Technical Brief

Cooling Capacity Figure of Merit for Phase Change Materials

[+] Author and Article Information
Patrick J. Shamberger

Department of Materials Science and Engineering,
Dwight Look College of Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: patrick.shamberger@tamu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 26, 2014; final manuscript received July 20, 2015; published online September 2, 2015. Assoc. Editor: Amy Fleischer.

J. Heat Transfer 138(2), 024502 (Sep 02, 2015) (8 pages) Paper No: HT-14-1644; doi: 10.1115/1.4031252 History: Received September 26, 2014; Revised July 20, 2015

In this paper, a figure of merit for the cooling capacity (FOMq) of phase change materials (PCMs) is defined from the analytical solution of the two-phase Neumann–Stefan problem of melting of a semi-infinite material with a fixed temperature boundary condition (BC). This figure of merit is a function of the thermophysical properties of a PCM and is proportional to the heat transfer across the interface with the surrounding medium in this general case. Thus, it has important implications for design and optimization of PCMs for high heat-flux thermal management applications. FOMq of example low melting point metals are presented which exceed those in common nonmetallic PCMs over the same temperature range by over an order of magnitude.

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Grahic Jump Location
Fig. 1

The system under consideration in the Neumann–Stefan problem at some arbitrary time. Light gray is the liquid phase; darker gray is the solid.

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Fig. 2

Solution to the transcendental equation, (6) and (6′). (a) Solution to the one-region problem (dotted line). For Stl < 1, λ∼Stl (dashed line). (b)–(d) Solutions to the two-region problem, with contours of C1=αs/αl (in most PCM systems, C1∼0.5−2.0). Each subplot illustrates a different ratio C2=Sts/Stl.

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Fig. 3

Normalized heat flux across the wall interface with time into different materials expressing a range of FOMq

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Fig. 4

Temperature profiles in paraffin wax and water system for (a) one-region problem (at t = 50, 100, 200, 400, and 800 s), (b) two-region problem (at t = 50 s). Lwwax  = 175 J/g, Cpwax  = 2.4 J/g/K, ρwax   = 900 g/m3, and kwax  = 0.2 W/m/K; Lwh2o  = 333 J/g, Cph2o = 4.2 J/g/K, ρh2o   = 1000 g/m3, and kh2o   = 0.56 W/m/K. For both substances, the properties of the liquid are assumed to be equal to the properties of the solid.

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Fig. 5

Reduced variation in the figure of merit versus scaled material parameter X/X0 (where X is kl, ρ, Lw, or Cp,l). Each solid black (gray) line is calculated for a different value of Lw (Cp,l), using the representative values shown in Table 1. Exact numerical scaling factors are shown in Table 2 for the case of X/X0 = 2 or ½.




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