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

  • Masoud Sobhani
  • Hossein AjamEmail author


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.


Partially heated Natural convection Nanofluid Lattice Boltzmann Taguchi optimization 

List of symbols


Lattice speed


Specific heat




Degrees of freedom


Velocity in discrete direction \(i\)


F value


Particle distribution function for velocity field


Particle distribution function for thermal field


Gravitational acceleration in the \(y\) direction


Height and width of enclosure


Buoyant body force term


Thermal conductivity




Total number of discrete lattice directions


Mach number


Mean squares


Number of case iteration


Outer normal unit vector


Nusselt number




Prandtl number


Ideal gas constant


Rayleigh number


Position vector


Geometric distance


Sums of squares


Signal-to-noise ratio




Macroscopic velocity vector


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




Dimensionless coordinate of the 2D rectangular cavity


Measured response

Greek symbols


Thermal diffusion


Coefficient of thermal expansion


Value of predicted SNR


Dimensionless temperature


Kinematic viscosity




Relaxation time for thermal field


Relaxation time for velocity field


Volume fraction





Cold, hot


Index for the discrete direction












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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFerdowsi University of MashhadMashhadIran

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