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Cu–Water Nanofluid MHD Mixed Convection in a Lid-Driven Cavity with Two Sinusoidal Heat Sources Considering Joule Heating Effect

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Abstract

The effects of magnetic field and Joule heating on the heat transfer and fluid flow in a Cu–water nanofluid-filled lid-driven cavity are investigated in this paper. The cavity left side wall is heated by two sinusoidal heat sources, while the other walls have constant temperatures. The top wall of the cavity moves with fixed velocity in + x direction, and the other walls are under no-slip boundary conditions. A constant magnetic flux density is applied to the cavity left side wall. Numerical procedures can be applied to solve the dimensionless equations governing the stream function and temperature at various Reynolds number (Re), Hartmann number (Ha), Eckert number (Ec), magnetic field angle(α) and the solid nanoparticles volume fraction(ϕ). The averaged Nusselt number (Nuavg) is used to specify the rate of the heat transfer. It can be observed that increasing ϕ and also increasing Re result in the significant increase of Nuavg, which enhances convective cooling, and furthermore, Nuavg is varied with α. The increase of Ha within the cavity causes decrease in heat transfer, which enhances conduction heat transfer and also reduces Nuavg. The negative influence of Joule heating on the convection within the cavity is observable in this regard, and the convection is decreased by increasing the value of Ec.

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Abbreviations

B:

Magnetic flux density vector (Wb·m−2)

C p :

Specific heat (J·kg−1·K−1)

d :

Particle size (diameter) (m)

g :

Gravitational acceleration vector (m·s−2)

h :

Grid spacing (m)

k b :

Boltzmann constant (kg·m2·s−2·K−1)

k :

Thermal conductivity (W·m−1·K−1)

L :

Dimension of cavity (m)

p :

Pressure (N·m−2)

T :

Temperature (K)

U s :

Brownian motion velocity (m·s−1)

ν :

Velocity vector (m·s−1)

x, y, z :

Cartesian coordinates (m)

α :

Angle of orientation of the magnetic field

β :

Coefficient of volumetric expansion (K−1)

ϕ :

Nanoparticle volumetric fraction

μ :

Dynamic viscosity (kg·m−1·s−1)

ρ :

Density (kg·m−3)

σ :

Electrical conductivity (mho·m−1)

Ψ :

Stream function (m2·s−1)

0:

Reference value

c:

Cold

f :

Fluid

max:

Maximum value

nf:

Nanofluid

s :

Nanoparticle

st :

Static

x, y, z :

Component of a vector quantity

V :

Velocity vector

P :

Pressure

X :

Cartesian coordinate in x direction

Y :

Cartesian coordinate in y direction

Ψ:

Stream function

θ :

Temperature

Ec :

Eckert number

Gr :

Grashof number

Ha :

Hartmann number

Nu :

Nusselt number

Pr :

Prandtl number

Ra :

Rayleigh number

Re :

Reynolds number

Ri :

Richardson number

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  1. Department of Engineering, Imam Khomeini International University, Qazvin, Iran

    Mohammad Ali Taghikhani

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Taghikhani, M.A. Cu–Water Nanofluid MHD Mixed Convection in a Lid-Driven Cavity with Two Sinusoidal Heat Sources Considering Joule Heating Effect. Int J Thermophys 40, 44 (2019). https://doi.org/10.1007/s10765-019-2507-3

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