KSME International Journal

, Volume 18, Issue 9, pp 1590–1603 | Cite as

Shape Optimization of a plate-fin type heat sink with triangular-shaped vortex generator

Article

Abstract

In this study the optimization of plate-fin type heat sink with vortex generator for the thermal stability is performed numerically. The optimum solutions in the heat sink are obtained when the temperature rise and the pressure drop are minimized simultaneously. Thermal performance of heat sink is influenced by the heat sink shape such as the base-part fin width, lower-part fin width, and basement thickness. To acquire the optimal design variables automatically, CFD and mathematical optimization are integrated. The flow and thermal fields are predicted using the finite volume method. The optimization is carried out by means of the sequential quadratic programming (SQP) method which is widely used for the constrained nonlinear optimization problem. The results show that the optimal design variables are as follows ; B1=2.584 mm, B2=1.741 mm, and t=7.914 mm when the temperature rise is less than 40 K. Comparing with the initial design, the temperature rise is reduced by 4.2 K, while the pressure drop is increased by 9.43 Pa. The relationship between the pressure drop and the temperature rise is also presented to select the heat sink shape for the designers.

Key words

Design Optimization Plate-Fin Heat Sink Vortex Generator CFD SQP Method 

Nomenclature

B1, B2

Base- and lower-part of fin [m]

B

Matrix in Eq. (24)

Cp

Specific heat at constant pressure [J/kgK]

C1, C2, C3, Cλ, Cμ

Empirical constants in the k-ε model

fR, fλ

Empirical functions in the k-ε model

F(X)

Objective function

gi

Acceleration of gravity [m/s2]

gj(X)

Inequality constraints

Gb, Gk

Generation terms in the k-ε equations

h

Fin height [m]

hi(X)

Equality constraints

H

Height of heat sink ( = h+t), [m]

H

Hessian matrix

k

Turbulent kinetic energy [m2/s2]

ks

Thermal conductivity of solid [W/m-K]

L

Length of heat sink [m]

Lh

Length of heat source [m]

P

Pressure [Pa]

ΔP

Pressure drop [Pa]

Pr

Prandtl number

Q

Dissipated heat [W]

R

Reynolds number

S

Fin-to-fin spacing [m]

S

Search direction in Eq. (20)

t

Basement thickness of heat sink [m]

T, T

Mean and fluctuating temperature, respectively [K]

ΔT

Temperature rise [K]

uj, uj

Mean and fluctuating velocities, respectively [m/s]

W

Width of heat sink [m]

Wh

Width of heat source [m]

x, y, z

Cartesian coordinates [m]

X

Design variable vector

Greek symbols

α

Step length parameter in Eq. (20)

αt

Eddy diffusivity for heat [m2/s]

β

Thermal expansion coefficient [l/K]

δij

Kronecker delta

ε

Dissipation rate of k [m2/s3]

ø

General dependent variable

μ, μt

Viscosity and eddy viscosity [N.s/m2]

μj

Thermal resistance [K/W] in Eq. (16)

Á

Density [kg/m3]

Ãk, Ãε

Turbulent Prandtl and Schmidt number for k and ε

Subscripts

in

Inlet

j

Junction or maximum

k

Number of iteration

Ambient

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References

  1. Abe, K., Kondoh, T. and Nagano, Y., 1996, “A Two-Equation Heat Transfer Model Reflecting Second-Moment Closures for Wall and Free Turbulent Flows,”Int. J. Heat and Flow Flow, Vol. 17, pp. 228–237.CrossRefGoogle Scholar
  2. FLUENT 5 User’s Guide, FLUENT Inc., 1998.Google Scholar
  3. Jang, J. Y., Wu, M. C. and Chang, W. J., 1996, “Numerical and Experimental Studied of Three-Dimensional Plate-Fin and Tube exchangers,”Int. J. Heat Mass Transfer, Vol. 39, No. 14, pp. 3057–3066.CrossRefGoogle Scholar
  4. Ledezma, G. and Bejan, A., 1996, “Heat Sinks with Sloped Plate Fins in Natural and Forced convection,”Int. J. Heat Mass Transfer, Vol. 39, No. 9, pp. 1773–1783.CrossRefGoogle Scholar
  5. Ma, H. B. and Peterson, G. P., 2002, “The Influence of the Thermal Conductivity on the Heat Transfer Performance in a Heat Sink,”ASME J. of Electronic Packaging, Vol. 124, pp. 164–169.CrossRefGoogle Scholar
  6. Park, K., Choi, D. H. and Lee, K. S., 2004, “Design Optimization of Plate-Fin and Tube Heat Exchanger,”Numerical Heat Transfer Part A, Vol. 45, pp. 347–361.CrossRefMathSciNetGoogle Scholar
  7. Patankar, S. V., 1980,Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington.MATHGoogle Scholar
  8. Rodi, W., 1984,Turbulence Models and Their Applications in Hydraulics a State-Art-of Review, Book Publication of International Association for Hydraulic Research, Delft, Netherlands.Google Scholar
  9. Ryu, J. H., Choi, D. H., and Kim, S. J., 2003, “Three-Dimensional Numerical Optimization of a Manifold Micro Channel Heat Sink,”Int. J. Heat Mass Transfer, Vol. 46, pp. 1553–1562.MATHCrossRefGoogle Scholar
  10. Vanderplaats, G. N., 1984,Numerical Optimization Techniques for Engineering Design with Application, Chap. 2, McGraw-Hill, New York.Google Scholar
  11. Wirtz, R. A. and Zcheng, N., 1998,Methodology for Predicting Pin-Fin Fan-Sink Assembly Performance, Prodc. of 6 th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Syatems (Itherm ’98),Google Scholar
  12. S.H. Bhavnani et al., ed., pp. 303-309.Google Scholar
  13. Wong, T., Leung, V. W., Li, Z. Y. and Tao, W. Q., 2003, “Turbulent Convection of Air-Cooled Rectangular Duct with Surface-Mounted Cross-Ribs,”Int. J. Heat Mass Transfer, Vol. 46, pp. 4629–4638.CrossRefGoogle Scholar
  14. Yuan, Z. X., Tao, W. and Wang, Q., 1998, “Numerical Prediction for Laminar Forced Convection Heat Transfer in Parallel-Plate Channel with Streamwise-Periodic Rod Disturbances,”Int. J. of Numerical Methods in Fluids, Vol. 28, pp. 1371–1387.MATHCrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2004

Authors and Affiliations

  1. 1.The Center of Innovative Design Optimization TechnologyHanyang University (HIT Rm# 312)SeoulKorea

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