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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 73, 2018 - Issue 5
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Original Articles

Coupled lattice Boltzmann finite volume method for conjugate heat transfer in porous media

ORCID Icon, &
Pages 291-306 | Received 11 Nov 2017, Accepted 18 Feb 2018, Published online: 14 Mar 2018
 

ABSTRACT

This work presents a coupled lattice Boltzmann finite volume method for dealing with conjugate heat transfer problems. Lattice Boltzmann scheme is used for fluid-dynamics, while high-order finite volume method is implemented for temperature reconstruction. After a first validation with literature test cases, the method is applied to a heat exchanger with an insert made of porous medium, representative of an open-cell metal foam, innovative material largely used for its thermomechanical properties. This allows maximizing heat exchange processes with advantages in terms of efficiencies. Thus, the coupled method allows dealing with complex boundaries in multiphysics problems.

Nomenclature

C=

specific heat

dt=

energy equation time-step

e=

lattice Boltzmann local velocity

f=

lattice Boltzmann population

F=

force vector

F=

force component in lattice Boltzmann stencil

g=

gravitational acceleration

h=

channel height

L=

characteristic length

n=

direction normal to surface

Npop=

number of stencil directions

Nu=

Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

Re=

Reynolds number

Q=

heat exchanged

=

heat flux

t=

time

T=

temperature

=

non-dimensional temperature

=

mean temperature

u=

fluid velocity vector

=

mean horizontal velocity

u, v=

velocity components

UC=

characteristic velocity

X=

position vector

x, y=

spatial coordinates

=

non-dimensional coordinate

w=

lattice Boltzmann weight

Greek symbols=
α=

lattice Boltzmann direction

β=

thermal expansion coefficient

δ=

metal layer height

Δx=

grid spacing

ΔT=

hot/Cold temperature difference

ϵ=

metal foam porosity

κ=

thermal conductivity

ν=

lattice Boltzmann kinematic viscosity

ρ=

density

τ=

lattice Boltzmann relaxation time

χ=

thermal diffusivity

Subscripts=
0=

reference property

1, 2, 3, 4=

heat exchanger sections

ave=

average value

C=

cold temperature

flu=

fluid property

H=

hot temperature

i, j=

cartesian directions

max=

maximum value

sol=

solid property;

wall=

wall property

Superscripts=
BW=

backward differencing

eq=

equilibrium distribution function

FW=

forward differencing

t=

time-step

Nomenclature

C=

specific heat

dt=

energy equation time-step

e=

lattice Boltzmann local velocity

f=

lattice Boltzmann population

F=

force vector

F=

force component in lattice Boltzmann stencil

g=

gravitational acceleration

h=

channel height

L=

characteristic length

n=

direction normal to surface

Npop=

number of stencil directions

Nu=

Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

Re=

Reynolds number

Q=

heat exchanged

=

heat flux

t=

time

T=

temperature

=

non-dimensional temperature

=

mean temperature

u=

fluid velocity vector

=

mean horizontal velocity

u, v=

velocity components

UC=

characteristic velocity

X=

position vector

x, y=

spatial coordinates

=

non-dimensional coordinate

w=

lattice Boltzmann weight

Greek symbols=
α=

lattice Boltzmann direction

β=

thermal expansion coefficient

δ=

metal layer height

Δx=

grid spacing

ΔT=

hot/Cold temperature difference

ϵ=

metal foam porosity

κ=

thermal conductivity

ν=

lattice Boltzmann kinematic viscosity

ρ=

density

τ=

lattice Boltzmann relaxation time

χ=

thermal diffusivity

Subscripts=
0=

reference property

1, 2, 3, 4=

heat exchanger sections

ave=

average value

C=

cold temperature

flu=

fluid property

H=

hot temperature

i, j=

cartesian directions

max=

maximum value

sol=

solid property;

wall=

wall property

Superscripts=
BW=

backward differencing

eq=

equilibrium distribution function

FW=

forward differencing

t=

time-step

Additional information

Funding

The numerical simulations were performed on Zeus HPC facility, at the University of Naples “Parthenope”; Zeus HPC has been realized through the Italian Government Grant PAC01_00119 MITO - Informazioni Multimediali per Oggetti Territoriali, with Prof. Elio Jannelli as the Scientific Responsible.

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