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Numerical Investigation of Natural Convection in a Partially Heated Square Cavity and at Different Inclinations Filled by (Water-Al2O3) Nanofluid, Using the Thermal Lattice Boltzmann Method

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Abstract

This study presents a numerical analysis of the enhancement in heat transfer through natural convection within a square enclosure filled with nanofluid at various inclinations. In order to achieve this objective, two-dimensional simulations were conducted using a customized code based on the thermal lattice Boltzmann method and a double distribution function approach with two different lattice configurations, namely D2Q9 for the dynamic field and D2Q5 for the thermal field. The comparison of the numerical results obtained in the validation work for the differentially heated square cavity problem for both pure fluid and nanofluid demonstrated a favourable agreement with the findings reported in literature. An investigation was carried out to analyse the flow and heat transfer characteristics by varying the Grashof number in the range of 103 ≤ Gr ≤ 105, the nanoparticle concentration in the range of 0% ≤ ϕ ≤ 3%, and the heater length and inclination angle in the ranges of 0.2 ≤ l/H ≤ 0.8 and 0˚ ≤ γ ≤ 60˚ respectively. The results indicated that the Nusselt number increases as the control parameters are increased, except for the inclination angle. The highest enhancements in heat transfer were observed at angles γ = 45˚ and γ = 30˚ for Gr = 103 and Gr > 103 respectively. A correlation for the Nusselt number was established specifically for the case of γ = 0˚, which could be of significant value in the field of thermal management for applications utilizing this particular configuration.

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Data availability

Enquiries about data availability should be directed to the authors.

Abbreviations

cp:

Specific heat (J/kg.°K)

\({{\varvec{e}}}_{{\varvec{i}}}\) :

Microscopic speed

\({\text{F}}\) :

Buoyancy force

f:

Distribution function for fluid

g:

Distribution function for temperature

\({\text{g}}\) :

: Acceleration due to gravity

Gr:

Grashof number

H:

Height of cavity (m)

k:

Thermal conductivity, (W/m°K)

l:

Dimensional length of heater (m)

L:

Dimensionless length of heater (l/H)

Nu:

Average Nusselt number

P:

Pressure (Pa)

Pr:

Prandtl number

T:

Temperature (°K)

t:

Time (s)

u, v:

Dimensional x and y components of velocity (m/s)

U, V:

Dimensionless x and y components of velocity

x, y:

Cartesian coordinates (m)

X, Y:

Dimensionless coordinates

\({\text{x}}\) :

Position vector

w:

Weight factor

α:

Thermal diffusivity (m2/s)

β:

Thermal expansion coefficient, (1/°K)

γ:

Inclination angle (°)

Δt:

Time step

θ:

Dimensionless temperature

μ:

Dynamic viscosity (W/m°K)

ν:

Kinematic viscosity (m2/s)

ρ:

Density (kg/m3)

τ:

Relaxation time

ϕ:

Nanoparticle concentration (%)

\(\Omega \) :

Collision operator

\(\Psi \) :

Dimensionless Stream function

eq:

Equilibrium

T:

Temperature

C:

Cold

f:

Base fluid

H:

Hot

i:

Streaming direction of particles

m:

Maximal value

nf:

Nanofluid

np:

Nanoparticle

x:

Horizontal component

α:

Correspondant to temperature

ν:

Correspondant to fluid

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Authors and Affiliations

  1. Laboratory of MNEPM, MSMPT Group, Department of Mechanical Engineering, Abdelhamid Ibn Badis University of Mostaganem, 27000, Mostaganem, Algeria

    Benameur Bouamoud & Samir Houat

  2. Department of Sciences and Technology, University of Tiaret, 14000, Tiaret, Algeria

    Benameur Bouamoud

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Bouamoud, B., Houat, S. Numerical Investigation of Natural Convection in a Partially Heated Square Cavity and at Different Inclinations Filled by (Water-Al2O3) Nanofluid, Using the Thermal Lattice Boltzmann Method. Int. J. Appl. Comput. Math 10, 97 (2024). https://doi.org/10.1007/s40819-024-01731-7

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