MULTI-OBJECTIVE OPTIMIZATION OF MICRO-PIN FIN ARRAYS … · 2018. 12. 13. · state conjugate heat transfer analysis was performed on each cooling configuration and a constrained

1 Copyright © 2015 by ASME

Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE15

November 13-19, 2015, Houston, Texas, USA

IMECE2015-54166

MULTI-OBJECTIVE OPTIMIZATION OF MICRO PIN-FIN ARRAYS FOR

COOLING OF HIGH HEAT FLUX ELECTRONICS

Sohail R. Reddy Florida International University

Department of Mechanical and Materials Eng., MAIDROC Laboratory, Miami, FL 33174, USA.

[email protected]

George S. Dulikravich Florida International University

Department of Mechanical and Materials Eng., MAIDROC Laboratory, Miami, FL 33174, USA.

[email protected]

ABSTRACT

The thermal management capability of various candidates of

micro-pin fin arrays is investigated. An integrated circuit having

a footprint of 4 x 3 mm with micro-pin fin array having circular,

airfoil and convex cross-section is considered. The three pin fin

cross-sections along with the cooling schemes are optimized to

handle a uniform heat flux of 500 W/cm2 applied to the top

surface of the electronic chip. A fully three-dimensional, steady-

state conjugate heat transfer analysis was performed on each

cooling configuration and a constrained multi-objective

optimization was carried out for each of the three micro-pin fin

shapes to find pin fin designs configurations capable of cooling

such high heat fluxes. The design variables were the geometric

parameters defining each pin fin cross section, height of the chip

and inlet speed of the coolant. The two simultaneous objectives

were to minimize maximum temperature and pressure drop

(pumping power), while keeping the maximum temperature

below 85oC. A response surface was constructed for each

objective function and was coupled with a genetic algorithm to

arrive at a Pareto frontier of the best trade-off solutions. Stress-

deformation analysis incorporating the hydrodynamic and

thermal loads was performed on each of the three optimized

configurations. The maximum displacement was found to be on

the nano-level, and the Von-Mises stress for each configuration

was found to be significantly below the yield strength of Silicon.

INTRODUCTION

A continuous growth in the demand of computing power

from electronic chips has led to extremely high production of

heat. The performance of cooling systems is quickly turning into

a major limiting factor in modern electronic devices. There are

various methods of cooling electronics, such as micro-channels,

micro-jets and spray cooling, to name a few. An alternative

method for thermal management in integrated circuits is the use

of micro-pin fins. Benefits of micro-pin fins include higher heat

removal capacity and compact packaging of chips since they

allow for stacking. Micro-pin fins not only acts as heat sinks but

also allow for interconnection between stacked layers of chips

due to the Through-Silicon Vias (TSV) housed inside.

Numerous authors have previously investigated various

methods of cooling. Abdoli et al. [1] carried out conjugate heat

transfer analysis on two floor, single phase flow in micro

channels to study their effects in cooling chips with hotspots. Wu

and Mudawar [2] investigated the thermal management

capabilities of heat sinks with rectangular cross-sections. Their

work considered a heat flux of 90 W cm-2 applied uniformly on

the top surface. In other research, Abdoli et al. [3] also

investigated single-floor and double-floor, various micro-pin fin

configurations and their ability to cool high heat flux chips with

hotspot. They investigated circular, airfoil and convex lens

shaped micro-pin fin arrays and their effects on temperature and

pumping power. It was shown that the convex shape require less

pumping power while offering similar performance in thermal

management. Alfieri et al. [4] numerically studied the effects of

size and distribution of pin fins on the thermal performance of

3D stacked circuits with integrated cooling. In another work,

Alfieri et al. [5] computationally modelled the vortex shedding

in water-cooled array of micro-pin fins. Their work showed that

even at low Reynolds number, vortex shedding is present.

In previous optimization work, Jelisavcic et al. [6] and

Gonzales et al. [7] found an optimum configuration of network

of cooling passages. Abdoli and Dulikravich [8, 9, 10, 11] also

optimized multi-floor microchannel configurations. Fabbri and

Dhir [12] optimized an array of microjet for cooling of high

performance electronics. Their work showed that a maximum

heat flux of 310 W/cm2 is attainable while keeping the maximum

temperature below a threshold. Tullius et al. [13] performed

parametric optimization of six micro-pin fin cross-sections that

lead to important correlations between geometric parameters,

Nusselt number and heat transfer coefficients. It can be seen that

optimization studies have previously been carried out but very

few efforts have been dedicated to find an optimum

configuration for micro-pin fin heat sinks.

An optimization study was carried out to find an optimum

shape for each of the three micro-pin fin geometries to handle a


uniform heat flux of 500 W cm-2 while keeping the maximum

temperature below 85oC. The simultaneous objectives include

minimizing maximum temperature while minimizing the inlet

pressure. The minimization of inlet pressure results in reduced

pumping power. A heat flux of 500 W cm-2 was chosen as a

realistic projection of future heat dissipation requirements, as

typical electronic chips experience heat fluxes around 100 W cm-

2. The optimization was carried out in a commercial software

modeFRONTIER [14] and involved a response surface coupled

with a genetic algorithm to arrive at a Pareto frontier. Figure 1

shows the typical micro-pin fin configuration used in this study.

Figure 1: Dimension of the chip used in this study

CONJUGATE HEAT TRANSFER ANALYSIS

The thermal management capabilities of the three proposed

micro-pin fin shapes were previously investigated by Abdoli et

al. [3]. Unlike the heat flux in this work which if uniform, Abdoli

et al. [3] applied a non-uniform heat flux featuring a hot spot.

Reddy et al. [15] optimized the proposed pin fin shapes for a

background heat flux of 500 W cm-2 and a hot spot heat flux of

1000 W cm-2.

Figure 2 shows the three pin fin shapes considered in this

study. Each configuration analyzed in this work was fitted with

special pin-fins at the outlet to increase heat transfer at the outlet

and suppress backflow.

a)

b)

c)

Figure 2. A micro pin-fin cooling configuration with pins having: a) circular, b) airfoil, and c) symmetric convex cross sections.

Figure 3 shows typical hybrid computational grids of

approximately seven to eight million cells, used for each

conjugate heat transfer analysis. A total of four layers of

structured cells were placed on each solid-fluid interface. The

minimum allowable length scale for the computational mesh was

one micron, to satisfy continuum so that the Reynolds Averaged

Navier-Stokes (RANS) [16] equations can be solved in the fluid

domain. The standard k-e turbulence model was used to model

vortex shedding displayed by Alfieri et al. [5]. This model was

chosen due to it stability and good convergence.

a) b)

c)

Figure 3. Typical hybrid structured/non-structured 3D computational grid for arrays of micro pin-fins having: a) circular, b) symmetric airfoil, and c) symmetric convex cross sections.

The mass and linear momentum balances are given as

0=⋅∇ Vr

(1)

ρr

V ⋅∇( )

r

V = ∇⋅ − pt

1+ µ ∇r

V +r

∇V( )T

( )

(2)

The energy balance for incompressible flows, neglecting viscous

dissipation and heat sources) takes the form

( ) ( ) ( )TkpVTVCp

∇⋅∇+∇⋅=∇⋅rr

ρ (3)

4 mm

1.5 mm

Line of Symmetry

Chord

Length

Thickness


The solid domain consists of the micro-pin fins and the

sidewalls. The steady-state heat equation was solved for the solid

domain, where k is the thermal conductivity and T is the absolute

temperature.

( ) 0=∇⋅∇ Tk (4)

Stress-deformation analysis was also performed on the three

optimized configuration to investigate the effect of

hydrodynamic and thermal loads on the configurations. The

conservation of momentum for an isotropic solid body element

is written as

2

2

u.σ F 0

tρ∂

−∇ − =∂ (5)

The stress tensor, σ, for a linear elastic solid is written as

σ 2G tr( ) Iε λ ε= + (6)

where G and λ are the modulus of elasticity and the first Lame

coefficient, respectively.

The strain tensor is defined as

v

1[ u ( u) ] ( T )I

2= ∇ + ∇ + ∆

Τε α

(7)

where

0T T T∆ = −

(8)

A computational grid of approximately 12-million grid cell

was used for each stress-deformation analysis.

PROBLEM FORMULATION

The gains in performance reported by Abdoli et al. [3] can

further be increased through an optimization study. The multi-

objective optimization in this work was carried out in the

commercial package, modeFRONTIER [14]. Three design

variables were used to define the circular pin fins configurations:

inlet velocity, diameter and pin fin height. The airfoil and convex

pin fin cooling configurations were defined using the inlet

velocity, pin fin height, chord length and thickness. The airfoil

profile was defined using a four series, NACA 00XX series

airfoil. The thickness of all sidewalls of the electronic chip were

held constant at 30 ��.

A gauge pressure of 20kPa was applied at the outlets since

most electronic cooling configurations are pressurized to avoid

cavitation. The inlet temperature of the water is held constant at

30oC. A heat flux of 500 W cm-2 was uniformly applied to the

top surface of all configurations. The bottom and sidewalls were

thermally insulated.

Table 1 shows the range and step size of each variable used

to define the three pin fin configurations. The ranges were

selected so as to avoid self-intersecting geometries.

Table 1. Range for design variables defining the pin-fin configuration.

Design Variable Range Step size

Inlet velocity (m/s) 1 - 5 0.2

Height of pin-fins (µm) 100 – 250 50

Diameter of circular pin-fins

(µm)

100 – 200 10

Chord length of pin-fins (µm) 200 – 300 10

Thickness of pin-fins (µm) 80 - 160 10

MULTI-OBJECTIVE OPTMIZATION

The optimization performed in this study features two

objectives:

1. Minimize maximum temperature

2. Minimize inlet pressure (pumping power)

A total of three optimization runs were performed, one for each

pin fin shape.

Figure 4 shows the various software packages used and the

optimization workflow used in this study. The computational

grids were created in ANSYS Meshing® and the conjugate heat

transfer analysis was performed in ANSYS Fluent® [16]. The

multi-objective optimization was performed using

modeFRONTIER [14] while the stress-deformation analysis was

performed in ANSYS Structural®.

Due to the large computational cost for each conjugate heat

transfer analysis (eight hours on eight cores), a metamodel in the

form of response surface approximation based on Hardy’s

Multiquadrics Radial Basis Functions (MRBF) [17] was used.

It is known that the accuracy of the metamodel is highly

dependent on the size and distribution of the dataset. The

response surfaces were constructed using 30 candidate design in

the case of circular pin fin and 50 designs in the case of airfoil

and convex pin fins. The SOBOL’s algorithm [18] was used to

evenly distribute the candidate configuration through the design

space.

The optimization was carried out by coupling the response

surfaces (one for each objective function) with the Non-

Dominated Sorting Genetic Algorithm (NSGA-II) [19]. The

NSGA-II algorithm was used to navigate the objective function

space produced by the response surfaces to arrive at Pareto

frontier of best trade-off solutions.


Figure 4. Workflow of different modules and software used.

RANDOM NON-OPTIMIZED CONFIGURATIONS

For comparison purposes, benchmark designs were creased

using SOBOL’s algorithm. Figure 5 shows the temperature field

for the three non-optimized configurations.

a)

b)

c)

Figure 5. Temperature field for non-optimized configurations of pin-fins having: a) circular, b) symmetric airfoil, and c) symmetric convex cross sections

Figure 6 shows the pressure field at mid-height of the three

non-optimized configurations. The high-pressure stagnation

regions can be seen for both circular and airfoil configurations.

This stagnation region virtually disappears for the convex shape.

a)

b)

c)

Figure 6. .Pressure field for non-optimized arrays of micro pin-fins having: a) circular, b) symmetric airfoil, and c) symmetric convex cross sections

OPTIMIZATION RESULTS

Figure 7 shows the Pareto fronts obtained by coupling

NSGA-II algorithm and the MRBF response surfaces as well as

the candidate designs used to create the response surfaces.

Although the response surfaces were validated before coupling

with the NSGA-II algorithm, global validation is extremely

difficult. For this reason five Pareto designs for each pin fin

configuration were randomly selected and analyzed in ANSYS

Fluent.


a)

b)

c)

Figure 7. Objective function space for initial population and virtual Pareto designs for arrays of micro pin-fins having: a) circular, b) airfoil, c) symmetric convex cross sections,

The objective function values calculated using the response

surfaces deviated by less than 3% from those computed by

ANSYS Fluent thereby demonstrating the acceptable accuracy

of the metamodels.

Table 2 shows the geometric parameters and inlet condition

for each of the three optimized configurations of arrays of pin

fins with the two objective function values.

Table 2. Parameters and objective function values for the three Pareto-optimized pin-fin geometries.

Pin-fin Configuration

Parameters

Circular Symmetric

airfoil

Symmetric

convex

Diameter (��) 120 - -

Chord length (��) - 210 290

Thickness (��) - 90 90

Height (��) 250 250 250

Inlet speed (m/s) 2.2 3 4.4

Max. temperature (C) 56 52 53

Inlet pressure (kPa) 101.40 96.55 89.00

Figure 8 shows the temperature distribution on the solid

domain of the three optimized configurations. Figure 8 and Table

2 show that the use of circular cross section pin-fins results in

both higher maximum temperature and inlet pressure. The lower

temperature towards the bottom of the airfoil pin-fin

configurations suggests that more heat is being transfer from the

pin-fins to working fluid.

a)

b)


c)

Figure 8. Temperature distribution on the solid domain due to Pareto-optimized: a) circular, b) symmetric airfoil and c) symmetric convex cross sections of micro pin-fins.

Figure 9 shows the pressure field at mid-height of the three

optimized configurations. It can be seen that the high-pressure

stagnation point for the circular and airfoil has reduced. Figure 8

and Table 2 show that the airfoil and convex shapes also result

in lower inlet pressure and therefore lower pumping power

requirement.

a)

b)

c)

Figure 9 Pressure distribution for Pareto-optimized arrays of pin-fins having: a) circular, b) symmetric airfoil, and c) symmetric convex cross sections.

Figure 10 shows the velocity magnitude and velocity vectors

for the three optimized configurations. The large separation

region behind the circular pin fin is clearly visible. The

stagnation point at the leading edge of the circular and airfoil pin

fins is clearly visible. This is not seen in the case of convex pin

fins.

Figure 10. Velocity magnitudes and flow vectors for the three Pareto-optimized pin-fin cross sections.

The objective function values for the three optimized and

non-optimized configurations are shown in Table 3. It is well

known that in the case of multi-objective optimization, there is

no single optimum design but rather best trade-off designs. When

selecting the three optimum configurations, priority was given to

a design with lower inlet pressure. It should be mentioned that

another Pareto optimum configuration can be selected from the

Pareto front that best meets the required performance. Table 3

shows that the airfoil and convex pin fin configurations result in

both lower temperature and lower pumping power than the

circular pin fin configurations. It shows that the convex pin fin

results in similar temperatures but require significantly lower

pumping power.

Table 3. Objective function values for non-optimized and Pareto-optimized arrays of micro pin-fins for each of the three pin-fin geometries.

T (oC) ∆T% p (kPa) ∆P%

Non-Optimized Circular 54 - 146.18 -

Optimized Circular 56 +2 101.4 -30

Non-Optimized Airfoil 57 - 188.36 -

Optimized Airfoil 52 -5 96.55 -49

Non-Optimized Convex 56 - 180.47 -

Optimized Convex 53 -6 89 -51


STRESS-DEFORMATION ANALYSIS

Depending on the sensitivity of the design, slight deviation

from the optimum configuration can significantly reduce

performance. These deviations can be due to manufacturing

defects or externally applied loads. For this reason, stress-

deformation analysis was performed on the three optimum

configurations to investigate the magnitude of deviation from the

optimum configurations. A typical grid of approximately four

million cells was used for each stress-deformation analysis.

The hydrodynamic and thermal loads from the conjugate

heat transfer analysis were applied and all external sides of the

chips were fixed to investigate the effects of the loads on the

micro-pin fin configurations.

Figure 11 shows the displacement field for the three

optimum configurations due to hydrodynamic and thermal loads.

It can be seen that the maximum displacement is on the nano-

level, suggesting geometric deviations from the optimum

configurations are miniscule.

a)

b)

c)

Figure 11. Displacement field due to hydrodynamic and thermal loads on Pareto-optimized pin-fins having: a) circular, b) airfoil, and c) symmetric convex cross sections

Figure 12 shows the Von-Mises stress field for the three

optimum configurations. It can be seen that the higher stress are

concentrated towards the outlets. This is due to the increased

thermal loads as the heat transfer properties of the warmer fluid

are diminished. It can be seen that the maximum Von-Mises

stress for the three configurations is between 47 and 75 MPa,

which is significantly lower than the yield strength of 7000 MPa

for silicon [20]. This suggests that, from a structural viewpoint,

the hydrodynamic and thermal loads can significantly be

increased without compromising structural integrity.

a)

b)

c)

Figure 12. Von-Mises stress distribution due to hydrodynamic and thermal loads on pin-fins having: a) circular, b) airfoil, and c) symmetric convex cross sections

CONCLUSION

This study investigated the thermal management capabilities

of three micro-pin fins geometries in cooling of micro-

electronics with a uniform heat flux of 500 W cm-2. Conjugate

heat transfer analysis was performed on each configuration and

showed that the airfoil and convex shapes virtually eliminated

the recirculation region experience by the circular pin fins. A

multi-objective optimization was performed for the three

configurations where the two objectives were to minimize

��

��


maximum temperature and pumping power. The design

variables were the geometric parameters defining each

configuration in conjunction with the inlet velocity. The

optimization was efficiency performed by coupling response

surfaces with the NSGA-II algorithm. The optimum

configurations showed that the airfoil and convex shapes

outperformed the circular pin fins in both objectives. Stress-

deformation analysis incorporating hydrodynamic and thermal

loads from the conjugate heat transfer analysis was also

performed to analyse the structural integrity of the three

optimum configurations. It was shown that the maximum

displacement for all three configurations is on the nano-level.

The maximum Von-Mises stress for the three configurations was

in the range of 47 to 75 MPa, which is significantly lower than

the yield strength for silicon of 7000 MPa, indicating the

structural integrity of the three optimum configurations.

ACKNOWLEDGMENTS The authors are grateful for the partial financial support of

this research provided by DARPA via GaTech in the framework

of ICECool project under supervision of Dr. Avram Bar-Cohen.

They are also grateful for the partial financial support

provided by DOE/NETL grant DE-FE0023114. The authors also

gratefully acknowledge the FIU Instructional and Research

Computing Center for providing HPC resources to perform

calculations for this project.

The first author would like to express his appreciation to

Prof. George S. Dulikravich and Dr. Abas Abdoli for their

guidance and for providing suggestions for the manuscript. He is

also grateful for Cesar Pacheco’s and Rajesh Jha’s help with

creation of hybrid computational grids.

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Documents

MULTI-OBJECTIVE OPTIMIZATION OF MICRO-PIN FIN ARRAYS … · 2018. 12. 13. · state conjugate heat transfer analysis was performed on each cooling configuration and a constrained