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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 4
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Original Articles

A three-dimensional enthalpic lattice Boltzmann formulation for convection–diffusion heat transfer problems in heterogeneous media

, , &
Pages 330-343 | Received 25 May 2017, Accepted 07 Aug 2017, Published online: 22 Sep 2017
 

ABSTRACT

In this paper, an enthalpic lattice Boltzmann method formulation for 3D unsteady convection–diffusion heat transfer problems is used to overcome discontinuity issues in heterogeneous media. The new formulation is based on the appearance of a source term added to the collision step. The major achievement of the proposed enthalpic LB formulation is avoiding any interface treatments or geometry considerations even when dealing with complex geometries. The performance of the present method is tested for several three-dimensional convection–diffusion problems. Comparisons are made with the control volume method, and numerical results show excellent agreements.

Nomenclature

a, b=

constants in analytical velocity profile

A, B=

length and high of the inner square duct

c=

lattice streaming speed

Cp=

heat capacity(J/kg · K)

cs=

speed of sound

ek=

propagation velocity in the kth direction in a lattice

fk=

particle distribution function in the k direction

=

equilibrium particle distribution function in the k direction

Fk=

source term in the kth direction in a lattice

h=

enthalpy

H=

characteristic height (m)

L=

characteristic length (m)

n=

normal to the interface

Nx, Ny=

grid mesh size

=

effective pressure

Pe=

Peclet number

rc1=

radius of inner cylinder

rc2=

radius of outer cylinder

r0=

pipe radius

S=

source term

t=

time

T=

temperature

U=

velocity vector

u, v=

velocity components

wk=

weight factor in the k direction

Δt=

time step

Δx=

lattice size

x, y=

axial coordinates

Greek symbols=
α=

thermal diffusivity (m2/s)

λ=

thermal conductivity (W/m · K)

ν=

viscosity of the fluid (m2/s)

ρ=

density (kg/m3)

τ=

relaxation time

=

angular velocity

Superscripts=
eq=

equilibrium

Subscripts=
i, j=

grid nodes indices

k=

direction k in a lattice

l=

layer suffix

Nomenclature

a, b=

constants in analytical velocity profile

A, B=

length and high of the inner square duct

c=

lattice streaming speed

Cp=

heat capacity(J/kg · K)

cs=

speed of sound

ek=

propagation velocity in the kth direction in a lattice

fk=

particle distribution function in the k direction

=

equilibrium particle distribution function in the k direction

Fk=

source term in the kth direction in a lattice

h=

enthalpy

H=

characteristic height (m)

L=

characteristic length (m)

n=

normal to the interface

Nx, Ny=

grid mesh size

=

effective pressure

Pe=

Peclet number

rc1=

radius of inner cylinder

rc2=

radius of outer cylinder

r0=

pipe radius

S=

source term

t=

time

T=

temperature

U=

velocity vector

u, v=

velocity components

wk=

weight factor in the k direction

Δt=

time step

Δx=

lattice size

x, y=

axial coordinates

Greek symbols=
α=

thermal diffusivity (m2/s)

λ=

thermal conductivity (W/m · K)

ν=

viscosity of the fluid (m2/s)

ρ=

density (kg/m3)

τ=

relaxation time

=

angular velocity

Superscripts=
eq=

equilibrium

Subscripts=
i, j=

grid nodes indices

k=

direction k in a lattice

l=

layer suffix

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