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Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid

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Abstract

This paper discusses the results of a study related to natural convection cooling of a heat source located on the bottom wall of an inclined isosceles triangular enclosure filled with a Cu water-nanofluid. The right and left walls of the enclosure are both maintained cold at constant equal temperatures, while the remaining parts of the bottom wall are insulated. The study has been carried out for a Rayleigh number in the range 104 ≤ Ra ≤ 106, for a heat source length in the range 0.2 ≤ ε ≤0.8, for a solid volume fraction in the range 0 ≤ ϕ≤0.06 and for an inclination angle in the range 0° ≤ δ≤45°. Results are presented in the form of streamline contours, isotherms, maximum temperature at the heat source surface and average Nusselt number. It is noticed that the addition of Cu nanoparticles enhances the heat transfer rate and therefore cooling effectiveness for all values of Rayleigh number, especially at low values of Ra. The effect of the inclination angle becomes more noticeable as one increases the value of Ra. For high Rayleigh numbers, a critical value for the inclination angle of δ = 15° is found for which the heat source maximum temperature is highest.

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Abbreviations

A:

Aspect ratio (H/L)

b:

Length of heat source (m)

ε:

Dimensionless length of heat source (b/L)

Cp :

Specific heat (J kg−1 K−1)

k:

Thermal conductivity (W m−1 K−1)

H:

Height of the cavity (m)

L:

Length of the cavity (m)

Nus :

Local Nusselt number on the heat source surface

Nu:

Average Nusselt number along the heat source

p:

Fluid pressure (Pa)

P:

Dimensionless pressure \( \left( {{\text{pL}}^{2} /{{\uprho}}_{\text{nf}} {{\upalpha}}_{\text{f}} } \right) \)

Pr:

Prandtl number \( \left( {{{\upnu}}_{\text{f}} /{{\upalpha}}_{\text{f}} } \right) \)

q″:

Heat generation per area (W m−2)

Ra:

Rayleigh number (gβfL3ΔT/νfαf)

T:

Temperature (K)

u, v:

Velocity components in directions x and y (m s−1)

U, V:

Dimensionless velocity components x and y \( \left( {{\text{uL}}/{{\upalpha}}_{\text{f}} ,{\text{vL}}/{{\upalpha}}_{\text{f}} } \right) \)

x, y:

Cartesian coordinates (m)

X, Y:

Dimensionless coordinates (x/L, y/L)

g:

Gravitational acceleration (m s−2)

α:

Thermal diffusivity (m2 s−1) (k/ρCp)

β:

Thermal expansion coefficient (K−1)

ΔT:

Ref. temperature difference (K) (q″L/Kf)

ϕ :

Solid volume fraction

θ:

Dimensionless temperature ((T − Tc)/ΔT)

δ:

Inclination angle (°)

μ:

Dynamic viscosity (Ns m−2)

υ:

Kinematic viscosity (m2 s−1) (μ/ρ)

ρ:

Density (kg m−3)

c:

Cold wall

f:

Pure fluid

nf:

Nanofluid

p:

Nanoparticle

s:

Active base surface

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Authors and Affiliations

  1. Laboratory of Applied Energetics and Pollution, Department of Mechanical Engineering, Constantine 1 University, 25000, Constantine, Algeria

    Issam Rezaiguia, Mahfoud Kadja, Ridha mebrouk & Noureddine Belghar

Authors
  1. Issam Rezaiguia
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  2. Mahfoud Kadja
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  3. Ridha mebrouk
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  4. Noureddine Belghar
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Correspondence to Issam Rezaiguia.

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Rezaiguia, I., Kadja, M., mebrouk, R. et al. Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid. Heat Mass Transfer 49, 1319–1331 (2013). https://doi.org/10.1007/s00231-013-1170-7

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  • DOI: https://doi.org/10.1007/s00231-013-1170-7

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