A computational analysis of the impact of nanofluids (Al2O3)on the PCM melting process in a rectangular container

Abstract

The effect of nanofluids on the melting process of PCMs (RT58 paraffin wax) in a rectangle container is a topic of interest for many researchers. The use of nanofluids in PCMs can lead to faster and more efficient melting, resulting in improved energy storage and cooling performance. This paper has studied four cases with varying percentages of nanofluids. The percentage of nanofluid in PCM can affect the material's thermal conductivity and heat transfer performance. By varying the percentage of nanofluids, researchers aim to optimize the use of these in PCMs to achieve the best melting performance. Findings have shown that increasing the percentage of nanofluids in PCM can lead to improved thermal conductivity and heat transfer performance. However, at high concentrations (30% percent), the viscosity of the nanofluid can increase, leading to a decrease in heat transfer performance. Results show that at 30 min, PCM with 30% nanofluid melts 13.79% more than PCM without. Using 20% nanofluid in the PCM results in a melting percentage of 7.41%, decreasing to 3.85% at 10%.The specific application and the type of nanofluid used determine the optimal concentration of nanofluid in PCMs. This study is important for the use of phase-change materials in the cooling of large electronic devices.

Introduction

Energy is a vital aspect of modern society, as it fuels the major sectors of the economy and impacts human daily existence. However, some energy resources are depleting rapidly, while others have a detrimental impact on the environment. Researchers around the world have been working tirelessly to find alternatives to conventional energy, with renewable energy being one of the most promising. Renewable energy sources, such as solar and wind power, have numerous benefits, including being long-term cost-effective, having no negative impact on the environment, and being versatile in terms of their applications. Nevertheless, a significant drawback of renewable energy is that it is not available all the time [1–4].

To overcome this challenge, researchers have been exploring the use of thermal energy storage, one of the most commonly used materials for this purpose being phase change materials (PCMs). Numerous studies have been conducted to investigate the impact of PCMs on heat storage and to identify the best materials and methods for increasing heat transfer. The use of copper rods has been found to be an effective way to enhance heat transfer, numerical forecasts of value in experimental research [2, 5–7]. Several studies by Shokouhmand et al. [8] and Sun et al. [9] have examined the melting process of PCMs in various containers and under different conditions. For instance, it has been found that any rise in temperature can accelerate the melting process, and that increasing the air inlet temperature can significantly increase the melting rate of PCM. Then Dhaidan et al. [10, 11] studies the melting process has also been found to be influenced by factors such as the diameter of the container, The parameters of interest are the temperature of the outer wall surface, the thermophysical properties, and the thickness of the tube shell.

Other studies deal with the applications that used PCM to improvement storage energy as well as mean enhancement the performance of these devices and applications. Shalaby et al. [12] this paper examines prior research on solar drying systems that utilized phase change material as an energy storage medium. Conclusion: the solar drier with a PCM reduces heat losses and increases the system's efficacy. Then Rostami et al. [12] using nanoparticles with PCM, results discovered that these materials (nanoparticles) generally enhance system performance. Without the use of mechanical apparatus, these materials are organically adapted to environmental temperature fluctuations, resulting in a decrease in energy consumption and, consequently, energy management. Cabeza et al. [13] a review of the PCM materials used for thermal energy storage in buildings other also for Cabeza et al. [14] Using water as a phase change material (PCM) for thermal energy storage improves heat transmission. Then Taha and Muhammed [15] study the comparison of single-PCM and multiple-PCM thermal energy storage designs. Results show that the efficacy of multi-PCM thermal energy storage improves as the number of stages increases. However, the addition of more than three stages does not result in a significant improvement. Other research by Barzin et al. [16] Utilization of PCM energy storage in conjunction with night ventilation to chill the space. Jisoo et al. [17] The purpose of this article is to reduce energy consumption by examining the evolution of available latent heat thermal energy storage technologies and discussing PCM application methods for residential buildings with radiant floor heating systems.

In conclusion, renewable energy and thermal energy storage are essential components of a sustainable energy future, with the use of PCMs showing promising results [18, 19]. This is due to the lack of continuity of renewable energy, and therefore we always need to store that energy to benefit from it in its absence until it returns from the source. This study aims to expand our understanding of the PCM melting process and provide insights into the impact of added nanoparticles on it. This study’s findings could have significant implications for the design and optimization of thermal energy storage systems. To accomplish this goal, this study will use computational methods to analyze the melting process of PCMs in a rectangular container with a nanofluid’s particles. This study will investigate the optimal proportions of nanomaterials to enhance performance and efficiency. The study will also examine the impact of different heat fluxes on the melting process, comparing these results to previous findings.

Numerical procedure

Physical model

See Fig. 1.

Fig. 1 [Images not available. See PDF.]

a Physical model configuration. b Grid independency without fins

Computational procedure

Numerical studies may be used to determine the needs for the melting process in the rectangular cell. The flow was determined to have characteristics of being two-dimensional, laminar, incompressible, and unstable [20, 21]. To elucidate the process of melting, it is postulated that both the liquid and solid phases exhibit uniformity and homogeneity, and that the temperature remains constant at the interface between them. The enthalpy-porosity approach was used to represent the phase-change zone in the PCM. The process of PCM melting is challenging because to its non-linearity, temporal variability, and constant motion of solid–liquid interface. PCM melting models include the following partial differential equations: continuity, momentum, and energy, represented as Eqs. (1), (2), and (3) accordingly. [22–24]:

1

$$\frac{\partial \mathrm{\rho }}{\partial \text{t}}+\mathrm{\nabla }·\left(\rho V\right)=0$$

2

$$\frac{\partial \left(\mathrm{\rho }\text{v}\right)}{\partial \text{t}}+\mathrm{\nabla }·\left(\mathrm{\rho }\text{V}\right)=-\mathrm{\nabla }\text{P}+\mu {\mathrm{\nabla }}^2\text{V}+\mathrm{\rho }\text{g}+\text{S}$$

3

$$\frac{\partial }{\partial \text{t}}\left(\mathrm{\rho }\text{H}\right)+\mathrm{\nabla }·\left(\mathrm{\rho }\text{VH}\right)=\mathrm{\nabla }·\left(\text{K}\mathrm{\nabla }\text{T}\right)$$

(H) Specific enthalpy, is the sum of sensible enthalpy (h) and latent heat (ΔH) [25],

4

$$\text{H}=\text{h}+\mathrm{\Delta }H$$where [26],

5

$$\text{h}={\text{h}}_{\text{ref}}+\underset{{\text{T}}_{\text{ref}}}{\overset{\text{T}}{\int }}{\text{C}}_{\text{p}}\text{dT}$$

6

$$\mathrm{\Delta }\text{H}=\beta {\text{L}}_{\text{f}}$$

The latent heat content can range from zero for solids to one for liquids. The liquid fraction (β), can be written as [27, 28]:

7

$$\beta \left\{\begin{array}{cc}0solidus& ifT<Ts\\ 1liquidus& ifT>{\text{T}}_{\text{l}}\\ \frac{\text{T}-{\text{T}}_{\text{s}}}{{\text{T}}_{\text{l}}-{\text{T}}_{\text{s}}}& if{\text{T}}_{\text{s}}\le T\le {\text{T}}_{\text{l}}\end{array}\right)$$

The phase shift impact on convection causes a slowing component from Darcy's law to be introduced to the momentum equation as the source term (S). The source term in the momentum equation is expressed as [29, 30]:

8

$$\text{S}=\frac{{\text{C}(1-\mathrm{\beta })}^2}{{\mathrm{\beta }}^3}\text{V}$$where the coefficient (C) is a constant that reflects the shape of the melting front and is found in the mushy zone [2, 31]. This constant is a large number, and its value ranges from 10⁴ to 10⁷ most of the time. 10⁵ is chosen as the value for C, which is expected to be constant throughout this investigation [32].

Boundary conditions

As a heat source, 100 °C water moves through the wall at a speed of 0.027 m/s and a rate of 0.027 m/s. The rectangular cell is separated from the rest of the PCM so that heat doesn't move from the wall to the rest of the PCM without being lost. The phase change medium is RT58 paraffin wax. Table 1 has a list of the thermophysical qualities of the wax [33–35].

Table 1. Thermal characteristics of the PCM substance [36, 37]

	Nano fluid	1%	5%	10%
PCM (RT58) [38–40]
$\mathrm{\rho }$= 840 kg/m3
K = 0.2 W/(m K)
CP = 2100 J/Kg. K
$\mathrm{\mu }$=0.0269 kg/m s
$\mathrm{\gamma }$=0.00011 1/K
$\mathrm{\Delta }\text{h}$=180,000 J/Kg
Ts = 48 ºC
TL = 62 ºC
Al2O3[41–43]
ρ = 3950 kg/m3		1151	1462	1773
K = 20 W/ (m K)		0.265	0.344	0.446
CP = 750 J/Kg. K		1636	1370	1197

Assumptions

When solving a mathematical model of the melting process within a rectangular cell, the following assumptions are considered: A two-dimensional model of the melting is presented [44]. Initially, the cell is completely filled with a solid PCM, the flow being erratic, laminar, and incompressible [45]. The viscous dissipation term is assumed to be negligible, assuming that the PCM's thermophysical properties are constant in both solid and liquid states [3, 46]. The effects of volume change resulting from the solid–liquid phase transition are disregarded, and there is no heat loss or gain from the environs.

Grid independency

Researchers have focused on investigating mesh independence, an essential first step in computational fluid dynamics (CFD) research, to evaluate the impact of varying mesh densities on phase change behaviour in a specific geometric configuration. The primary objective of this study was to trace the progression of phase change. We carefully selected four unique mesh densities to address a variety of computational requirements. These mesh densities matched element counts of 34,567, 36,789, 38,987, and 40,123. We conducted a comprehensive analysis of the entire network ensemble and found that the phase change progression pattern remained consistent across all element counts. This indicates that the network was autonomous, meaning that the choice of network density had no significant effect on the calculated outcomes. In order to maximize computational efficiency without compromising accuracy, the lowest element number (34,567) was deliberately chosen for the next simulations, as seen in Fig. 1b.

Results and discussion

The use of nanofluids in PCMs can lead to faster and more efficient melting, which can result in improved energy storage and cooling performance. The objective of this research is to study the behavior of nanofluids in PCMs and their impact on the melting process in a rectangle container. This information is critical for the development of advanced PCM-based energy storage and cooling systems.

Case one (without nanofluid)

Figure 2 shows the progression of the melting phase of PCM with no nanofluid, in a rectangular shape over time, in this case, 135 min to completion. The change from the solid to liquid phase is observed according to the heat source.

Fig. 2 [Images not available. See PDF.]

Evolutionary forecast of the melting process without nanofluid

The temperature distribution of the PCM is shown in Fig. 3 where it is noted that the temperature changes (over time) throughout the material, as the body gains heat.

Fig. 3 [Images not available. See PDF.]

Temperature distributions without nanofluid

The phase change of the PCM can be observed by showing the flow velocity of the fluid through the material in the rectangular shape, as seen in Fig. 4.

Fig. 4 [Images not available. See PDF.]

Velocity distributions without nanofluid

The effect of nanofluids

The addition of nanoparticles to the fluid can enhance thermal conductivity, leading to improved heat transfer and more efficient energy storage. Nanofluids can also increase thermal stability and reduce the range of both melting and solidification temperatures in PCMs. However, it is important to note that the specific effect of nanofluid on PCM performance can vary depending on the type of nanoparticles and base fluid used, as well as the manufacturing process and storage conditions.

Melting process

At the beginning of the melting process, the nanofluid and PCM are in a solid state. The temperature of the system begins to increase due to the input of heat, and the PCM begins to absorb said heat. The presence of AL₂O₃ nanoparticles enhances the thermal conductivity of the nanofluid, allowing for improved heat transfer from the surrounding environment to the PCM.

As the temperature continues to increase, the PCM begins to undergo a phase change from solid to liquid as shown in Fig. 5. The presence of the AL₂O₃ nanoparticles help to promote and enhance this melting process by improving the heat transfer characteristics of the system.

Fig. 5 [Images not available. See PDF.]

Melting steps at a 30 min, b 60 min, and c 90 min

Temperature distribution

The temperature distribution of Al₂O₃ nanofluid with PCM, can vary based on the concentration of the nanofluid. The higher the concentration of the nanofluid, the greater the thermal conductivity and therefore, the better the temperature distribution. When the concentration of Al2O3 nanofluid is 10%, the temperature distribution is relatively low, as thermal conductivity is not as high as compared to higher concentrations. At 20% concentration, the temperature distribution will be better than at 10%, thermal conductivity also higher as shown in Fig. 6. At 30% concentration, the temperature distribution will be at its best, as thermal conductivity is at its highest across these the three cases.

Fig. 6 [Images not available. See PDF.]

Temperature distributions of a 10%, b 20%, and c 30% nanofluid concentrations

Effect of melting velocity

The melting speed of nanofluid Aluminum Oxide (AL₂O₃) nanoparticles and PCM is influenced by the thermal conductivity improvements created by the nanofluid. The addition of nanoparticles to a PCM can improve thermal conductivity and therefore enhance the heat transfer characteristics of the system which can lead to increased melting. An increase in the concentration of the nanofluid, leads to a change in the properties of the original material which has no nanofluids, which will directly affect and increase the phase transition speed of the PCM, as shown in Fig. 7.

Fig. 7 [Images not available. See PDF.]

Velocity distributions of a 10%, b 20%, and c 30% nanofluid concentrations

A comparison of the four cases

PCMs are materials that can store and release large amounts of thermal energy by changing from a solid to a liquid or vice versa (Fig. 8). Nanofluids are suspensions of nanoscale particles in a base fluid, which are used to enhance the thermal conductivity of the PCM. Figure 8 lists the change in time in minutes along the horizontal axis, and the change in nanofluid concentration in percent along the vertical axis. The data shows that as time increases, the nanofluid concentration in the PCM decreases.

Fig. 8 [Images not available. See PDF.]

Variation of melt fraction

Validation

A comparison of the findings of the present study and previous relevant research are present in Table 2. Which shows the extent of the effect of the difference in shape with other shapes, and in other research it shows the effect of the shape of the content with the content used (see Fig. 9).

Table 2. Comparison with previous research

Temperature distributions improvement (%)	Melt fraction improvement (%)	Type of enhancement of heat transfer	Authors (Reference)
33.56	12.1	Copper rods	A Basem et al. [26]
34.2	35.9	Air bubbles	AF Khalaf et al. [47]

Fig. 9 [Images not available. See PDF.]

Melting time of the current study and Ref. [24] in the same conditions

Conclusions

We did a computer simulation using the ANSYS programme to look into what would happen if we added nanomaterials to a phase change material (PCM). Our goal was to find out how much this could improve the heat transfer for that material. The use of phase-change materials for energy storage and cooling applications has gained significant attention in recent years. PCMs store and release thermal energy through the phase change process (melting and solidification). However, traditional PCMs have limited thermal conductivity, leading to slow and inefficient melting. To address this issue, researchers have explored the use of nanofluids in PCMs. We found that nanofluids, which are suspensions of nanoscale particles in liquid, significantly enhance thermal conductivity and heat transfer performance. The study was carried out by using three different percentages of nanomaterials (30%, 20%, and 10%) and comparing them with the absence of nanomaterials. We can summarize and present these results based on the following points:

1. At 30 min, the melting fraction is 13.79% when there is 30% of nanofluid in the PCM compared with PCM without nanofluid.

2. At 20% of the nanofluid in the PCM, the melting fraction is 7.41%, dropping to 3.85%.

3. At 10% of the nanofluid in the PCM, the data also demonstrates that the melting fraction changes at a faster rate when the initial concentration is higher.

This suggests that the concentration of the nanofluid influences the PCM's rates of thermal energy storage and release.

Author contribution

We work together.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

List of symbols

C_p

Specific heat pressure (J/kg. K)

h

Average heat transfer coefficient (W/m². K)

k

Thermal conductivity (W/m. K)

ΔH

Latent heat of melting (kJ/kg)

H

Enthalpy (kJ/kg)

te

Elapsed time for each test run (s)

T

Temperature (K)

H

Hot water

l

Liquid PCM

m

Melting

S

Solid PCM

PCM

Phase change material

β

Melt fraction

α

Thermal diffusivity (m²/s)

${\mathrm{\beta }}_{\text{f}}$

Liquid thermal expansion coefficient (1/K)

$\mathrm{\rho }$

Density (kg/m³)

$\text{v}$

Kinematic viscosity (m2/s)

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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