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Numerical analysis of natural convection of Cu–water nanofluid filling triangular cavity with semicircular bottom wall

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Abstract

This study provides numerical analysis of the free convection of copper–water-based nanofluid filling a triangular cavity with semicircular bottom wall. The cavity sidewalls are maintained at cold temperature, while the semicircular wall is maintained at hot temperature. The other wall segments are thermally insulated. To control the energy transport within the cavity, a uniform magnetic field is applied horizontally. The physical domain is discretized according to the control volume finite element method which has been used to solve the governing equations. The physical and geometrical aspects of the current problem are investigated by inspecting the impacts of Rayleigh number, Hartman number, aspect ratio and the volume fraction of the Cu nanoparticles. Decreasing the radius of the hot semicircle enlarges the average Nusselt number at the absence of the magnetic field. When the magnetic field is applied, this effect is conversed within Ra ≤ 104. This conversed impact does not hold up when Ra is raised to 105. The numerical results are correlated in a sophisticated correlation of the average Nusselt number with other parameters.

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Abbreviations

Ha :

Hartmann number (–)

Pr :

Prandtl number (–)

B 0 :

Magnetic field (–)

c :

Specific heat (J kg−1 K−1)

T :

Temperature (K)

Nu loc. :

Local Nusselt number (–)

Nu ave. :

Average Nusselt number (–)

k :

Thermal conductivity (W m−1 K−1)

u, v :

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

Ra :

Rayleigh number (–)

AR:

Aspect ratio (–)

p :

Pressure term (Pa)

β :

Thermal expansion coefficient (K−1)

ρ :

Density (kg m−3)

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

σ :

Electrical conductivity (Ω−1 m−1)

ϕ :

Nanoparticles volume fraction (–)

θ :

Dimensionless temperature

f:

Base fluid

nf:

Nanofluid

s:

Solid nanoparticles

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Authors and Affiliations

  1. Young Researchers and Elite Club, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

    A. S. Dogonchi

  2. Mechanical Engineering Department, University of Basrah, Basra, Iraq

    Muneer A. Ismael

  3. Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    Ali J. Chamkha

  4. RAK Research and Innovation Center, American University of Ras Al Khaimah, Ras al-Khaimah, United Arab Emirates

    Ali J. Chamkha

  5. Mechanical Engineering Department, Babol Noshirvani University of Technology, Babol, Iran

    D. D. Ganji

Authors
  1. A. S. Dogonchi
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  2. Muneer A. Ismael
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  3. Ali J. Chamkha
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  4. D. D. Ganji
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Corresponding authors

Correspondence to A. S. Dogonchi, Muneer A. Ismael or Ali J. Chamkha.

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Dogonchi, A.S., Ismael, M.A., Chamkha, A.J. et al. Numerical analysis of natural convection of Cu–water nanofluid filling triangular cavity with semicircular bottom wall. J Therm Anal Calorim 135, 3485–3497 (2019). https://doi.org/10.1007/s10973-018-7520-4

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