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Indian Journal of Physics

, Volume 93, Issue 1, pp 123–138 | Cite as

The effect of obstacles’ characteristics on heat transfer and fluid flow in a porous channel

  • Saida ChattiEmail author
  • Chekib Ghabi
  • Abdallah Mhimid
Original Paper
  • 68 Downloads

Abstract

The fluid flow and heat transfer around obstacles are an engineering and research interest. This paper dealt with this matter in a porous channel. It explained the features of the presence of hot solid obstacles in porous media. These obstacles were located at different positions inside the medium. The particularity of this work is coupling two complex phenomena: the heat transfer in porous media and the presence of hot solid obstacles. This is the first time that these phenomenona were studied. The diffusion–convection equation is adopted to calculate the temperature. The viscous heat dissipation and compression work due to the pressure were not taken into consideration. This choice and assumptions were based on our previous work. The numerical simulation was done using the generalized lattice Boltzmann method. To ensure that our numerical code is free of errors, we resorted to benchmark cases. Then, we were interested in the effect of triangular and rectangular obstacles on the heat transfer and fluid flow in a porous channel. The isotherms and the velocity contours were studied for several dynamic parameters. The fluid behavior was described by the streamlines and the velocity fields. The velocity profile was followed along the porous channel. These results allow concluding that the Reynolds number increment led to the increase in the heat transfer and the fluid velocity. The increment of the distance between the inlet and the obstacle generates the same conclusion.

Keywords

Thermal lattice Boltzmann method Porous channel Laminar fluid flow Convection Obstacle position and geometries 

List of symbols

c

Lattice spacing

ci

Discrete velocity for D2Q9 model

cpf

Specific heat capacity of fluid

cpc

Specific heat capacity of solid

c0

Coefficient

c1

Coefficient

Da

Darcy number

dx, dy

Spatial step

f

Density distribution function

feq

Density equilibrium distribution function

F

Total body force

\(F_{\varepsilon }\)

Geometric factor

G

An external force

g0

Gravity acceleration

g

Thermal distribution function

geq

Thermal equilibrium distribution function

H

Channel width

i

Lattice index in the x direction

j

Lattice index in the y direction

K

Permeability

k

Thermal conductivity

m

Fluid particle mass

n

The position on the right boundary

p

Pressure

Pr

Prandtl number

Ra

Rayleigh number

Re

Reynolds number

T

Fluid temperature

t

Time

Tc

Cold temperature

Th

Hot temperature

U

Fluid velocity

Uin

X-Component velocity in the inlet

U0

Top wall velocity

\(\nu\)

Temporal velocity

\(\nu_{n}\)

Y-Component velocity of the upper plate

\(\nu_{0}\)

Injection velocity

Greek letters

α

Thermal diffusivity

β

Thermal expansion

\(\Gamma_{c}\)

Thermal relaxation time

\(\Gamma_{\nu }\)

Density relaxation time

δt

Time step

ε

Porosity

\(\upsilon\)

Viscosity

\(\upsilon_{\text{e}}\)

Effective viscosity

ρ

Density

ρf

Fluid density

ρs

Solid density

ρin

Inlet density

ρN

Density of the upper plate

σ

The ratio between cpc and cpf

Σ

Internal energy

Ω

Collision operator

ωi

Weight coefficient in the direction i

Subscripts

e

Effective

f

Fluid

i

Discrete velocity direction

in

Inlet

m

Average

Superscript

eq

Equilibrium

PACS No.

44.05.+e 44.25.+f 44.30.+v 02.70.−c 

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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.Laboratory of Thermal and Energy Systems Studies, National Engineering School of MonastirMonastir UniversityMonastirTunisia

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