KSME International Journal

, Volume 18, Issue 9, pp 1590–1603

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations