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Convective heat transfer over two blocks arbitrary located in a 2D plane channel using a hybrid lattice Boltzmann-finite difference method

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Abstract

The present paper deals with the numerical investigation of a 2D laminar fluid flow and heat transfer in a plane channel with two square blocks located at arbitrary positions. The numerical model is based on a coupling between the multiple relaxation time-lattice Boltzmann equation and the finite difference method for incompressible flow. Both the horizontal and the vertical separation distances between the two blocks are varied. Particular attention was paid to the distribution patterns of the time averaged local Nusselt number on the top and bottom walls. Results obtained from the present study show a complex flow patterns developed in the channel due to the change of the square blocks positions.

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Abbreviations

g :

Gravitational acceleration (m s−1)

d :

Blocks height (m)

d h :

Block separation distance in X direction (m)

d V :

Block separation distance in Y direction ( m)

H :

Channel height (m)

k :

Thermal conductivity (W m−1 K−1)

L :

Length of the channel (m)

<Nu> :

Time averaged local Nusselt number

Pr :

Prandtl number (v/α)

Re :

Channel Reynolds number (ρU max H/μ)

T :

Temperature (K)

u, v :

Velocity components (m s−1)

U max :

Maximum velocity at the channel inlet (m s−1)

x, y :

Cartesian coordinates

X, Y :

Dimensionless coordinates (X = x/H, Y = y/H)

α :

Thermal diffusivity (m2 s−1)

β:

Blockage ratio (d/H)

θ :

Dimensionless temperature (T − T c)/(T h− T c)

ρ :

Density of fluid (kg m−3)

μ :

Dynamic viscosity of fluid (kg m−1 s−1)

v :

Kinematic viscosity (m2 s−1)

τ :

Time nondimensionalized by U max/H

c:

Cold

f:

Fluid

h:

Hot

s:

Inner solid

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Authors and Affiliations

  1. Laboratoire de Mécanique & Energétique, Département de Physique, Faculté des Ssciences, Université Mohammed 1er, 60000, Oujda, Morocco

    Mohammed Amine Moussaoui, Mohammed Jami & Ahmed Mezrhab

  2. Laboratoire de Mécanique de Lille, UMR CNRS 8107, Université Lille 1- Sciences et Technologies/Polytech’Lille, 59655, Villeneuve d’Ascq Cedex, France

    Hassan Naji

Authors
  1. Mohammed Amine Moussaoui
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  2. Mohammed Jami
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  3. Ahmed Mezrhab
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  4. Hassan Naji
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Correspondence to Ahmed Mezrhab.

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Moussaoui, M.A., Jami, M., Mezrhab, A. et al. Convective heat transfer over two blocks arbitrary located in a 2D plane channel using a hybrid lattice Boltzmann-finite difference method. Heat Mass Transfer 45, 1373–1381 (2009). https://doi.org/10.1007/s00231-009-0514-9

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