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Taguchi optimization for natural convection heat transfer of Al2O3 nanofluid in a partially heated cavity using LBM

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Abstract

In the present study for the first time, Taguchi approach was applied to specify the optimal condition of the parameters in the natural convection heat transfer of Al2O3 nanofluid for a partially heated cavity. The flow and energy equations are solved by the lattice Boltzmann method. The influence of the 5 factors including Rayleigh number, position, hot length, cold length, volume concentration of the Al2O3 nanoparticles is examined. The Nusselt number on the hot section is measured for the response factor. In Taguchi optimization method, the levels of every factor were fixed at 3 levels and the L27 orthogonal array. The conclusions of the Taguchi–LBM technique indicated that the optimum conditions were attained at the maximum Rayleigh number, cold length and volume fraction and the minimum hot length in the bottom–bottom configuration in the variety of the design parameters. Also, the most significant parameter influencing the Nusselt number on the hot wall was the Rayleigh number, while changing the volume fraction had a negligible effect.

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Abbreviations

\(C\) :

Lattice speed

\(C_{\text{p}}\) :

Specific heat

dB:

Decibel

DF :

Degrees of freedom

\(\vec{e}_{\text{i}}\) :

Velocity in discrete direction \(i\)

\(F\) :

F value

\(f_{\text{i}}\) :

Particle distribution function for velocity field

\(g_{\text{i}}\) :

Particle distribution function for thermal field

\(g_{\text{y}}\) :

Gravitational acceleration in the \(y\) direction

\(H\) :

Height and width of enclosure

\(\dot{B}_{\text{i}}\) :

Buoyant body force term

\(k_{\text{t}}\) :

Thermal conductivity

L :

Length

\(M\) :

Total number of discrete lattice directions

\(Ma\) :

Mach number

\({\text{MS}}\) :

Mean squares

\(n\) :

Number of case iteration

\(\vec{n}\) :

Outer normal unit vector

\(Nu\) :

Nusselt number

\(P\) :

Position

\(Pr\) :

Prandtl number

\(R\) :

Ideal gas constant

\(Ra\) :

Rayleigh number

\(\vec{r}\) :

Position vector

\(s\) :

Geometric distance

\({\text{SS}}\) :

Sums of squares

SNR:

Signal-to-noise ratio

T :

Temperature

\(\vec{u}\) :

Macroscopic velocity vector

\(x,y\) :

\(x\)- and \(y\)-coordinate system

t :

Time

\(X,Y\) :

Dimensionless coordinate of the 2D rectangular cavity

\(y_{\text{n}}\) :

Measured response

\(\alpha\) :

Thermal diffusion

\(\beta\) :

Coefficient of thermal expansion

\(\eta\) :

Value of predicted SNR

\(\theta\) :

Dimensionless temperature

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Density

\(\tau_{\text{t}}\) :

Relaxation time for thermal field

\(\tau_{\upnu}\) :

Relaxation time for velocity field

\(\phi\) :

Volume fraction

\({\text{nf}}\) :

Nanofluid

\(C,H\) :

Cold, hot

\(i\) :

Index for the discrete direction

T :

Total

w :

Wall

p :

Particle

(eq):

Equilibrium

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Acknowledgements

The authors would like to gratefully acknowledge the Ferdowsi University of Mashhad, Mashhad, Iran, for their support and funding (No. 47970) provided for the research.

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  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Masoud Sobhani & Hossein Ajam

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  1. Masoud Sobhani
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Correspondence to Hossein Ajam.

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Sobhani, M., Ajam, H. Taguchi optimization for natural convection heat transfer of Al2O3 nanofluid in a partially heated cavity using LBM. J Therm Anal Calorim 138, 889–904 (2019). https://doi.org/10.1007/s10973-019-08170-3

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