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Investigation of FHD effects on heat transfer in a differentially heated cavity partially filled with porous medium utilizing Buongiorno’s model

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Abstract

The present work reports the effects of ferro-hydrodynamics on heat transfer and fluid flow in a cavity partially filled with a porous medium for the first time. Different magnetic, flow and porosity parameters, including magnetic number, magnet position, Rayleigh number, Darcy number and the porous medium filling ratio, are studied numerically. To calculate the nanoparticle distribution inside the cavity, Buongiorno’s two-phase non-homogenous model has been utilized. The results of validation tests with the previous works show very good agreement between the results. Based on the outcomes, the best heat transfer enhancement will occur at a specific position of the magnet near the wall. At this position, the average Nusselt number enhancement amounts to 12%. On the other hand, the intensity of the magnetic field can cause more than 55% increase in the average Nusselt number. This enhancement is shown to fade in large Rayleigh numbers. Magnet size is another important magnetic property that causes up to 48% intensification in Nu. Furthermore, the ratio of the fluid to porous region is shown to have a significant effect on heat transfer rates which can grow up to 150%. Rayleigh number is shown to have a strong influence on the Nusselt number. Impermeability of the porous medium alters the heat transfer rates up to 80%.

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Abbreviations

C:

Concentration

C0 :

Bulk nanoparticle volume fraction

\({c}_{p}\) :

Specific heat (J/kg.K)

DB :

Brownian diffusion coefficient (m2/s)

DT :

Thermophoresis diffusion coefficient (m2/s)

Da:

Darcy number (K/H2)

Ec:

Eckert number

F:

Forchheimer drag coefficient

Gr:

Grashof number

\(\stackrel{-}{H}\) :

Magnetic field strength (A/m)

k:

Thermal conductivity (W/mK)

kb :

Boltzmann constant (1.380648 × 10–23 J/K)

K:

Permeability (m2)

L:

Length (m)

Le :

Lewis number

m:

Shape factor of nanoparticle

Ms :

Saturation magnetization (A/m)

M:

Magnetization (A/m)

Mn:

Magnetic number

Nb :

Brownian motion number

Nt :

Thermophoresis number

Nu:

Nusselt number (hL/k)

p:

Pressure (Pa)

Pr:

Prandtl number

Ra:

Rayleigh Number

T:

Temperature (K)

U:

Dimensionless velocity (x-component)

V:

Dimensionless velocity (y-component)

X:

Dimensionless x-component of location

X′:

Dimensionless x-component of the magnet

Y:

Dimensionless y-component of location

Y′:

Dimensionless y-component of the magnet

β :

Thermal expansion coefficient (K−1)

ε:

Porosity

ε1 :

Curie temperature ratio

ε2 :

Temperature ratio

\(\mu \) :

Viscosity (Pa.s)

\({\mu }_{0}\) :

Magnetic permeability (H/m)

\(\theta \) :

Dimensionless temperature

\(\rho \) :

Density (kg/m3)

α:

Thermal diffusivity (m2/s)

\(\nu\) :

Momentum diffusivity (m2/s)

\(\varphi\) :

Nanoparticle volume fraction

avg:

Average

c:

Cold

eff:

Effective

f:

Base fluid

H:

Hot

nf:

Nanofluid

P:

Nanoparticle

w:

Wall

m:

Magnet

*:

Dimensional values

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Authors and Affiliations

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

    Farrokh Mobadersani

  2. Department of Mechanical Engineering, Laval University, Quebec, Canada

    Araz Rezavand Hesari

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  1. Farrokh Mobadersani
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  2. Araz Rezavand Hesari
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Correspondence to Farrokh Mobadersani.

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Mobadersani, F., Rezavand Hesari, A. Investigation of FHD effects on heat transfer in a differentially heated cavity partially filled with porous medium utilizing Buongiorno’s model. Eur. Phys. J. Plus 136, 707 (2021). https://doi.org/10.1140/epjp/s13360-021-01679-3

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