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Research Papers: Melting and Solidification

Melting of Phase Change Materials With Volume Change in Metal Foams

[+] Author and Article Information
Zhen Yang

Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088

Suresh V. Garimella1

Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088sureshg@purdue.edu

1

Corresponding author.

J. Heat Transfer 132(6), 062301 (Mar 24, 2010) (11 pages) doi:10.1115/1.4000747 History: Received April 09, 2009; Revised October 20, 2009; Published March 24, 2010; Online March 24, 2010

Melting of phase change materials (PCMs) embedded in metal foams is investigated. The two-temperature model developed accounts for volume change in the PCM upon melting. Volume-averaged mass and momentum equations are solved, with the Brinkman–Forchheimer extension to Darcy’s law employed to model the porous-medium resistance. Local thermal equilibrium does not hold due to the large difference in thermal diffusivity between the metal foam and the PCM. Therefore, a two-temperature approach is adopted, with the heat transfer between the metal foam and the PCM being coupled by means of an interstitial Nusselt number. The enthalpy method is applied to account for phase change. The governing equations are solved using a finite-volume approach. Effects of volume shrinkage/expansion are considered for different interstitial heat transfer rates between the foam and PCM. The detailed behavior of the melting region as a function of buoyancy-driven convection and interstitial Nusselt number is analyzed. For strong interstitial heat transfer, the melting region is significantly reduced in extent and the melting process is greatly enhanced as is heat transfer from the wall; the converse applies for weak interstitial heat transfer. The melting process at a low interstitial Nusselt number is significantly influenced by melt convection, while the behavior is dominated by conduction at high interstitial Nusselt numbers. Volume shrinkage/expansion due to phase change induces an added flow, which affects the PCM melting rate.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic illustration of the physical problem

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Figure 2

Comparison of the evolution of the melt front from the present work as well as from experimental and modeling results in the literature (12)

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Figure 3

Temperature profiles for the comparison in Fig. 2: (a) t=5 min and (b) t=20 min

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Figure 4

Melt front at ε=0.5ε0 with different solid-liquid density ratios fρ at Nui=1.82: (a) Ra=106 and (b) Ra=108. A larger Rayleigh number is seen to distort the melt front away from the vertical.

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Figure 5

Melt front at ε=0.5ε0 with different solid-liquid density ratios fρ at Nui=0: (a) Ra=106 and (b) Ra=108. Compared with Figs.  44, the melt fronts here deviate much more from the vertical.

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Figure 6

Temperature profiles at half height (Y=0.5) with Nui=1.82 and fρ=1: (a) Ra=106 and (b) Ra=108

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Figure 7

Temperature profiles at half height (Y=0.5) with Nui=0 and fρ=1: (a) Ra=106 and (b) Ra=108

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Figure 8

Melting region colored by ε for Ra=108 and Nui=0.0182: (a) τ=0.15, (b) τ=0.625, and (c) τ=1.125. To the left of the line ε=0.8 is the liquid area (ε=ε0), to the right of the line ε=0.0 is the solid area (ε=0), and between the two lines is the melting region (0<ε<ε0). Flow streamlines are also plotted in the melt and mushy zones.

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Figure 9

Melting region colored by ε for Ra=108 and Nui=1.82: (a) τ=0.02, (b) τ=0.08, and (c) τ=0.25. To the left of the line ε=0.8 is the liquid area (ε=ε0), to the right of the line ε=0.0 is the solid area (ε=0), and between the two lines is the melting region (0<ε<ε0). It is noted that the melting times at this higher interstitial Nusselt number are significantly smaller than in Figs.  888. Flow streamlines are also plotted in the melt and mushy zones.

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Figure 10

Melt volume fractions at different times with Ra=108

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Figure 11

Variation in melting rate as a function of melt volume fraction for different interfacial Nusselt numbers: (a) Nui=1.82, (b) Nui=0.0182, and (c) Nui=0. The influence of volume expansion and shrinkage is also brought out.

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Figure 12

Variation in wall Nusselt number with time for different interstitial Nusselt numbers, and under volume expansion/contraction upon melting

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