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Natural convection in F-shaped cavity filled with Ag-water non-Newtonian nanofluid saturated with a porous medium and subjected to a horizontal periodic magnetic field

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Abstract

Natural convection in an F-shaped cavity containing Ag-water non-Newtonian nanofluid (NF) saturated with a porous medium was investigated numerically. The left wall of the cavity was maintained at a constant hot temperature and subjected to a horizontal periodic magnetic field. The right wall was maintained at a constant cold temperature. Both the top and bottom walls of the cavity were kept thermally insulated. In the present work, the Hartmann number varied as (0≤Ha≤60), the power law index varied as (0.6≤n≤1.4), the periodic shape parameter varied as (0.1≤λ≤1), the Rayleigh number varied as (103≤Ra≤106), the aspect ratio of the cavity varied as (0.1≤AR≤0.4), the Darcy number varied as (10−5≤Da≤10−1) and the solid volume fraction varied as (0≤φ≤0.06). It was found that the average Nusselt number (Nu) increases by increasing the (φ, Da and Ra), whereas it decreases when (n) and (Ha) increase. Furthermore, it was realized that the relationship between the (Nu) and (λ) exhibits a different behavior depending on the considered values of (Ra) and (n).

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Abbreviations

AR:

aspect ratio (H/L) [-]

\(\overset{\rightharpoonup}{\mathrm{B}}\) :

magnetic strength [Tesla]

Bo :

amplitude of magnetic strength [Tesla]

Cp :

specific heat capacity [kJ/kg·K]

Da:

Darcy number [-]

F:

coefficient of weight function

g :

gravitational acceleration [m/s2]

H:

step length [m]

Ha:

Hartmann number [-]

J:

Jacobian of residual equation

k:

thermal conductivity [W/m·K]

K:

permeability of porous medium [m2]

L:

length & height of the cavity [m]

m:

total number of nodes [-]

N:

consistency coefficient [kg/m·s]

n:

power-law index [-]

Ṗ:

dimensionless pressure [-]

ṗ:

pressure [Pa]

Pr:

Prandtl number [-]

Ra:

Rayleigh number [-]

Ṫ:

temperature[K]

Nul :

local Nusselt number [-]

Nuave :

average Nusselt number [-]

\(\dot{\mathrm{U}}\) :

Dimensionless x-direction velocity component [-]

\(\dot{\mathrm{u}}\) :

x-direction velocity component [m/s]

\(\dot{\mathrm{V}}\) :

dimensionless y-direction velocity component [-]

\(\dot{\mathrm{v}}\) :

y-direction velocity component [m/s]

X, Y:

dimensionless coordinate [-]

x, y:

cartesian coordinates [m]

α :

thermal diffusivity [m2/s]

\(\dot \theta \) :

dimensionless temperature [-]

λ :

periodnumber

Ψ :

dimensionless stream function

μ :

dynamic viscosity [kg/m·s]

σ :

electrical conductivity [S/m]

ν :

kinematic viscosity \((\dot \nu = {\mu \over \rho })\;[{{\rm{m}}^2}/{\rm{s}}]\)

φ :

nanoparticle volume fraction [%]

\(\dot \tau \) :

shear stress tensor

Ø :

basic function

β :

thermal expansion coefficient [1/K]

ρ :

density [kg/m3]

c:

cold

bf:

base fluid (pure)

sp:

solid particle

na:

nanofluid

so:

conductive solid cylinder

h:

hot

Cond.:

Conduction

Conv.:

Convection

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Acknowledgements

The first author would like to very thank Mrs. Topsy N. Smalley from United States of America for her kind assistance in completing this work.

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Authors and Affiliations

  1. College of Engineering, Mechanical Engineering Department, University of Babylon, Babylon City, Hilla, Iraq

    Ahmed Kadhim Hussein, Hameed Kadhem Hamzah & Farooq Hassan Ali

  2. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Masoud Afrand

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  1. Ahmed Kadhim Hussein
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  2. Hameed Kadhem Hamzah
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Hussein, A.K., Hamzah, H.K., Ali, F.H. et al. Natural convection in F-shaped cavity filled with Ag-water non-Newtonian nanofluid saturated with a porous medium and subjected to a horizontal periodic magnetic field. Korean J. Chem. Eng. 39, 887–901 (2022). https://doi.org/10.1007/s11814-021-1004-0

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