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Conjugate Natural Convection of Nanofluids in an Enclosure with a Volumetric Heat Source

  • Research Article - Mechanical Engineering
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Abstract

This article presents a numerical investigation of conjugate natural convection of water-based nanofluids in a square cavity. Two different types of nanofluids, namely Al2O3–water and CuO–water are considered as the working fluids. A square volumetric heat generating source is located within the cavity, resembling a heat generating electronic device. All the cavity walls are considered to be adiabatic except the right-hand side wall which is at the cold temperature. Transport equations for Newtonian fluid have been solved numerically, using finite volume method. The effects of relevant parameters such as Rayleigh number (103 ≤ Ra ≤ 106), type of nanofluid, solid volume fraction of the nanoparticles, and the location of the heat source on the cooling performance of the cavity have been studied. The results show that in natural convection flows, nanofluids are more effective in heat transfer enhancement for moderate values of Rayleigh number and low values of solid particles volume fractions. In addition, to maximize the heat transfer performance, the best placement of heat source has been determined. Also it is shown that CuO–water nanofluid exhibits elevated thermal performance in comparison with Al2O3–water nanofluid.

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Abbreviations

B :

Length of inner body

C :

Experimental constant (Eq. (9))

C p :

Specific heat capacity (J kg−1 K−1)

d :

Diameter (m)

F(Ω):

Step function

g :

Gravitational acceleration (m s−2)

H :

Vertical wall length (m)

k :

Thermal conductivity (Wm−1 K−1)

k B :

Boltzmann constant = 1.38066 × 10−23 J K−1

L :

Horizontal wall length (m)

l x :

Horizontal distance of inner body

l y :

Vertical distance of inner body

M :

Molecular weight of the base fluid

N :

Avogadro number = 6.022 × 1023 mol−1

n :

Either X or Y  (Eq. (19))

Nu:

Nusselt number

Num :

Average Nusselt number

p :

Pressure (N/m2)

P :

Dimensionless pressure (p/ρ nf U 20 )

Pe:

Peclet number (u p d p /α f)

Pr:

Prandtl number (υ f /α f)

q′′′:

Heat generation of heat source

Ra:

Rayleigh number (β gH 3ΔT/(υ f α f))

R k :

Thermal conductivity ratio (k s /k nf)

T :

Temperature (K)

u, v :

Velocity components in x, y directions (ms−1)

u s :

Brownian motion velocity (ms−1)

U, V :

Dimensionless velocity components (u/ U 0,v/ U 0)

x, v :

Cartesian coordinates (m)

X, Y :

Dimensionless coordinates (x/ H, y/ H)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

Δ:

Difference

\({\phi}\) :

Solid volume fraction

λ :

Viscosity ratio

μ :

Dynamic viscosity (Ns m−2)

υ :

Kinematic viscosity (m2 s−1

θ :

Dimensionless temperature (T − T C )/ΔT

ρ :

Density (kg m−3)

0:

Reference

c:

Cold wall

eff:

Effective

eq:

Equivalent

f:

Fluid (pure)

i:

Representative of solid or fluid

max:

Maximum

nf:

Nanofluid

p:

Nanoparticle

s:

Solid region

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Authors and Affiliations

  1. School of Mechanical Engineering, Yazd University, P.O. box: 89195-741, Yazd, Iran

    M. R. Alizadeh & A. A. Dehghan

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  1. M. R. Alizadeh
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  2. A. A. Dehghan
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Correspondence to A. A. Dehghan.

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Alizadeh, M.R., Dehghan, A.A. Conjugate Natural Convection of Nanofluids in an Enclosure with a Volumetric Heat Source. Arab J Sci Eng 39, 1195–1207 (2014). https://doi.org/10.1007/s13369-013-0658-2

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  • DOI: https://doi.org/10.1007/s13369-013-0658-2

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