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MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid

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Abstract

In this paper, the steady mixed convection flow and heat transfer of water-copper oxide nanofluid in an open C-shaped enclosure is investigated numerically. The enclosure is under constant magnetic field. Effects of Richardson number, magnetic and nanofluid volume fraction parameters are studied and discussed. The nanofluid with a cold temperature of T C and a velocity of u c enters the enclosure from the top right corner and exits from the bottom right corner. The vertical wall of the left side is subjected to a hot and constant temperature T h . Also, other walls are insulated. It is found that the heat transfer is increased via increasing the Hartmann and Reynolds numbers. For low Reynolds numbers, the enhances of the Hartman number leads to a slightly increases of the average Nusselt number, but for high Reynolds numbers, the average Nusselt number gets an ascending trend and the increase in the Hartmann number shows its effect more pronounced. Also, with increase in Ri, the effect of nanofluid on the heat transfer increases. Due to practical impotence, the study of mixed convection heat transfer in enclosures and various shaped of cavities has attracted remarkable attentions in the past few decades. Significant applications of the mixed convection flow can be found in atmospheric flows, solar energy storage, heat exchangers, lubrication technology, drying technologies, cooling of the electronic devices, etc. The present results are original and new for the problem of MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Comparison of the obtained results with those from the open literature (Mahmoodi et al. [24]) is acceptable.

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Abbreviations

B0 :

magnetic field strength, T

c :

experimental constant, Eq. (8)

C p :

specific heat, J. kg. K−1

g :

gravitational acceleration, m.s−2

H :

length of heat source, m

Ha :

Hartmann number, \( {B}_0L\;\sqrt{\sigma_f/{\rho}_f{\nu}_f} \)

k :

thermal conductivity, W m −1 K−1

L :

length of cavity, m

Nu :

local Nusselt number

Nu m :

average Nusselt number of heat source

p :

fluid pressure, Pa

P :

dimensionless pressure, \( p/{\rho}_{nf}\;{v}_0^2 \)

Pe :

Péclet number, u s d s /α f

Pr :

Prandtl number, v f /α f

Re :

Reynolds number, ρ v0L/μ f

Ri :

Richardson number, Gr/Re2

T :

temperature, K

T c :

inlet flow temperature, K

T h :

heated wall temperature, K

u 0 :

inlet flow velocity, m.s−1

u,v :

velocity components in x and y directions, m.s−1

U,V :

dimensionless velocity components, u/v0, v/v0

x,y :

Cartesian coordinates, m

X,Y :

dimensionless coordinates, x/L, y/L

α :

thermal diffusivity, m2. s−1, k/ρc p

β :

thermal expansion coefficient, K−1

ϕ :

solid volume fraction

σ :

effective electrical conductivity, μ S/cm

θ :

dimensionless temperature, (T − T c )/(T h  − T c )

μ :

dynamic viscosity, N.s.m−2

v :

kinematic viscosity, m2. s−1

ρ :

density, kg.m−3

c :

cold

eff :

effective

f :

pure fluid

h :

hot wall

m :

average

nf :

nanofluid

s :

nanoparticle

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Acknowledgements

The authors wish to express their thanks to the very competent Reviewers for the very good comments and suggestions. The work of I. Pop has been partially supported from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania.

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Authors and Affiliations

  1. Department of Engineering, Mahdishahr Branch, Islamic Azad University, Mahdishahr, Iran

    T. Armaghani

  2. Department of Chemical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran

    H. Esmaeili

  3. Department of Mechanical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran

    Y. A. Mohammadpoor

  4. Department of Mathematics, Babeş-Bolyai University, 40084, Cluj-Napoca, Romania

    I. Pop

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  1. T. Armaghani
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Correspondence to I. Pop.

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Armaghani, T., Esmaeili, H., Mohammadpoor, Y.A. et al. MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Heat Mass Transfer 54, 1791–1801 (2018). https://doi.org/10.1007/s00231-017-2265-3

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