Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 6
198
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Analysis of the volumetric phenomenon in porous beds subject to irradiation

, &
Pages 567-580 | Received 11 Jan 2016, Accepted 01 Apr 2016, Published online: 17 Aug 2016
 

ABSTRACT

This work examines the volumetric effect of convection within a packed bed in the presence of collimated irradiation. Using a modified P-1 approximation incorporating a local thermal nonequilibrium (LTNE) model, the energy transportation through convection and thermal conduction, and collimated and diffuse radiative transfer are investigated. The impact of pertinent parameters such as porosity φ, pore diameter dp, and optical thickness τ on the volumetric effect are analyzed. In addition, the mechanisms of how the volumetric effect impacts LTNE and radiative heat loss are revealed. The effect of the volumetric heat transfer coefficient hv, the fluid flow velocity u, and the ratio of solid to fluid thermal conductivities ζ versus the volumetric effect are systematically analyzed and displayed through a number of contour maps to assess the efficiency η. Our analysis shows that enhancing the volumetric effect and extending the thickness of the porous medium improves the efficiency η.

Nomenclature

cp=

specific heat of fluid at constant pressure (J kg−1 K−1)

F=

inertial coefficient

dp=

pore diameter (m)

G=

incident radiation

hsf=

fluid-to-solid heat transfer coefficient (W m−2 K)

K=

permeability (m2)

L=

thickness of a absorber (m)

Nu=

Nusselt number

P=

pressure (Pa)

Pr=

Prandtl number

q0=

initial heat flux (W m−2)

q=

heat flux

=

unit vector in the direction of fluid flow

T=

temperature (K)

u=

velocity (m s−1)

V=

velocity vector (m s−1)

αsf=

specific surface area of the porous medium (m−1)

ε=

emissivity

φ=

porosity

λ=

thermal conductivity (W m−1 K−1)

μ=

dynamic viscosity (kg m−1 s−1)

β=

extinction coefficient (m−1)

σ=

Stefan−Boltzmann constant

σs=

scattering coefficient

θ=

dimensionless temperature

ζ=

ratio of solid to fluid thermal conductivities

ρ=

density (kg m−3)

τ=

optical thickness

ω=

single scattering albedo

Ψ=

dimensionless heat flux

Subscripts=
a=

average

c=

collimated

d=

diffuse

e=

effective/environment

f=

fluid phase

l=

heat loss

r=

radiative

s=

solid phase

t=

total

v=

void

w=

wall

Nomenclature

cp=

specific heat of fluid at constant pressure (J kg−1 K−1)

F=

inertial coefficient

dp=

pore diameter (m)

G=

incident radiation

hsf=

fluid-to-solid heat transfer coefficient (W m−2 K)

K=

permeability (m2)

L=

thickness of a absorber (m)

Nu=

Nusselt number

P=

pressure (Pa)

Pr=

Prandtl number

q0=

initial heat flux (W m−2)

q=

heat flux

=

unit vector in the direction of fluid flow

T=

temperature (K)

u=

velocity (m s−1)

V=

velocity vector (m s−1)

αsf=

specific surface area of the porous medium (m−1)

ε=

emissivity

φ=

porosity

λ=

thermal conductivity (W m−1 K−1)

μ=

dynamic viscosity (kg m−1 s−1)

β=

extinction coefficient (m−1)

σ=

Stefan−Boltzmann constant

σs=

scattering coefficient

θ=

dimensionless temperature

ζ=

ratio of solid to fluid thermal conductivities

ρ=

density (kg m−3)

τ=

optical thickness

ω=

single scattering albedo

Ψ=

dimensionless heat flux

Subscripts=
a=

average

c=

collimated

d=

diffuse

e=

effective/environment

f=

fluid phase

l=

heat loss

r=

radiative

s=

solid phase

t=

total

v=

void

w=

wall

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.