Incorporation of nanomaterial for the thermal management of the solidification process in mechanical storage

Abstract

Improving the performance of storage units is important for saving energy. An implicit approach has been combined with the adaptive grid in this modelling for the presentation of solidification inside the tank with a sinusoidal cold surface. Not only the implementation of curved will but also the inclusion of nanoparticles was assumed as a passive technique for expediting freezing. The scalars were extracted by the Galerkin approach. The formulation of nanomaterial features was done by considering uniform concentration inside the domain. Increasing the fraction of CuO can reduce the freezing time from 2211.13 to 1943.72 s and 1675.37 s if the blade shape is selected. The augmentation of shape factor and fraction of nanomaterial lead to the reduction of freezing time by about 6.98% and 24.23%, respectively. The results proved that ϕ has a stronger effect than other active parameters.

KEYWORDS:

• NEPCM
• grid adaption
• numerical transient modelling
• solidification
• complex tank

1. Introduction

Because of the great ability of PCM in saving heat, it can be applied for different usages [1–3]. For these applications, various kinds of PCM can be implemented [4–8] which depend on the type of usages and ranges of temperature [9–12]. If the material has low conductivity, it can reduce the speed of the process [13–16]. To remove this drawback and ameliorate the amount of stored energy, different remedies have been suggested [17–20]. Several researchers offered passive approaches, such as adding nanoparticles to modify the feature of PCM [21–23]. Besides, mounting fins can augment the movement of the solid front [23–26]. Lacroix and Benmadda [27] utilized the special style of fins with variable sizes to increase the hot flow penetration. They utilized a fixed style grid incorporating implicit methods and showed that augmenting the length of the fin can enhance the melting process.

The reduction of the period of melting phenomena within a finned enclosure was scrutinized in Ref. [28]. The authors prepared an experimental system and considered various ranges of heat flux. They proved that the completion time augments with the rise of the number of fins. The charging process with close contact with nanoparticles was analysed by Hu et al. [29]. The authors added graphene powder to the paraffin and conducted an empirical test. They discovered that augmenting a fraction of nanomaterial more than 3%wt could lead to a reverse effect. The optimization of the configuration of fins was premeditated by Deng et al. [30] who exploited FVM in modelling, involving buoyancy force impact. They depicted that the arrangement of fins can play a key role in minimizing the period of the process. The container with edges was scrutinized by Tian et al. [31] to evaluate the melting. They applied various types of fins and found that copper fins could show the best performance in which the period of melting was reduced by 41.6%.

In previous articles, the authors tried to suggest a new approach for reducing the time of the process and they found that adding additives in addition to changing geometry can be helpful. In this attempt, two different shapes of nanoparticles made from copper oxide were mixed with water. The container was filled with NEPCM and it had one right sinusoidal wall to maintain cold conditions. The model of the present unsteady problem was solved by the Galerkin method. It was verified first and then the impacts of active factors were illustrated in results.

2. Solidification process and modelling

The container, as depicted in Figure 1, contains three insulated walls and one sinusoidal cold right wall. The applied PCM is H₂O which can be mixed with CuO nanoparticles to enhance the thermal treatment. The concentration of powders is lower than 0.07 and a uniform concentration was applied for all positions inside the domain. Since the velocity has a low role in freezing, the equations become simpler as below [32]: (1) $\begin{array}{rl}& \mathrm{\nabla }(k_{nf}\mathrm{\nabla }T)=\frac{dT}{dt}(\rho C_p{)}_{nf}-\frac{dS}{dt}{L}_{nf}\end{array}$(1) (2) $\begin{array}{rl}& \{\begin{array}{l}S=1(T-T_m)<(-T_0)\\ S=0(T-T_m)>(-T_0)\\ S=(T_m+0.5T_0-T)/T_0(-T_0)<(T-T_m)<T_0\end{array}\end{array}$(2) To discover the required properties needed for solving Equation (1), the below equations have been implemented [32]: (3) $\begin{array}{rl}& {\rho }_{nf}={\rho }_f(1-\varphi )+{\rho }_p\varphi \end{array}$(3) (4) $\begin{array}{rl}& \frac{k_{nf}}{k_f}=\frac{(k_p-k_f)\varphi m+k_{f}m+k_p(1+\varphi )+k_f(1-\varphi )}{k_f(m+2)+\varphi k_f+k_p(1-\varphi )}\end{array}$(4) (5) $\begin{array}{rl}& \frac{{(C_p\rho )}_{nf}-{(C_p\rho )}_f}{({(\rho C_p)}_p-{(C_p\rho )}_f)}=\varphi \end{array}$(5) (6) $\begin{array}{rl}& (L\rho {)}_{nf}=(L\rho {)}_f(1-\varphi )\end{array}$(6)

Figure 1. Progress of freezing with nanomaterial.

The main assumption for utilizing the above equation is considering a homogeneous mixture for nanomaterial and also in deriving k_nf, the impact of shape factor has been included. For finding the solution, the Galerkin approach was utilized incorporating an adaptive grid, as suggested by Sheikholeslami, [33] who published several papers in this field. The utilizing time-dependent grid and automatic time step make this approach more powerful.

3. Results and discussion

The development of a powerful numerical approach for simulating the transient problem involving implicit technique has been utilized in the current attempt. Freezing of water within a container with a sinusoidal wall was modelled with nanoparticles (CuO). The inner sinusoidal wall makes the solid front a curved shape and dispersing nanomaterial augments the process. Although gravity has some effect on this process, to reduce the computational cost, this effect has been ignored because liquid water has a low velocity during freezing. Galerkin approaches for this work have been implemented to solve the two remaining equations and the amounts of T and S have been extracted in each time step. For more description of nanomaterial impact, two factors were analysed:shape factor and the fraction of nanoparticles. The grid should be denser near the region of the solid front and this note was applied in this study, as demonstrated in Figure 2. Low deviation, shown in Figure 3 in comparison with the previous publications [33,34], proves the nice accuracy of the present model.

Figure 2. A denser mesh near the ice front.

Figure 3. Testing accommodation of the code with Ref. [33,34].

The efficacy of active factors on the distribution of scalars has been illustrated in Figures 4 and 5. In these figures, the amounts of S and T inside the various positions of the domain in three time levels were demonstrated. The NEPCM begins to convert ice near the sinusoidal wall. Both factors can augment the conduction mode, thus reducing the required time of the process. With increasing the mass of nanoparticles, the time of phenomena changes from 2211.13 to 1675.32 and 1943.72 s when blade and cylinder particles are utilized. Also, altering the shape factor can change the time from 2023.29 to 1943.72 s (when ϕ = 0.02) and from 1801.09 to 1675.37 s (when ϕ = 0.04). Augmenting ϕ has a more sensible impact on this process. Figures 6 and 7 portray the impact of ϕ on the promotion of freezing with reporting heat released profile in addition to solid front curves. With the inclusion of more nanomaterial, the conduction can play a more effective role and quicker freezing can take place. The volume of solid PCM surges as the time augments which compromises lower latent heat. A greater value of S can be seen when a higher level of ϕ is utilized.

Figure 4. How m can change the freezing behaviour.

Figure 5. How ϕ can change the freezing behaviour.

Figure 6. Augmentation of the speed of process with growing ϕ.

Figure 7. Time-dependent functions with the augmentation of ϕ.

The shape factors depicted in Figures 8 and 9 show a greater speed of solidification. The shape of particles canimpact the performance of the system and the result shows that higher levels of this parameter can increase the amount of solid fraction and the time of achieving the full solid phase declines. It can be seen from time-dependent graphs that the amount of latent heat will be decreased with the augmentation of time and considering a higher shape factor can also reduce this function. The time for converting whole liquid to ice is essential in analysing the system illustrated in Figure 10. The time for reaching SF = 1 has been derived for all cases and according to those data, correlations have been derived and have been shown as contours and plots. When m = 4.8 and 8.6, augmenting ϕ from 0 to 0.02 leads the freezing time to reduce by about 8.49% and 12.09%. Also, this change can be more effective when ϕ reaches 0.04 and freezing time declines about 18.54% and 24.23%. As the shape factor grows, the time declines by about 3.93% and 6.89%. With the growth of ϕ from 0.02 to –0.04, the time can be reduced by around 10.98% and 13.8%.

Figure 8. Augmentation of the speed of process with growing m.

Figure 9. Time-dependent functions with the augmentation of m.

Figure 10. Freezing time for different ranks of ϕ and m.

4. Conclusion

Nanoparticles with two shapes were considered the technique of increment of the rate of freezing in this research. The governing equations were simplified by involving the assumption of neglecting the impact of the velocity of liquid NEPCM. The container has three insulated walls and one sinusoidal cold wall. As anticipated, the freezing starts from the vicinity of the curved wall and the ice front goes to the outer wall as time increases. The formulation of nanomaterial was based on a single-phase model and unsteady terms were modelled based on an implicit technique. To obtain the solution to the present problem, the Galerkin method was incorporated and distributions of solid fraction and T were extracted in various time steps. The verification, based on previous numerical data, shows great accuracy of the present approach. For more accurate results, the mesh has been considered as time-dependent in which a denser grid was applied near the position of SF = 0.95. The performances of systems with various levels of active parameters have been presented in the outputs. In the freezing process, the velocity of PECM is not high and the chief mechanism during the phenomena is conduction. Thus, changing the features of PCM with the inclusion of nanoparticles can help expedite the process. The features of NEPCM were measured by considering the assumption of a uniform fraction of particles within the domain. The time of reaching SF = 1 was estimated for all cases and accordingly, contours and plots were derived. As m grows the time drops about 3.93% and 6.89%. With the growth of ϕ from 0.02 to –0.04, the time can be reduced by about 10.98% and 13.8%. Given m = 4.8 and 8.6, increasing ϕ from zero to 0.02 leads the discharging time to decrease about 8.49% and 12.09%. Also, this alteration can be more effective when ϕ reaches 0.04 and solidification time reduces by about 18.54% and 24.23%. The NEPCM begins to convert ice near the sinusoidal wall. Both factors can augment the conduction mode, thus decreasing the required time of the process. By augmenting the mass of nanoparticles, the time of phenomena alters from 2211.13 to 1675.32 s and 1943.72 s when blade and cylinder particles were utilized. Also, altering the shape factor can change the time from 2023.29 to 1943.72 s (when ϕ = 0.02) and from 1801.09 to 1675.37 s (when ϕ = 0.04). With the inclusion of more nanomaterial and increasing shape factor, the conduction can play a more effective role and faster solidification can take place. The volume of solid PCM rises as time increases which offer lower latent heat and the temperature of the domain decreases. A greater amount of S can be seen when a higher level of m and ϕ is incorporated. The quickest process takes 1675.37 s when m = 8.6 and ϕ = 0.04.

Disclosure statement

No potential conflict of interest was reported by the author(s).