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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 6
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Original Articles

Effects of natural convection, wall thermal conduction, and thermal radiation on heat transfer uniformity at a heated plate located at the bottom of a three-dimensional rectangular enclosure

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Pages 589-606 | Received 20 Jan 2015, Accepted 26 Jun 2015, Published online: 04 Jan 2016
 

ABSTRACT

A numerical investigation is carried out to understand the effect of natural convection, surface thermal radiation, and wall thermal conduction on the heat transfer from a plate heat source located at the bottom of a three-dimensional rectangular enclosure. The distributions of convective, radiative, and total Nusselt numbers and the average Nusselt number at the surface of the heat source are obtained for the ranges of parameters of 1 × 102 ≤ Ra ≤ 1 × 106, 0 ≤ ϵ ≤ 1, 1 ≤ kr ≤ 15, and 0.5 ≤ AR ≤ 1.5. The increase of thermal radiation restrains the convective heat transfer, but increases the total heat transfer and the overall heat transfer uniformity. Useful correlations have been developed for the average and the standard deviation of the Nusselt numbers at the heat source.

Nomenclature

Bi=

Biot number

cp=

specific heat of the fluid

Fi-j=

view factor from element i to element j

g=

gravitational acceleration

H=

height of the cavity

k=

thermal conductivity

l=

thickness of the wall

L=

width of the cavity

Nrad=

radiation number, defined by Eq. (11)

Nu=

local Nusselt number

=

average Nusselt number

P=

dimensionless pressure

Pr=

Prantdl number

Qrad=

dimensionless radiative heat flux

R=

dimensionless radiosity

Ra=

Rayleigh number

T=

temperature

=

dimensionless velocity vector

x,y,z=

coordinate system

α=

thermal diffusivity

β=

coefficient of volumetric expansion

ϵ=

surface emissivity

υ=

kinematic viscosity

ξ=

temperature parameter (= Tam/Ths).

ρ=

density of the fluid

σ=

standard deviation

τ=

dimensionless time

Subscripts=
am=

ambient

con=

convective

f=

fluid

hs=

heat source

r=

the ratio of the solid to fluid properties

rad=

radiative

s=

solid

tot=

total

Nomenclature

Bi=

Biot number

cp=

specific heat of the fluid

Fi-j=

view factor from element i to element j

g=

gravitational acceleration

H=

height of the cavity

k=

thermal conductivity

l=

thickness of the wall

L=

width of the cavity

Nrad=

radiation number, defined by Eq. (11)

Nu=

local Nusselt number

=

average Nusselt number

P=

dimensionless pressure

Pr=

Prantdl number

Qrad=

dimensionless radiative heat flux

R=

dimensionless radiosity

Ra=

Rayleigh number

T=

temperature

=

dimensionless velocity vector

x,y,z=

coordinate system

α=

thermal diffusivity

β=

coefficient of volumetric expansion

ϵ=

surface emissivity

υ=

kinematic viscosity

ξ=

temperature parameter (= Tam/Ths).

ρ=

density of the fluid

σ=

standard deviation

τ=

dimensionless time

Subscripts=
am=

ambient

con=

convective

f=

fluid

hs=

heat source

r=

the ratio of the solid to fluid properties

rad=

radiative

s=

solid

tot=

total

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