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The effect of the baffle length on the natural convection in an enclosure filled with different nanofluids

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Abstract

This paper presents a numerical investigation of the natural convection in an inclined rectangular enclosure with a baffle filled with Cu/water and then with Al2O3/water nanofluids using the finite difference method for tracking the thermal behavior within it versus the baffle length. The horizontal enclosure walls are assumed to be adiabatic, while the vertical ones are supposed to be a differentially heated. A thin horizontal baffle was attached to its left sidewall and is assumed to be cold. The flow and thermal fields are computed, respectively, for various values of Rayleigh number (103 ≤ Ra ≤ 105), inclination angle (0° ≤ \(\emptyset\) ≤ 60°), baffle length (0.25 ≤ Lb ≤ 0.5), solid volume fraction (0.02 ≤ \(\phi\) ≤ 0.06), and aspect ratio (1 ≤ AR ≤ 2). It was found that as the Rayleigh number, solid volume fraction, baffle length, and aspect ratio increase, an enhancement in the intensity of fluid flow in the enclosure was observed. In comparison, it reduces when the inclination angle increases. Moreover, it was found that the local Nusselt number (Nuc) enhances with the rise in Rayleigh number and the solid volume fraction. In contrast, it reduces with the increase in the aspect ratio and the inclination angle.

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Abbreviations

A :

Aspect ratio of the baffle

AR:

Aspect ratio of the enclosure (H/W)

D b :

Dimensionless baffle position

d b :

Baffle positionm

d p :

Nanoparticle diameter/Nm

g :

Gravitational acceleration/m s−2

H :

Height of enclosure/m

h :

Convection heat transfer coefficient/W m−2 K−1

\(K_{\text{eff}}\) :

Effective thermal conductivity ratio \(\left( {\frac{{k_{\text{nf}} }}{{k_{\text{f}} }}} \right)\)

k r :

Thermal conductivity ratio of the baffle

L b :

Dimensionless baffle length

l b :

Baffle length/m

N p :

Partition number

Nu:

Local Nusselt number

P :

Dimensionless pressure \(\left( {\frac{{pH^{2} }}{{\rho_{\text{nf}} \alpha_{\text{f}}^{2} }}} \right)\)

p :

Pressure/Pa

\({ \Pr }\) :

Prandtl number

\(q_{\text{w}}\) :

Heat flux per unit area/W m−2

\({\text{Ra}}\) :

Rayleigh number \(\left( {\frac{{g\beta_{\text{f}} H^{3} \left( {T_{\text{h}} - T_{\text{c}} } \right)}}{{\upsilon_{\text{f}}^{2} }}} \right)\)

r p :

Nanoparticles radius/Nm

T :

Temperature/°K

U :

Velocity component in X-direction (dimensionless)

u :

Velocity component in X-direction (dimensionless)/m s−1

V :

Velocity component in Y-direction (dimensionless)

v :

Velocity component in the Y-direction (dimensionless)/m s−1

W :

Width of the enclosure/m

w :

Partition thickness/m

X :

Non-dimensional coordinate in horizontal direction (x/W)

x :

Cartesian coordinate in the horizontal direction/m

Y :

Non-dimensional coordinate in vertical direction (y/H)

y :

Cartesian coordinate in the vertical direction/m

\(\alpha_{\text{f}}\) :

Thermal diffusivity of the base fluid (k/ρ·cp)/m2 s−1

\(\alpha_{\text{nf}}\) :

Thermal diffusivity of the nanofluid (k/ρ·cp)nf/m2 s−1

\(\lambda\) :

Thermal diffusivity of the nanofluid \(\left( {\frac{{\alpha_{\text{nf}} }}{{\alpha_{\text{f}} }}} \right)\) (dimensionless)

\(\beta_{\text{f}}\) :

Coefficient of thermal expansion/K−1

\(\beta_{\text{nf}}\) :

Thermal expansion coefficient of the nanofluid/K−1

\(\rho_{\text{nf}}\) :

Density of the nanofluid/Kg m−3

\(\rho_{\text{f}}\) :

Density of the base fluid/Kg m−3

\(\rho_{\text{s}}\) :

Density of the solid nanoparticles/Kg m−3

\(\mu_{\text{nf}}\) :

Dynamic viscosity of the nanofluid/Kg m−1 s−1

\(\theta\) :

Temperature distribution [(T − Tc)/\(\Delta T\)] (dimensionless)

\(\emptyset\) :

Enclosure inclination angle/Degree

Γ :

Inclination angle of the partition/Degree

\(\eta\) :

Criteria of convergence

\(\phi\) :

Solid volume fraction of the nanoparticles

\(\psi\) :

Stream function/m s−2

\(\varPsi\) :

Dimensionless stream function

\(\varOmega\) :

Dimensionless vorticity

\(\upsilon_{\text{f}}\) :

Kinematic viscosity of base fluid/m2 s−1

av:

Average

c:

Cold

E:

External

eff:

Effective

f:

Fluid phase

h:

Hot

I:

Internal

i, j:

Unit vector in x and y directions

\({\text{nf}}\) :

Nanofluid phase

\({\text{s}}\) :

Solid wall

ADI:

Alternating direct implicit

CFD:

Computational fluid dynamic

DQ:

Differential quadrature

FDM:

Finite difference method

FEM:

Finite element method

FVM:

Finite volume method

LBM:

Lattice Boltzmann method

PDQ:

Partial differential quadrature

SUR:

Successive under relaxation

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Authors and Affiliations

  1. College of Engineering, Mechanical Engineering Department, University of Babylon, Babylon City, Hilla, Iraq

    Ahmed Kadhim Hussein

  2. Department of Mechanical Engineering, Faculty of Technology, Saad Dahlab University of Blida 1, 09000, Blida, Algeria

    Mokhtar Ghodbane

  3. Sustainable and Renewable Energy Engineering Department, University of Sharjah, PO Box 27272, Sharjah, UAE

    Zafar Said

  4. Ministry of Electricity, Hilla, Iraq

    Rusul Salman Ward

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  1. Ahmed Kadhim Hussein
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  2. Mokhtar Ghodbane
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  3. Zafar Said
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  4. Rusul Salman Ward
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Correspondence to Ahmed Kadhim Hussein or Zafar Said.

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Hussein, A.K., Ghodbane, M., Said, Z. et al. The effect of the baffle length on the natural convection in an enclosure filled with different nanofluids. J Therm Anal Calorim 147, 791–813 (2022). https://doi.org/10.1007/s10973-020-10300-1

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  • DOI: https://doi.org/10.1007/s10973-020-10300-1

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