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Numerical investigation of natural convection on Al2O3–water porous enclosure partially heated with two fins attached to its hot wall: under the MHD effects

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Abstract

Numerical investigation for the steady-state laminar nanofluid 2D natural convection in a partially heated porous cavity equipped with two fins at the hot wall under the effect of a uniform magnetic field is carried out. Effects of wide ranges of variables including: Hartman number (0−80), direction of the magnetic field (0o−90°), Rayleigh number (103−106), Darcy number (10–2−10–5), nano-solid particles volume fraction (ϕ = 0% and 6%), length of the attached hot fins (0.25, 0.5, and 0.75) and the length of the partially heated (0.25, 0.5, and 0.6) wall are analyzed. The study results show that by increasing the Hartman number, the average Nusselt number will decrease. Moreover, by increasing the nano-solid particle volume fraction, Rayleigh number, Darcy number, the length of the hot fins, and the partially heated wall, a better heat transfer rate is achieved; consequently, the average Nusselt number will increase. Results show no consistent trend for the effect of the magnetic field direction on the average Nusselt number. The results show an enhancement in the average Nusselt number by 22.46% in the case of b = 0.6 and ϕ = 0.06 compared to the base case of b = 0.25 and ϕ = 0.06.

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Abbreviations

a :

Fins length (dimensionless)

b :

Length of the partially heated wall (dimensionless)

Cp:

Specific heat, J kg−1 K−1

Da:

Darcy number

g :

Gravitational acceleration, m s−2

Ha:

Hartman number

k :

Thermal conductivity, W m−1 K−1

K :

Permeability, m2

L :

Length of the enclosure, m

Nu:

Local Nusselt number

P :

Non-dimensional pressure

Pr:

Prandtl number

Ra:

Rayleigh number

T :

Dimensional temperature, K

U :

Non-dimensional velocity component X-direction

V :

Non-dimensional velocity component Y-direction

X :

Non-dimensional X-coordinates

Y :

Non-dimensional Y-coordinates

Ψ :

Absolute stream function

ϕ :

Solid volume fraction

θ :

Dimensionless temperature

γ :

Magnetic field angle

ε :

Porosity

µ :

Dynamic viscosity, kg m−1 s−1

α :

Thermal diffusivity, m2 s−1

β :

Thermal expansion coefficient, K−1

avg:

Average

c:

Cold

eff:

Effective

f:

Fluid (pure water)

h:

Hot

loc:

Local

nf:

Nanofluid

p:

Porous

s:

Nanoparticle

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq

    Khaled Al-Farhany, Mohamed F. Al-dawody & Dhafer A. Hamzah

  2. Mechatronics Engineering Department, German Jordanian University, Amman, Jordan

    Wael Al-Kouz

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

    Zafar Said

  4. U.S.-Pakistan Center for Advanced Studies in Energy (USPCAS-E), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Zafar Said

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  1. Khaled Al-Farhany
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  2. Mohamed F. Al-dawody
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  4. Wael Al-Kouz
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Correspondence to Khaled Al-Farhany or Zafar Said.

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Al-Farhany, K., Al-dawody, M.F., Hamzah, D.A. et al. Numerical investigation of natural convection on Al2O3–water porous enclosure partially heated with two fins attached to its hot wall: under the MHD effects. Appl Nanosci 13, 555–572 (2023). https://doi.org/10.1007/s13204-021-01855-y

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