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Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above

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Abstract

A two-dimensional numerical simulation of natural convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurry with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations have been done using the finite volume method. Both natural convection and heat transfer characteristics are discussed about natural convection with PCM microcapsulate slurry, which exhibits the pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity with latent heat. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of phase-change material, the mass concentration, and the aspect ratio Ar on the natural convection heat transfer are described, respectively. By comparing with the results of microcapsule slurry without phase change, the enhancement in heat transfer is found in microcapsule slurry with phase change during the phase change temperature range. Numerical simulations are performed in the following parametric ranges: the width–height aspect ratio of the enclosure Ar from 2 to 20, the mass concentrations C m of the slurry from 10 to 40%, power law index n of the slurry from 0.89 to 1.0 and Rayleigh numbers Ra ranges from 103 to 107.

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Abbreviations

Ar:

aspect ratio = W/H

a :

thermal diffusivity (m2 s−1)

B :

dimensionless term defined in Eq. 10

C m :

mass concentration (%)

C p :

apparent specific heat including latent heat (kJ kg−1 K−1)

C p25 :

specific heat at 25°C (kJ kg−1 K−1)

D :

depth of rectangular enclosure (m)

e :

strain rate (s−1)

\(\bar{e}\) :

dimensionless strain rate

g :

gravitational acceleration (m s−2)

Gr:

Grashof number = Ra/Pr

H :

height of rectangular enclosure (m)

k :

thermal conductivity of the PCM slurry (W m−1 K−1)

K :

consistency index of power law model fluids (Pa sn)

n :

pseudoplastic index of power law model fluid

Nu:

Nusselt number = α·H/k

p :

pressure (Pa)

P * :

dimensionless pressure

Pr:

Prandtl number, in Eq. 8

Q :

ratio of specific heat capacity = C p /C p0

R :

ratio of density = ρ /ρ0

Ra:

Raleigh number, in Eq. 9

S x :

dimensionless term defined in Eq. 11

S y :

dimensionless term defined in Eq. 12

t :

time (s)

t * :

dimensionless time = t/(H 2/a 0)

T :

temperature (°C)

u :

velocity in horizontal x coordinate (m s−1)

U :

dimensionless velocity in horizontal x coordinate

v :

velocity in vertical y coordinate (m s−1)

V :

dimensionless velocity in vertical y coordinate

W :

width of rectangular enclosure (m)

X, Y :

coordinates in dimensionless form, x/H, y/H

x, y :

coordinates

α:

heat transfer coefficient (W m−2 K−1)

\(\beta\) :

volumetric expansion coefficient (K−1)

μ:

dynamic viscosity of Newtonian fluid or PCM slurry (Pa s, Pa sn)

Θ:

dimensionless temperature

\(\tau\) :

shear stress (N m−2)

\(\bar{\tau }\) :

dimensionless stress rate = τ/[K(a 0/H 2)n]

\(\rho\) :

density (kg m−3)

0:

reference state

b:

bottom plate

C:

cooling plate

H:

heating plate

n :

without phase change material

w :

with phase change material

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Authors and Affiliations

  1. Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushimanaka, Okayama, 700-8530, Japan

    Hideo Inaba, Yanlai Zhang, Akihiko Horibe & Naoto Haruki

Authors
  1. Hideo Inaba
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  2. Yanlai Zhang
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  3. Akihiko Horibe
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  4. Naoto Haruki
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Correspondence to Hideo Inaba.

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Inaba, H., Zhang, Y., Horibe, A. et al. Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above. Heat Mass Transfer 43, 459–470 (2007). https://doi.org/10.1007/s00231-006-0121-y

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  • DOI: https://doi.org/10.1007/s00231-006-0121-y

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