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Research Papers: Two-Phase Flow and Heat Transfer

Numerical Simulation of the Effect of the Size of Suspensions on the Solidification Process of Nanoparticle-Enhanced Phase Change Materials

[+] Author and Article Information
Yousef M. F. El Hasadi

Graduate Student

J. M. Khodadadi

Alumni Professor
e-mail: khodajm@auburn.edu
Mechanical Engineering Department,
Auburn University,
1418 Wiggins Hall,
Auburn, AL 36849-5341

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 6, 2012; final manuscript received January 26, 2013; published online April 11, 2013. Assoc. Editor: Joon Sik Lee.

J. Heat Transfer 135(5), 052901 (Apr 11, 2013) (11 pages) Paper No: HT-12-1210; doi: 10.1115/1.4023542 History: Received May 06, 2012; Revised January 26, 2013

Nanostructure-enhanced phase change materials (NePCM) have been widely studied in recent years due to their enhanced thermal conductivity and improved charge/discharge in thermal energy storage applications. In this study, the effect of the size of the nanoparticles on the morphology of the solid–liquid interface and the evolving concentration field during solidification is reported. Combining a one-fluid-mixture approach with the single-domain enthalpy-porosity model for phase change and assuming a linear dependence of the liquidus and solidus temperatures of the mushy zone on the local concentration of the nanoparticles subject to a constant value of the segregation coefficient, thermal-solutal convection as well as the Brownian and thermophoretic effects are taken into account. A square cavity containing a suspension of copper nanoparticles (diameter of 5 and 2 nm) in water was the model NePCM considered. Subject to a 5 °C temperature difference between the hot (top) and cold (bottom) sides and with an initial loading of the nanoparticles equal to 10 wt. % (1.22 vol. %), the colloid was solidified from the bottom. The solid–liquid interface for the case of NePCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NePCM with particle size of 2 nm, the solid–liquid interface evolved from a stable planar shape to an unstable dendritic structure. This transition was attributed to the constitutional supercooling effect, whereby the rejected particles that are pushed away from the interface into the liquid zone form regions of high concentration thus leading to a lower solidus temperature. Moreover, for the smaller particle size of 2 nm, the ensuing solutal convection at the liquid–solid interface due to the concentration gradient is affected by the increased Brownian diffusivity. Due to size-dependent rejection of nanoparticles, the frozen layer that resulted from a dendritic growth contains regions of depleted concentration. Despite the higher thermal conductivity of the colloids, the amount of frozen phase during a fixed time period diminished as the particle size decreased.

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Figures

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Fig. 1

Geometry of the physical model

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Fig. 2

Grid independence results showing (a) temperature, (b) liquid fraction, and (c) mass fraction of the nanoparticles at x = 0.5 H for different grids (dp = 5 nm) at two time instants

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Fig. 3

Comparison between the results of the current model and [25]: (a) stream function at t = 100 s [25], (b) stream function at t = 100 s (current model), (c) stream function at t = 200 s [25], (d) stream function for t = 200 s (current model), and (e) instantaneous positions of the liquid–solid interfaces

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Fig. 4

Development of the liquid fraction field (λ) at different time instants: (a) 10 s, (b) 100 s, (c) 500 s, and (d) 1000 s for an initial mass concentration field of 10% and dp = 5 nm

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Fig. 5

Development of the liquid fraction field (λ) at different time instants: (a) 10 s, (b) 100 s, (c) 500 s, and (d) 1000 s for an initial mass concentration field of 10% and dp = 2 nm

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Fig. 6

Development of the nanoparticle concentration field (φw) at different time instants: (a) 10 s, (b) 100 s, (c) 500 s, and (d) 1000 s for an initial mass concentration field of 10% and dp = 5 nm

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Fig. 7

Development of the nanoparticle concentration field (φw) at different time instants: (a) 10 s, (b) 100 s, (c) 500 s, and (d) 1000 s for an initial mass concentration field of 10% and dp = 2 nm

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Fig. 8

Isometric view of the nanoparticle concentration field (φw) at 1000 s for an initial mass concentration field of 10% and dp = 2 nm

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Fig. 9

Velocity vectors in the vicinity of the liquid–solid interface (0.3≤x/H≤0.8) at 1000 s for an initial mass concentration field of 10% and dp = 2 nm

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Fig. 10

Development of the liquidus temperature at different time instants: (a) t = 10 s, (b) t = 100 s, (c) t = 500 s, and (d) t = 1000 s for an initial mass concentration field of 10% and dp = 5 nm

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Fig. 11

Development of the liquidus temperature at different time instants: (a) t = 10 s, (b) t = 100 s, (c) t = 500 s, and (d) t = 1000 s for an initial mass concentration field of 10% and dp = 2 nm

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Fig. 12

Transient development of the nanoparticle concentration profiles at x = 0.5 H and along the y-axis for dp = 5 nm

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Fig. 13

Transient development of the nanoparticle concentration profiles along the y-axis for dp = 2 nm at: (a) x = 0.0043 m, (b) x = 0.005 m = 0.5 H, and (c) x = 0.0055 m

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Fig. 14

Solid–liquid fraction fields at t = 1000 s for: (a) φw = 0, (b) φw = 10%, dp = 5 nm, and (c) φw = 10%, dp = 2 nm

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