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Gravity-Assisted Melting in Enclosures

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Energy Storage Systems

Part of the book series: NATO ASI Series ((NSSE,volume 167))

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Abstract

The gradual depletion of fossil fuels over the past few decades has resulted in an increase in energy costs which can be expected to rise sharply over the next few decades as supplies become scarce. Current worries regarding the disposal of nuclear wastes have caused many countries to put less stress on nuclear energy, and higher air pollution causing acid rain and possible long term change in global weather patterns make the use of solar energy a very attractive option in the long run. Though the amount of solar energy falling on the earth’s surface far exceeds our requirements, the diffuse and unpredictable nature of solar radiation makes it extremely difficult to harness. Efficient energy storage devices are essential if solar energy is ever to be used on a large scale. Considerable research is being done on many different kinds of storage devices like electrochemical batteries, flywheels, compressed air, pumped water storage, etc. However, thermal energy storage devices using phase change materials have some major advantages which make them extremely attractive for certain applications. These include a high energy density of storage and an uniform temperature at which the energy is released or absorbed. Such latent heat thermal energy storage devices can also be used over a wide range of temperatures since different materials can be used as required.

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Abbreviations

Ar:

Archimedes number (ρs – ρ1)gD3/(ρν2)

D:

Diameter

Gr:

Grashof Number [gβΔATD3/ν2]

Md:

Non-dimensional parameter ((Steρ°/Pr)/Ars)1/4

Mt:

Non-dimensional parameter ((Steρ°/Pr)3Ars)-1/4

Nu:

Nusselt number qD/k(TH - TC)

P:

Pressure (including hydrostatic pressure)

Pr:

Prandt1 number ν/α

Q:

Average wall heat flux for the complete process

R:

Transformed radial coordinate

R:

Rayleigh number (GrPr)

S:

Annulus ratio ((Do - D(inner cylinder))/Do)

Sb:

Degree of subcooling (TF - TC)/(TH - TC)

Ste:

Stefan number cp (TH - TF)/l

T:

Temperature

c:

Constant in Eq. 40

cp :

Specific heat at constant pressure

g:

Gravitational constant

h:

Heat transfer coefficient

k:

Thermal conductivity

k̄:

Also used as unit vector in vertical direction

n:

Normal direction

n̄:

Unit vector in normal direction

p:

Pressure (not including the hydrostatic pressure)

q:

Average wall heat flux at a particular time

r:

Radial coordinate

s:

Length along the interface

t:

Time; Also used as enclosure wall thickness (Eq. 6.13)

v:

Velocity

z:

Drop of solid core

l:

Latent heat of fusion

θ:

Transformed angular coordinate

α:

Thermal diffusivity

ß:

Coefficient of thermal expansion

δ:

Film thickness in lower region ro - ri

ζ:

Position of interface at θ = π

η:

Coordinate in toroidal coordinate system

θ:

Angular coordinate

θA :

Angle defining junction between upper and lower zones

v:

Order of a variable

μ:

Dynamic viscosity

ν:

Kinematic viscosity

ρ:

Density

τ:

Shear stress

°:

Non-dimensional property ratio (Liquid/Solid)

C:

Cold

F:

Fusion (melting)

H:

Hot

a:

Average (over surface area)

f:

Liquid Film

i:

Inner (Interface)

l:

Liquid

m:

Mean (averaged over surface area and time)

n:

Normal direction

o:

Outer

r:

Radial direction

s:

Solid

w:

Wall

θ:

θ-direction

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Miami, Coral Gables, FL, USA

    Subrata Sengupta & Sanjay K. Roy

Authors
  1. Subrata Sengupta
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  2. Sanjay K. Roy
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey

    Birol Kılkısş

  2. Department of Mechanical Engineering, University of Miami, Coral Gables, Florida, USA

    Sadık Kakaç

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© 1989 Kluwer Academic Publishers

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Sengupta, S., Roy, S.K. (1989). Gravity-Assisted Melting in Enclosures. In: Kılkısş, B., Kakaç, S. (eds) Energy Storage Systems. NATO ASI Series, vol 167. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2350-8_16

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  • DOI: https://doi.org/10.1007/978-94-009-2350-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7558-9

  • Online ISBN: 978-94-009-2350-8

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