Heat and Mass Transfer

, Volume 46, Issue 1, pp 63–74 | Cite as

Optimization of a stepped circular pin-fin array to enhance heat transfer performance

  • Kwang-Yong KimEmail author
  • Mi-Ae Moon


A Stepped circular pin-fin array is formulated numerically and optimized with Kriging metamodeling technique to enhance heat transfer performance. The problem is defined by two non-dimensional geometric design variables composed of height of the channel, height of smaller diameter part of the pin-fins, and smaller diameter of the pin-fins, to maximize heat transfer rate compromising with friction loss. Ten designs generated by Latin hypercube sampling were evaluated by three-dimensional Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct the surrogate model. The predictions of objective function by Kriging model at optimum point show reasonable accuracy in comparison with the values calculated by RANS analysis. Optimum shape of pin-fins strongly depends on the weighting factor which measures importance of the friction loss term in the objective function. The thermal performances are much higher than that of the straight pin-fin at sampling optimum points with different weighting factors.


Heat Transfer Design Variable Kriging Nusselt Number Heat Transfer Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Areas of heat transfer surface


Areas of heat transfer surface and inlet plane, respectively


Specific heat


Larger diameter of the pin-fins


Channel hydraulic diameter


Smaller diameter of the pin-fins


Objective function


Friction factor


Reference friction factor


Height of the channel


Height of smaller diameter part of the pin-fins


Turbulence kinetic energy


Number of design variables


Local Nusselt number


Reference Nusselt number


Average Nusselt number

\( \overline{Nu} \)

Endwall area-averaged Nusselt number

p, Δp

Pressure and pressure drop in a channel, respectively

\( \hat{p} \)

Periodic component of pressure




Prandtl number


Turbulent Prandtl number


Wall heat flux


Reynolds number (= u b D h /ν)


Strain rate


Local mean temperature


Wall temperature

\( \hat{T} \)

Periodic component of temperature


Average axial velocity


Mean velocity components (i = 1, 2, 3)


Cross-streamwise distance between two neighbored pin-fins


Rectangular coordinates (i = 1, 2, 3) or design variables (Eq. 12)


Weighting factor in objective function in Eq. 10 or model constant in Eq. 6


Kronecker delta (i = 1, 2, 3)


Pressure gradient in streamwise direction

μ, μt

Viscosity and turbulent viscosity, respectively

ν, νt

Kinematic viscosity and eddy viscosity, respectively


Fluid density


Increasing rate of bulk temperature in axial direction (Eq. 4) or standard deviation of the population (Eq. 12)

σk, σω

Turbulence model constants in Eqs. 5 and 6, respectively


Specific turbulence dissipation rate



This research was supported by ‘Multi-Phenomena CFD Engineering Research Center’ grant funded by National Research Foundation of Korea.


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringInha UniversityIncheonRepublic of Korea

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