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Transient behaviors of natural convective heat transfer through a vertical porous layer

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Abstract

The present investigation is devoted to study numerically and experimentally on the transient behaviors of natural convective heat transfer in a rectangular cavity (whose two opposing vertical walls are kept at uniform (but different) temperatures, while the other walls are thermally insulated) packed with a fluid and spherical solid particles. The natural convection occurred in dependence on the dimensions of the cavity, the diameter of the solid particle and the thermal physical properties of the porous media plays an important role in an evaluation of the transient behaviors of the heat transfer in the porous layer. It can be clarified that the natural convection occurring in the porous layer has the effects of homogenizing thermally the porous layer and shortening the time period to reach a thermally steady state after starting the heating to porous layer. Consequently it might be possible to control the transient time period and the amount of heat stored into the porous layer by managing the intensity of natural convection with proper combinations of fluid and solid particles and dimensions of the cavity.

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Abbreviations

A, B, C :

arbitrary constants in equation (7)

a :

thermal diffusivity

a*:

modified thermal diffusivity, λ*/(ρc ρ ) f

c p :

specific heat at constant pressure

D :

non-dimensional heat transfer coefficient in (6)

d :

mean diameter of spherical solid particle

E :

volumetric ratio of solid phase to fluid phase in (6)

G :

constant, (1.75dρ f )/[150k(1−ε)]

g :

gravitational acceleration

H :

height of rectangular cavity

H/W :

aspect-ratio

h :

heat transfer coefficient per unit volume between fluid and solid phases

k :

permeability

L :

heat capacity ratio of solid phase to fluid phase in (6)

Nu * h , Nu * c :

modified Nusselt number at hot and cold walls in (12) and (13), respectively

Nu*:

modified Nusselt number at steady state

n :

number of iteration computation

Pr*:

modified Prandtl number

p :

pressure

Ra*:

modified Rayleigh number

T :

temperature

ΔT :

temperature difference between hot and cold walls, (T h −T c )

t :

time

U, V :

velocity in theX andY directions, respectively

W :

width of rectangular cavity

X, Y :

co-ordinates

β :

cubical thermal expansion coefficient

ψ :

stream function

Ψ:

non-dimensional stream function

ε :

porosity

λ:

thermal conductivity

λ*:

effective thermal conductivity of porous medium (without convection)

λ * f :

effective thermal conductivity resulted from the contribution of fluid phase to λ*

λ * s :

effective thermal conductivity resulted from the contribution of solid phase to λ*

Λ:

non-dimensional thermal conductivity in (6)

ν :

kinematic viscosity

ρ :

density

τ :

non-dimensional time in (6)

δ :

relaxation factor

c, h :

cold and hot walls, respectively

f, s :

fluid and solid phases, respectively

i, j :

grid points of computative mesh in theX* andY* directions, respectively

*:

non-dimensional value excepta, λ, λ f and λ s

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kitami Institute of Technology, Kitami, 090, Hokkaido, Japan

    Hideo Inaba

  2. Department of Mechanical Engineering, Faculty of Engineering, Hokkaido University, 060, Sapporo, Japan

    Nobuhiro Seki

Authors
  1. Hideo Inaba
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  2. Nobuhiro Seki
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Inaba, H., Seki, N. Transient behaviors of natural convective heat transfer through a vertical porous layer. Appl. Sci. Res. 37, 257–273 (1981). https://doi.org/10.1007/BF00951251

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  • DOI: https://doi.org/10.1007/BF00951251

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