similar before and after the phase change. The major difference between two models lies during the phase transition; while using “Effective Heat Capacity” model, by changing the value of “heat capacity” proportional to the temperature of the PCM in each time interval, the outlet temperature changes slowly. On the other hand in “Enthalpy Method” the outlet air temperature is almost kept constant in accordance to constant temperature of the phase transition.

Since in this study the used PCM (PEG1000), melts/solidifies during a wide temperature difference, “Effective Heat Capacity” is used in the following calculations.

4.2 Parametric study of the LHTES models

Simulations are carried out at different inlet temperatures and for a range of mass flow rates. Effects of the inlet temperature and mass flow rate on the charge (hot) and discharge (cold) cycles are shown in Figs. 9, 10, 11 and 12. As shown in these figures, temperature of the inlet air plays an important role in the time needed for the process termination. In the hot cycle, higher temperatures and in the cold cycle, lower temperatures reduce the time needed for the process termination. According to the Figs. 11 and 12, higher velocities for the inlet air make the needed time for the process termination shorter. But as shown in the foregoing plots, in higher flow rates, decreasing trend of process termination becomes slower.
Fig. 9

Temperature distribution of the cold cycle at different inlet temperatures, air velocity between flat slabs = 0.25 m/s. Effective Heat Capacity is used for simulations

Fig. 10

Temperature distribution of the hot cycle at different inlet temperatures, air velocity between flat slabs = 0.2 m/s. Effective Heat Capacity is used for simulations

Fig. 11

Temperature distribution of the cold cycle at different inlet air velocities, inlet air temperature = 15 °C. Effective Heat Capacity is used for simulations

Fig. 12

Temperature distribution of the hot cycle at different mass velocities, inlet air temperature = 50 °C. Effective Heat Capacity is used for simulations

In order to evaluate the performance of the built LHTES system, the following correlation was used for efficiency:

$$ E=\frac{m_g{c}_{pg}{\int}_0^{\tau}\left({T}_{hi}-{T}_{he}\right) dt}{m_g{c}_{pg}\left({T}_{hi}-{T}_{ci}\right)\tau } $$
in which τ stands for the process duration. Effects of dimensionless parameter and process duration on the LHTES efficiency are shown in Figs. 13 and 14. As can be seen, by reducing the process duration, efficiency enhances. In this part, there is a tradeoff between complete phase change and efficiency, which must be considered. Because shortening the process duration makes the aborted phase change more possible and this phenomenon not only is not suitable for some applications like free cooling, but it makes the required energy used by the active coolant systems more.
Fig. 13

Effect of process duration on efficiency in constant Λ

Fig. 14

Effect of Λ on efficiency in the constant period (termination of the processes is considered)

As shown in Fig. 13, process duration has a significant effect on the efficiency. So for evaluating the effect of Λ on the efficiency, considering a constant criterion for the process duration seems to be necessary. Thus for all of the calculations, process termination, i.e., the time in which inlet and outlet temperatures become the same, was considered for the process duration. As shown in Fig. 14, by increasing Λ, efficiency can be improved. It means that in the same length reducing the inlet air velocity is the solution to improve the performance of the LHTES system.

4.3 Experimental results

In this part eight experiments were designed with Factorial method, four experiments for the cold cycle and four experiments for the hot cycle, in which effects of operational parameters, such as the temperature of the inlet air and its velocity, on the process duration and efficiency were investigated. Tables 2 and 3 contain the related data and results for each cycle and Fig. 15 represents the experimental outputs completely. According to the illustrated results for the hot cycles in Fig. 15a, the outlet temperature never reaches to the inlet temperature due to the heat loss and non ideal insulation.
Table 2

Cold cycle related data and results






Inlet air temperature [°C]





Air velocity between slabs [m/s]





Process termination [min]





Qmax [J] = mgcpg(Tinitial − Tinlet(t))τ





\( {Q}_{real}\ \left[\mathrm{J}\right]={m}_g{c}_{pg}{\int}_0^{\tau}\left({T}_{out}(t)-{T}_{inlet}(t)\right) d\theta \)





Efficiency [%]





Table 3

Hot cycle related data and results






Inlet air temperature [°C]





Air velocity between slabs [m/s]





Process termination [min]





Qmax [J] = mgcpg(Tinitial − Tinlet(t))τ





\( {Q}_{real}\ \left[\mathrm{J}\right]={m}_g{c}_{pg}{\int}_0^{\tau}\left({T}_{out}(t)-{T}_{inlet}(t)\right) d\theta \)










Fig. 15

Experimental results: (a) hot cycles, (b) cold cycles

According to the Table 2, following results can be concluded for the cold cycle:
  1. 1-

    In the cold cycle, increasing the passing air velocity and reducing its temperature, are two possible ways to shorten the process duration.

  2. 2-

    Increasing passing air velocity reduces the efficiency. It is probably related to the shortened residence time of the air in the bed.

  3. 3-

    In the cold cycle, increasing inlet air temperature reduces the efficiency.

According to the Table 3, following results can be concluded for the hot cycle:
  1. 1-

    In the hot cycle, increasing passing air velocity and increasing its temperature are two possible ways for shortening the process duration.

  2. 2-

    Increasing passing air velocity reduces the efficiency. It is probably related to the shortened residence time of the air in the bed.

  3. 3-

    In the hot cycle, increasing the inlet air temperature increases the efficiency.


As can be seen there is a consistency between numerical and experimental results and analyses.

4.4 The feasibility study on the possible applications of LHTES

4.4.1 Simulation of the greenhouse

To simulate a greenhouse using LHTES system for passive cooling, Eqs. (3), (12) and (16) must be solved simultaneously. For the case in which LHTES system does not exist in the greenhouse, solving the Eq. (16) with mLHTES = 0 is enough. As mentioned in the forgoing parts, temperature of the environment and also solar radiation, have major effects on the final answer. Fig. 16a illustrates the variations of the global solar radiation and ambient temperature as a function of time in 3 days in Borj Cedria area, near the city of Tunis in Tunisia. Other necessary properties are listed in Table 4. To validate the written correlation describing the variations of the internal air (in the absence of PCM storage system), model outputs are compared with the experimental values reported in [11] for greenhouse placed in Tunisia and the results are reported in Fig. 16b. As can be seen the promising consistency guaranties the accuracy of the model.
Fig. 16

(a) Solar radiation and ambient temperature variations [11] and (b) comparison between theoretical and experimental values for internal air without using PCM. Effective Heat Capacity is used for simulations

Table 4

Other parameters for the greenhouse and the LHTES system



Greenhouse volume[m3]

3 (height) × 1.5(width) × 2(length)


Single polyethylene

τG = 0.6 [15]

γG = 0.4 [11]

UG = 8


ρair = 1.12 [kg/m3]

cpg = 1005 [J/kg. °C]

Air change per hour(ACH)


Number of slabs


Dimensions of slabs [m]

0.42 × 0.205 × 0.003

Velocity of air between slabs [m/s]



ρ = 1093 [kg/m3]

ΔTm = 33 − 40 [°C]

Total mass = 10 kg

CaCl2.6H2O was used by Lazaar et al. [11] as PCM in their experimental quest for applications of passive cooler in greenhouses. Our theoretical results with PEG1000 as PCM have been compared with values reported by Lazaar. The discrepancies are illustrated in Fig. 17. Although differences exist between these two studies, like different types of PCMs (CaCl2.6H2O vs. PEG1000) and different geometries of the heat-exchangers (shell & tube vs. flat slabs), it can be concluded that the calculated values for air temperature inside the greenhouse are not irrational.
Fig. 17

(a) Solar radiation and ambient temperature variations [11] and (b) comparison between theoretical and experimental values for internal air with using PCM. Effective Heat Capacity is used for simulations

Temperature changes of the inside air of the greenhouse, with and without using PCM, are compared in Fig. 18. As long as TG < TE, heat exchange with environment and inlet fresh air accelerates the increasing trend of TG. This phenomenon continues up to the time TG = TE. After equivalency of TG and TE, just solar radiation accelerates this trend and all the other factors weaken it. This increasing trend lasts as long as the heat loss to the environment and inlet fresh air equals the heat gain via radiation. When the LHTES system exists in the greenhouse, via a phase change from solid to liquid, it absorbs the excessive heat and temperature increase becomes weaker. During the night, LHTES system delivers the absorbed heat and prevents sudden temperature drop. It also becomes ready for the next day by phase change from liquid to solid.
Fig. 18

Comparison of internal air with and without using PCM. Effective Heat Capacity is used for simulations

4.4.2 Effect of mass flow rate on air temperature inside the greenhouse

The air temperature inside the greenhouse has been calculated for different mass flow rates of the circulated air (Fig. 19). As it was predictable from the foregoing parts, temperature reduction in low velocities is more tangible in charge period, since this lower mass flow rate increases the residence time of the passing air inside the heat exchanger. Another positive point is that, low velocities reduce the power consumption of the fan. It’s noted that in discharge period, since cold air availability is limited, higher velocities are suggested.
Fig. 19

Effect of mass flow rate on internal temperature. Effective Heat Capacity is used for simulations

5 Conclusion

With the importance of thermal energy, there is a major need to expand the optimizing utilities. In the present research work, by using experimental and numerical studies, a small scale built heat exchanger packed with flat slabs of PCM has been evaluated comprehensively. A one dimensional model considering the axial conduction in the PCM has been solved through two different approaches; both solutions have been validated by experimental values gained from the built prototype. Through comparing both mechanisms, it can be concluded that effective heat capacity solution is preferred when the phase transition takes place in a wide temperature range and also an accurate correlation exists between temperature and heat capacity. However, in the lack of the precise correlation, the proposed Enthalpy method can generates promising outputs.

Experimental investigations on the effects of inlet temperature and velocity of the passing air have proved that process termination and efficiency can be affected significantly, i.e., higher temperature difference can shorten the process termination and enhance the efficiency, while higher velocities can reduce the process duration and efficiency.

Existence of the “greenhouse effect” in greenhouses leads to a peak in diurnal temperature. To evaluate the applicability of LHTES systems as a solution for this problem, a scale up study has been performed numerically and it has been proved that by using PCMs, the excess unwanted heat during the hot days can be absorbed and the internal air can be cooled for 10 °C during the hottest hours. Importance of using a multi-speed fan is an important note that must be brought to attention; i.e., during hot days lower speed improves the cooling performance of LHTES while during short nights higher speed guaranties complete solidification. For further investigations, more realistic experimental studies may be proper for those who are interested.



The authors would like to thank “Iranian Fuel Conservation Organization” and research department of Tarbiat Modares University for their financial supports.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Process Engineering Department, Faculty of Chemical EngineeringTarbiat Modares UniversityTehranIran

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