Study on phase change material thermal characteristics during air charging/discharging for energy saving of air-conditioner


In this study, RT-18 HC phase change material (PCM) having a melting point at 18 °C in a form of packed bed was used to reduce the power consumption of a 1 TR inverter air conditioner. A set of spherical balls was packed and integrated with the air conditioner for reducing the air temperature before entering the evaporator coil. The enthalpy method was developed for calculating the PCM temperatures and verified by testing results. The operating parameters such as bed thickness, air mass flow rate, inlet air temperature, operating time and properties of air and PCM during charging and discharging modes were also correlated in dimensionless forms. With the correlations, the charging and the discharging modes for three PCM bed thicknesses: 0.08 m, 0.16 m, and 0.24 m were evaluated, and it could be found that the results from the correlations agreed well with those from the experimental data within ±6% deviation. In addition, the electrical power consumptions of the air conditioner with these integrated PCM beds were 4.96 kWh/d, 4.7 kWh/d and 4.34 kWh/d compared with 5.04 kWh/d of the normal unit or 1.58, 6.80 and 13.84% of electrical energy could be saved, respectively.

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L :

packed bed length (m)

X :

packed bed thickness (m)

A :

cross-sectional area (m2)

M :

mass of PCM (kg)

D :

diameter (m)

e :

void fraction

T :

temperatures (°C)

\( \dot{m} \) :

mass flow rate (kg/s)

Cp :

specific heat capacity (kJ/kg K)

h v :

volumetric heat transfer coefficient (W/m3 K)

G :

mass flow rate per area (kg/s m2)

V :

volume (m3)

h :

specific enthalpy of the PCM (kJ/kg)

t :

time (s)

l :

PCM latent heat (kJ/kg)

x :

the position at any section

Y :

dimensionless of thickness and mass flow rate


phase change material





P :

power (kW)

Q :

cooling load (kW)

i and i + 1:

the entering and the exit of the ith section

a :


s :


l :


m :


b :


ref :

reference at initial condition

AC :

air conditioner

amb :


r :


Eva :



normal condition





ρ :

density (kg/m3)

τ :

dimensionless of time

θ :

dimensionless of temperature




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This research project is supported by Faculty of Engineering (Research Assistant Program); Center of Excellence for Renewable Energy, Chiang Mai University and National Research Council of Thailand through the project on “Development of Alternative Energy Prototypes for Green Communities”.

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Correspondence to Thoranis Deethayat.

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Annex 1

Annex 1

Uncertainties of some important parameters

$$ {\displaystyle \begin{array}{c}\kern1em G=m/A\\ {}\kern0.66em {h}_v=650{\left(\frac{G}{D_b}\right)}^{0.7}\\ {}\;\theta =\frac{T_{a, inlet}-{T}_{a, outlet}}{T_{a, inlet}-{T}_m}\\ {}\kern1em Y=\frac{h_vA}{{\overset{\cdot }{m}}_aC{p}_a}x\\ {}\tau =\frac{h_vV\left|{T}_{a, inlet}-{T}_m\right|}{M_bl}t\end{array}} $$
Equation Differential Uncertainty
\( G=\frac{m}{A} \) \( \frac{\partial G}{\partial {\dot{m}}_a}=\frac{1}{A} \) \( \delta G=\left|\frac{1}{A}\delta {\dot{m}}_a\right| \)
\( {h}_v=650{\left(\frac{G}{D_b}\right)}^{0.7} \) \( \frac{\partial {h}_v}{\partial G}=650\left(\frac{0.7}{D_b}\right){\left(\frac{G}{D_b}\right)}^{0.3} \) \( \delta {h}_v=\left|650\left(\frac{0.7}{D_b}\right){\left(\frac{G}{D_b}\right)}^{0.3}\delta G\right| \)
\( \theta =\frac{T_{a, inlet}-{T}_{a, outlet}}{T_{a, inlet}-{T}_m} \) \( \frac{\partial \theta }{\partial {T}_{a, inlet}}=\frac{T_{a, outlet}-{T}_m}{{\left({T}_{a, inlet}-{T}_m\right)}^2} \)
\( \frac{\partial \theta }{\partial {T}_{a, outlet}}=\frac{-1}{T_{a, inlet}-{T}_m} \)
\( \delta \theta =\sqrt{{\left(\frac{\partial \theta }{\partial {T}_{a, inlet}}\delta {T}_{a, inlet}\right)}^2+{\left(\frac{\partial \theta }{\partial {T}_{a, outlet}}\delta {T}_{a, outlet}\right)}^2} \)
\( Y=\frac{h_vA}{{\dot{m}}_aC{p}_a}x \) \( \frac{\partial Y}{\partial {h}_v}=\frac{Ax}{{\dot{m}}_aC{p}_a} \)
\( \frac{\partial Y}{\partial {\dot{m}}_a}=\left(\frac{h_v Ax}{C{p}_a}\right)\left(-\frac{1}{{\dot{m}}_a^2}\right) \)
\( \delta Y=\sqrt{{\left(\frac{\partial Y}{\partial {h}_v}\delta {h}_v\right)}^2+{\left(\frac{\partial Y}{\partial {\dot{m}}_a}\delta {\dot{m}}_a\right)}^2} \)
\( \tau =\frac{h_vV\left|{T}_{a, inlet}-{T}_m\right|}{M_bl}t \) \( \frac{\partial \tau }{\partial {h}_v}=\frac{V\left({T}_{a, inlet}-{T}_m\right)}{M_bL}t \) \( \delta \tau =\left|\frac{V\left({T}_{a, inlet}-{T}_m\right)}{M_bL}t\bullet \delta {h}_v\right| \)
$$ {\displaystyle \begin{array}{l}\kern0.33em {T}_{a, outlet}={T}_b+\left({T}_{a, inlet}-{T}_b\right){e}^{\frac{h_vA}{{\overset{.}{m}}_aC{p}_a}L}\\ {}{T}_b^{t+\Delta t}={T}_b^t+\frac{\overset{.}{m}C{p}_a\left({T}_{a, inlet}-{T}_{a, outlet}\right)}{\rho_b AL\left(1-e\right)C{p}_b}\Delta t\end{array}} $$
Equation Differential
\( {T}_{a, outlet}={T}_b+\left({T}_{a, inlet}-{T}_b\right){e}^{-\frac{h_vA}{{\dot{m}}_aC{p}_a}L} \) \( \frac{\partial {T}_{a, outlet}}{\partial {T}_b}=1-{e}^{-\frac{h_vA}{{\dot{m}}_aC{p}_a}L} \)
\( \frac{\partial {T}_{a, outlet}}{\partial {T}_{a, inlet}}={e}^{-\frac{h_vA}{{\dot{m}}_aC{p}_a}L} \)
\( \frac{\partial {T}_{a, outlet}}{\partial {h}_v}=\left({T}_{a, inlet}-{T}_b\right)\left(-\frac{A}{{\dot{m}}_aC{p}_a}L\right){e}^{-\frac{h_vA}{{\dot{m}}_aC{p}_a}L} \)
\( \frac{\partial {T}_{a, outlet}}{\partial {\dot{m}}_a}=\left({T}_{a, inlet}-{T}_b\right)\left(\frac{h_vA}{{\dot{m}}_a^2C{p}_a}L\right){e}^{-\frac{h_vA}{{\dot{m}}_aC{p}_a}L} \)
\( {T}_b^{t+\Delta t}={T}_b^t+\frac{\dot{m}C{p}_a\left({T}_{a, inlet}-{T}_{a, outlet}\right)}{\rho_b AL\left(1-e\right){Cp}_b} \) \( \frac{\partial {T}_b^{t+\Delta t}}{\partial {T}_b^t}=1 \)
\( \frac{\partial {T}_b^{t+\Delta t}}{\partial {T}_{a, inlet}}=\frac{\dot{m}C{p}_a}{\rho_b AL\left(1-e\right){Cp}_b}\Delta t \)
\( \frac{\partial {T}_b^{t+\Delta t}}{\partial {T}_{a, otlet}}=\frac{-\dot{m}C{p}_a}{\rho_b AL\left(1-e\right){Cp}_b}\Delta t \)
\( \frac{\partial {T}_b^{t+\Delta t}}{\partial {\dot{m}}_a}=\frac{C{p}_a\left({T}_{a, inlet}-{T}_{a, outlet}\right)}{\rho_b AL\left(1-e\right){Cp}_b}\Delta t \)


$$ {\displaystyle \begin{array}{c}\delta {T}_{a, outlet}=\sqrt{{\left(\frac{\partial {T}_{a, outlet}}{\partial {T}_b}\delta {T}_b\right)}^2+{\left(\frac{\partial {T}_{a, outlet}}{\partial {T}_{a, inlet}}\delta {T}_{a, inlet}\right)}^2+{\left(\frac{\partial {T}_{a, outlet}}{\partial {T}_{a, otlet}}\delta {T}_{a, otlet}\right)}^2+{\left(\frac{\partial {T}_{a, outlet}}{\partial {\overset{.}{m}}_a}\delta {\overset{.}{m}}_a\right)}^2}\\ {}\kern2em \delta {T}_b^{t+\Delta t}=\sqrt{{\left(\frac{\partial {T}_b^{t+\Delta t}}{\partial {T}_b^t}\delta {T}_b^t\right)}^2+{\left(\frac{\partial {T}_b^{t+\Delta t}}{\partial {T}_{a, inlet}}\delta {T}_{a, inlet}\right)}^2+{\left(\frac{\partial {T}_b^{t+\Delta t}}{\partial {h}_v}\delta {h}_v\right)}^2{\left(\frac{\partial {T}_b^{t+\Delta t}}{\partial {\overset{.}{m}}_a}\delta {\overset{.}{m}}_a\right)}^2}\end{array}} $$
Table 6 Uncertainty of important parameters

Uncertainty of the evaporator heat rate (\( {\dot{Q}}_{eva} \))

$$ {\dot{Q}}_{eva}={\dot{m}}_a\left({h}_{in}-{h}_{out}\right)-{\dot{m}}_a\left({\omega}_{in}-{\omega}_{out}\right){h}_f $$

By measuring Tdb and Twb the following parameters could be calculated as [22, 23]:

$$ {\displaystyle \begin{array}{l}h=1.006{T}_{db}+\omega \left(1.84{T}_{db}+2501\right)\\ {}\kern1em \omega =0.62069\times \frac{p_v}{103-{p}_v}\\ {}\kern0.33em {p}_v={p}_{sat}-0.067193\left({T}_{db}-{T}_{wb}\right)\\ {}{p}_{sat}=0.61078\times \exp \left(\frac{17.2694{T}_{wb}}{238.3+{T}_{wb}}\right)\end{array}} $$
\( {p}_{sat}=0.61078\times \exp \left(\frac{17.2694{T}_{wb}}{238.3+{T}_{wb}}\right) \)\( \frac{\partial {p}_{sat}}{\partial {T}_{wb}}=\frac{2510.38}{238.3+{T}_{wb}}\exp \left(\frac{17.2694{T}_{wb}}{238.3+{T}_{wb}}\right) \)
pv = psat − 0.067193(Tdb − Twb)\( \frac{\partial {p}_v}{\partial {p}_{sat}}=1 \)
\( \frac{\partial {p}_v}{\partial {T}_{db}}=-0.067193 \)
\( \frac{\partial {p}_v}{\partial {T}_{wb}}=0.067193 \)
\( \omega =0.62069\times \frac{p_v}{103-{p}_v} \)\( \frac{\partial \omega }{\partial {p}_v}=\frac{103}{{\left(103-{p}_v\right)}^2} \)
h = 1.006Tdb + ω (1.84Tdb + 2501)\( \frac{\partial h}{\partial {T}_{db}}=1.006+1.84\omega \)
\( \frac{\partial h}{\partial \omega }=1.84{T}_{db}+2501 \)
\( {\dot{Q}}_{eva}={\dot{m}}_a\left({h}_{in}-{h}_{out}\right)-{\dot{m}}_a\left({\omega}_{in}-{\omega}_{out}\right){h}_f \)\( \frac{\partial {\dot{Q}}_{eva}}{\partial {\dot{m}}_a}=\left({h}_{in}-{h}_{out}\right)-\left({\omega}_{in}-{\omega}_{out}\right){h}_f \)
\( \frac{\partial {\dot{Q}}_{eva}}{\partial {h}_{in}}={\dot{m}}_a \)
\( \frac{\partial {\dot{Q}}_{eva}}{\partial {h}_{out}}=-{\dot{m}}_a \)
\( \frac{\partial {\dot{Q}}_{eva}}{\partial {\omega}_{in}}=-{\dot{m}}_a{h}_f \)
\( \frac{\partial {\dot{Q}}_{eva}}{\partial {\omega}_{out}}={\dot{m}}_a{h}_f \)
\( \frac{\partial {\dot{Q}}_{eva}}{\partial {h}_f}={\dot{m}}_a\left({\omega}_{in}-{\omega}_{out}\right) \)
$$ {\displaystyle \begin{array}{c}\kern8em \delta {p}_{sat}=\left|\frac{\partial {p}_{sat}}{\partial {T}_{wb}}\delta {T}_{wb}\right|\\ {}\delta {p}_v=\sqrt{{\left(\frac{\partial {p}_v}{\partial {p}_{sat}}\delta {p}_{sat}\right)}^2+{\left(\frac{\partial {p}_v}{\partial {T}_{db}}\delta {T}_{db}\right)}^2+{\left(\frac{\partial {p}_v}{\partial {T}_{wb}}\delta {T}_{wb}\right)}^2}\\ {}\kern9em \delta \omega =\left|\frac{\partial \omega }{\partial {p}_v}\delta {p}_v\right|\\ {}\delta {\overset{.}{Q}}_{eva}=\sqrt{{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {\overset{.}{m}}_a}\delta {\overset{.}{m}}_a\right)}^2+{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {h}_{in}}\delta {h}_{in}\right)}^2{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {h}_{out}}\delta {h}_{out}\right)}^2+{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {\omega}_{in}}\delta {\omega}_{in}\right)}^2+{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {\omega}_{out}}\delta {\omega}_{out}\right)}^2+{\left(\frac{\partial {\overset{.}{Q}}_{eva}}{\partial {h}_f}\delta {h}_f\right)}^2}\\ {}\delta h=\sqrt{{\left(\frac{\partial h}{\partial {T}_{db}}\delta {T}_{db}\right)}^2+{\left(\frac{\partial h}{\partial \omega}\delta \omega \right)}^2}\end{array}} $$
δT wb 0.5 °C
δT db 0.5 °C
\( \delta {\dot{m}}_a \) 5%
δh f 5.02%
δp sat, in 3.08%
δp v, in 3.80%
δω in 3.87%
δh in 2.92%
δp sat, out 3.34%
δp v, out 3.33%
δω out 3.37%
δh out 3.98%
\( \delta {\dot{Q}}_{eva} \) 1.81%

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Loem, S., Deethayat, T., Asanakham, A. et al. Study on phase change material thermal characteristics during air charging/discharging for energy saving of air-conditioner. Heat Mass Transfer 56, 2121–2133 (2020).

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  • Charging/discharging
  • Packed bed cool storage
  • Phase change material
  • Correlation
  • Inverter air-conditioner