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MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM

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Abstract

Magnetohydrodynamic flow in a nanofluid filled inclined enclosure is investigated numerically using the Control Volume based Finite Element Method. The cold wall of cavity is assumed to mimic a sinusoidal profile with different dimensionless amplitude, and the fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclination angle of enclosure. The results show that in presence of magnetic field, velocity field retarded, and hence, convection and Nusselt number decreases. At Ra = 103, maximum value of enhancement for low Hartmann number is obtained at γ = 0°, but for higher values of Hartmann number, maximum values of E occurs at γ = 90°. Also, it can be found that for all values of Hartmann number, at Ra = 104 and 105, maximum value of E is obtained at γ = 60° and γ = 0°, respectively.

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Abbreviations

a :

Dimensionless amplitude of the sinusoidal wall

C p :

Specific heat at constant pressure

Gr :

Grashof number

\( \vec{g} \) :

Gravitational acceleration vector

Ha :

Hartmann number \( (=HB_{x} \sqrt {\sigma_{f} /\mu_{f} } ) \)

\( H \) :

Dimensionless width of the enclosure

k :

Thermal conductivity

Nu :

Local Nusselt number

Pr :

Prandtl number (=υ f /α f )

T :

Fluid temperature

u, v :

Velocity components in the x-direction and y-direction

U, V :

Dimensionless velocity components in X-direction and Y-direction

x, y :

Space coordinates

X, Y :

Dimensionless space coordinates

Ra:

Rayleigh number (=gβ f ΔT(H)3/α f υ f )

α :

Thermal diffusivity

μ :

Dynamic viscosity

υ :

Kinematic viscosity

\( \Uptheta \) :

Dimensionless temperature

σ :

Electrical conductivity

ρ :

Fluid density

ϕ :

Volume fraction

γ :

Inclined angle of enclosure

ψ and Ψ :

Stream function and dimensionless stream function

c :

Cold

h :

Hot

ave:

Average

loc:

Local

nf:

Nanofluid

f :

Base fluid

s :

Solid particles

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    M. Sheikholeslami, M. Gorji-Bandpy, D. D. Ganji & Soheil Soleimani

Authors
  1. M. Sheikholeslami
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  2. M. Gorji-Bandpy
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  3. D. D. Ganji
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  4. Soheil Soleimani
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Correspondence to M. Sheikholeslami.

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Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D.D. et al. MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM. Neural Comput & Applic 24, 873–882 (2014). https://doi.org/10.1007/s00521-012-1316-4

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  • DOI: https://doi.org/10.1007/s00521-012-1316-4

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