Experimental Analysis and Neural Network Model of MWCNTs Enhanced Phase Change Materials

Abstract

In this article, the thermophysical properties of binary eutectic PCM salt (LiNO₃ + NaCl) are investigated experimentally using the dispersion of multi-walled carbon nanotubes (MWCNTs) with varying weight fractions (i.e., 0.25 %, 0.5 %, and 1 %). According to the XRD and FTIR results, MWCNTs physically amalgamated with base eutectic salt without affecting their chemical structure. The Kissinger model is used to assess the phase change kinetics of the prepared nano-PCM composites. With the addition of MWCNTs, the activation energy of the chosen PCM is significantly increased. The thermophysical properties of the nano-PCM samples, such as phase transition temperature and latent heat value, are measured using differential scanning calorimetry (DSC) and thermal conductivity using a laser flash apparatus. The results show that dispersing 1 % MWCNTs in PCM salt improved the thermal conductivity enhancement ratio by 38.59 %, while decreasing the latent heat storage capacity by 14.98 %. Furthermore, by training the experimental DSC values of nano-PCM samples at various heating rates, an artificial neural network is developed to predict the thermophysical properties of nanocomposites. With an R² value of 0.998, the developed neural network accurately predicted the experimental DSC values.

Appendix 1

1.1 Laser Flash Apparatus (LFA)

Thermal conductivity is a key thermophysical parameters for characterizing LiNO₃ + NaCl binary eutectic PCM with different MWCNT compositions. The thermal conductivity was measured using a NETZSCH 467 laser flash instrument with an accuracy of ± 2 % within the range of 0.1–2000 W·mK⁻¹. The laser flash apparatus operated in the presence of a thermally insulated infinite slab that was uniformly subjected to a radiant energy heat pulse over the front surface. The instantaneous energy pulse was induced on the front surface of the sample by irradiating the laser beam in the laser flash method. The laser energy absorbed by the sample's front surface was transformed to heat energy, which spread throughout the sample. A photovoltaic infrared detector was used to measure the temperature of the sample's back surface. The temperature of the sample's back surface is used to compute the thermal diffusivity. The Fourier series can be used to express the temperature history of the back surface.

$$T\left(\tau ,t\right)= \frac{{Q}_{R}}{{\rho }_{PCM}\times {C}_{{P}_{PCM}}\times \tau }\left[1+2\sum_{m=1}^{\infty }{(-1)}^{m}exp\left(\frac{-{m}^{2}{\pi }^{2}}{{\tau }^{2}}\alpha t\right)\right]$$

Q_R = Radiant energy per unit surface area (J·m⁻²), ρ_PCM = density of the PCM sample (kg·m⁻³), ${C}_{{P}_{PCM}}$ = Specific heat capacity of the PCM (J·kg⁻¹ K⁻¹), τ = thickness of the sample (m).

The thermal diffusivity of each sample can be computed by following equation:

$$\alpha = 0.1388\times \frac{{\tau }^{2}}{{t}_{1/2}}.$$

The following equation can be used to compute the mass density value of nano-dispersed PCM samples. Meanwhile, the specific heat capacity of the sample can be obtained through DSC data.

$$\rho = {\rho }_{MWCNT} \left(\omega \right)+\left(1-\omega \right){\rho }_{PCM}.$$

Finally, thermal conductivity of sample can be determined by following expression:

$$K= \alpha \times {\rho }_{PCM} \times {C}_{{P}_{PCM}}.$$

The uncertainty of the thermal conductivity using LFA method was estimated based on the following parameters, i.e., thermal diffusivity ($\alpha$), density ($\rho$), and specific heat capacity (${C}_{P}$).

The uncertainty of the thermal conductivity can be determined by following equation:

$${E}_{K}=\sqrt{{(\frac{\partial K}{\partial \alpha }\bullet {E}_{\alpha })}^{2}+{(\frac{\partial K}{\partial \rho }\bullet {E}_{\rho })}^{2}+{(\frac{\partial K}{\partial {C}_{P}}\bullet {E}_{{C}_{P}})}^{2}.}$$

Using the above expression, the uncertainty of the thermal conductivity is calculated as 4.2 %.

1.2 Sample Preparation

Initially, an equal amount (i.e., 2gm) of prepared samples was inserted in the hydraulic press and uniform pressure was applied all around until the cylindrical-shaped pallets were formed. To determine thermal conductivity, materials were compressed into pellets with a diameter of 25 mm and a thickness of 3 mm using a hydraulic press at 8Mpa. The prepared samples are shown in Fig. 22.

Fig. 22

Prepared samples for measuring the thermal conductivity using laser flash apparatus

1.3 KD₂ Pro Thermal Conductivity Analyzer

The KD₂ Pro thermal conductivity analyzer is used to measure thermal conductivity of the prepared nano-PCM samples. TR-1 needle sensor is used to measure the thermal conductivity of PCM and nano-dispersed PCMs. The following points should be noted before conducting the experiment:

• Insert the TR-1 needle into the standard verification block to calibrate the equipment, and repeat the experiment at least four times to estimate the equipment’s accuracy.

• Prepare the PCM samples according to ASTM 5334 guidelines, before inserting the needle.

• Hold the needle for at least 15 min to get more accurate results.

• Thermal grease is applied to the needle to reduce the thermal contact resistance between the sample and the needle.

Before measuring the thermal conductivity of the PCM sample, it is necessary to calibrate the instrument using standard verification gauge. Measure the thermal conductivity of the verification standard gauge and validate with the certified value (Fig. 23). After calibration, the samples are allowed to measure the thermal conductivity using TR-1 sensor (Fig. 24).

Fig. 23

Calibration of TR-1 sensor

Fig. 24

Measurement of thermal conductivity of PCM sample using KD₂ Pro thermal conductivity analyzer

1.4 Measurement of Thermal Conductivity Using TR-1 Sensor

The thermal conductivity of PCM was measured using the TR-1 needle after it was filled in a centrifuge tube. PCM is found to have a thermal conductivity of 1.551 W·mK⁻¹ (Fig. 25). The thermal conductivity of 1 % MWCNT PCM was measured using a TR-1 needle after it was poured and compressed in the centrifuge tube. The thermal conductivity data are shown in Fig. 25, and it is found that the thermal conductivity of 1 % MWCNT PCM sample is 2.1723 W·mK⁻¹, which is 40 % greater than that of pure PCM. The following result confirms that adding MWCNT increased thermal conductivity greatly, which would improve the PCM’s thermal response even more.

Fig. 25

Thermal conductivity of nanosamples using KD₂ Pro thermal conductivity analyzer

The measured thermal conductivities of prepared PCM samples using LFA and KD₂ Pro thermal conductivity analyzers are given in Table

Table 7 Thermal conductivity of the nano-PCM samples measured by LFA and KD₂ pro thermal conductivity analyzers

7. The error deviation between these two methods for measure the PCM samples like pure PCM, 0.25 % MWCNT, 0.5 % MWCNT, and 1 % MWCNT are 5 %, 4.5 %, 3 %, and 4 %, respectively.

Similarly, the sample after thermal durability test was measured using LFA and KD₂ Pro thermal conductivity approaches and results are listed in Table

Table 8 Thermal conductivity of the nano-PCM samples measured by LFA and KD₂ Pro thermal conductivity analyzers after thermal durability test

8. The error deviation between these two methods for measure the PCM samples like pure PCM and 1 % MWCNT are 4.7 % and 4 %, respectively. From the results, it is observed that LFA method is most effectively used to measure the thermal conductivity of the PCM samples as compared with the KD₂ Pro method.