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Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer

Wärmedämmverhalten einer vertikalen, rechteckigen Zelle, die zwei Schichten — PCM Material und Luft — enthält

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Abstract

The present paper presents a numerical analysis concerning thermal protection characteristics of a vertical rectangular composite cell filled with a solid-liquid phase change material (PCM) and air layer. Inside the composite cell the PCM layer is separated from air layer by a solid partition of negligible thickness. The buoyancy-induced flows developed in both the air-filled layer and the molten PCM zone inside the PCM layer were modeled as two-dimensional laminar Newtonian fluid flow adhering to the Boussinesq approximation. Meanwhile, two-dimensional conduction heat transfer was accounted for the unmelted solid PCM region. Delineation is made via a parametric simulation of the effects of the pertinent parameters:Ste (Stefan number),Sc (subcooling factor),Ra (Rayleigh number), aspect ratio of composite cell,A, and relative thickness ratioA p /A a , on the transient thermal protection performance of the composite cell. Results demonstrate that by means of the latent-heat absorption inside the PCM layer, heat penetration across the composite cell can be greatly retarded over an effective duration until a critical instant until the melting front of PCM reaches the partition wall. Such an effective thermal protection duration is found to be a strong function ofRa, Ste, A p /A a , andA. In addition, the results of the transient heat transfer rate penetrating through the composite cell are examined as a function of the pertinent parameters of the problem.

Zusammenfassung

In der Arbeit wird eine numerische Untersuchung dargelegt, die sich auf das Wärmedämmverhalten einer vertikalen, rechteckigen Kompositzelle bezieht, die neben einer Luftschicht Material enthält, das einem Phasenwechsel „fest-flüssig“ unterliegt (PCM). Innerhalb der Kompositzelle ist die PCM-Schicht durch eine feste Trennwand vernachlässigbarer Dicke von der Luftschicht separiert. Die auftriebinduzierten Strömungen in der Luftschicht und in der Schmelzzone der PCM-Schicht werden als zweidimensionale, laminare Strömung Newtonscher Fluide modelliert, die der Boussinesq-Appoximation genügen, während in der noch nicht aufgeschmolzenen PCM-Zone zweidimensionale Wärmeleitung erfolgen soll. Eine Parameterstudie zeigt den Einfluß der Haupteinflußgrößen (der Stefan-ZahlSte, des UnterkühlungsfaktorsSc, der Rayleigh-ZahlRa, des Seitenverhältnisses der KompositzelleA und des DickenverhältnisseA p /A a ) auf das transiente Wärmedämmverhalten der Kompositzelle. Die Ergebnisse belegen, daß sich infolge der Aufnahme latenter Wärme in der PCM-Schicht der Wärmetransport durch die Kompositzelle für einen beträchtlichen Zeitraum verzögern läßt, bis schließlich die Schmelzfront im PCM-Material die Trennwand erreicht hat. Die Dauer dieser Wärmedämmphase hängt stark von den ParameternRa, Ste, A p /A a undA ab. Weitere Ergebnisse bezüglich des transienten Wärmestroms durch die Kompositzelle sind in Abhängigkeit von den das problem regierenden Einflußparametern in Diagrammform dargestellt.

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Abbreviations

A :

aspect ratio, (W p +W a )/H

A a :

dimensionless thickness of air layer,W a /H

A p :

dimensionless thickness of PCM layer,W p /H

c p :

specific heat

Fo :

Fourier number,α l t/H 2

g :

gravitational acceleration

H :

height of enclosure

k :

thermal conductivity

L :

latent heat

Pr :

Prandtl number,ν l /α l

q″:

heat flux

Q c :

dimensionless local heat flux at the cold wall, Eq. (13)

Q d :

dimensionless local heat flux at the partition surface, Eq. (12)

Q h :

dimensionless local heat flux at the hot wall, Eq. (11)

\(\bar Q_{r,i} \) :

instantaneous, fractional averaged heat flux, Eq. (16)

\(\bar Q_{r,t} \) :

total, fractional averaged heat flux, Eq. (17)

Ra :

Rayleigh number,gβΔTH 3/(ν l α l )

S :

dimensionless position of solid-liquid interface

Sc :

subcooling factor, (T) f) −T) c)/ΔT

Ste :

Stefan number,c p,l ΔT/L

t :

time

T :

temperature

ΔT :

temperature difference, (T h −T f )

V m :

volume of liquid PCM

V 0 :

total volume of PCM

V⋆:

volumetric fraction of liquid PCM,V m /V 0

W a :

width of air layer

W p :

width of PCM layer

x +,y + :

Cartesian coordinates

x,y :

dimensionless coordinates,x +/H, y +/H

α :

thermal diffusivity,k/(ρc p )

β :

thermal volumetric expansion coefficient

θ :

dimensionaless temperature, (T−T f )/ΔT

ν :

kinematic viscosity

ρ :

density

ψ + :

stream function

ψ :

dimensionless stream function,ψ +/α l

ω + :

vorticity

ω :

dimensionless vorticity,ω + H 2/α l

a :

air

c :

cold surface

cr:

critical value

f :

fusion point

h :

hot surface

l :

liquid phase of PCM

s :

solid phase of PCM

ss :

steady-state quantity

⋆:

ratio of a quantity to that of liquid PCM

−:

surface-averaged value

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China

    C. J. Ho & C. H. Chu

Authors
  1. C. J. Ho
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  2. C. H. Chu
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Ho, C.J., Chu, C.H. Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer. Heat and Mass Transfer 31, 191–198 (1996). https://doi.org/10.1007/BF02333319

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  • DOI: https://doi.org/10.1007/BF02333319

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