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RESEARCH PAPERS: Melting and Solidification

A Two-Temperature Model for Solid-Liquid Phase Change in Metal Foams

[+] Author and Article Information
Shankar Krishnan, Jayathi Y. Murthy

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

Suresh V. Garimella1

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

1

Author to whom correspondence should be addressed.

J. Heat Transfer 127(9), 995-1004 (Nov 13, 2004) (10 pages) doi:10.1115/1.2010494 History: Received July 21, 2004; Revised November 13, 2004

Transient solid-liquid phase change occurring in a phase-change material (PCM) embedded in a metal foam is investigated. Natural convection in the melt is considered. Volume-averaged mass and momentum equations are employed, with the Brinkman-Forchheimer extension to the Darcy law to model the porous resistance. Owing to the difference in the thermal diffusivities between the metal foam and the PCM, local thermal equilibrium between the two is not assured. Assuming equilibrium melting at the pore scale, separate volume-averaged energy equations are written for the solid metal foam and the PCM and are closed using an interstitial heat transfer coefficient. The enthalpy method is employed to account for phase change. The governing equations are solved implicitly using the finite volume method on a fixed grid. The influence of Rayleigh, Stefan, and interstitial Nusselt numbers on the temporal evolution of the melt front location, wall Nusselt number, temperature differentials between the solid and fluid, and the melting rate is documented and discussed. The merits of incorporating metal foam for improving the effective thermal conductivity of thermal storage systems are discussed.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 10

Predicted temporal evolution of melt front locations (γ=0.5) for Ra=108, Nui,d=5.9, Ste=1.0, Pr=50, and Da=10−2

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Figure 15

Predicted total hot wall Nusselt number for various Rayleigh, Stefan, and interstitial Nusselt numbers

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Figure 1

Schematic of the problem under investigation

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Figure 2

Comparison of experimentally measured (5) and predicted (from (5) and present work) interface locations at various times

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Figure 3

Comparison of measured (5) and predicted (from (5) and present work) temperature distributions at three different vertical locations at a dimensionless time of (a) 1.829 (5min) and (b) 7.314 (20min)

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Figure 4

Predicted temporal evolution of the thermal field for Ra=106, Nui=0, Ste=0.1, Pr=50, and Da=10−2 at the midheight of the domain (η=0.5): (a) solid-to-fluid temperature difference, and (b) solid and fluid temperature distributions. Also plotted in the figure is the nondimensional melting temperature (horizontal dashed line).

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Figure 5

Predicted temporal evolution of the melt front location for Ra=106, Nui=0, Ste=0.1, Pr=50, and Da=10−2

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Figure 6

Predicted temporal evolution of thermal field for Ra=106, Nui=0, Ste=1.0, Pr=50, and Da=10−2 at the midheight of the domain (η=0.5): (a) Solid-to-fluid temperature difference, and (b) Solid and fluid temperature distributions. Also plotted in the figure is the nondimensional melting temperature (horizontal dashed line).

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Figure 7

Predicted temporal evolution of thermal field for Ra=106, Nuid=5.9, Ste=1.0, Pr=50, and Da=10−2 at the midheight of the domain (η=0.5): (a) Solid-to-fluid temperature difference, and (b) solid and fluid temperature distributions. Also plotted in the figure is the nondimensional melting temperature (horizontal dashed line).

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Figure 8

Predicted temporal evolution of melt front locations (γ=0.5) for Ra=106, Nui,d=5.9, Ste=1.0, Pr=50 and Da=10−2

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Figure 9

Predicted temporal evolution of thermal field for Ra=108, Nui,d=5.9, Ste=1.0, Pr=50, and Da=10−2 at the midheight of the domain (η=0.5): (a) Solid-to-fluid temperature difference, and (b) solid and fluid temperature distributions. Also plotted in the figure is the nondimensional melting temperature (horizontal dashed line).

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Figure 11

Predicted melt volume fractions as a function of τ for Ra=106, Da=10−2, Ste=1.0, and Pr=50 for various interstitial Nusselt numbers (Nui,d). Also shown are the τeq(=αeqt∕H2) values for comparison.

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Figure 12

Predicted melt volume fractions as a function of τ for different Rayleigh, Stefan, and interstitial Nusselt numbers. Also shown are the τeq values for comparison.

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Figure 13

Predicted hot wall Nusselt number for the no-foam case as a function of τ for Ste=1 and two different Rayleigh numbers. Also shown are the melt fronts at several critical time instants during flow evolution.

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Figure 14

Predicted hot wall Nusselt number for (a) metal foam and (b) PCM for various Rayleigh, Stefan, and interstitial Nusselt numbers

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