This document summarizes a research project that aims to thermally enhance a plate-fin heat exchanger using secondary structures called cross-cuts. Cross-cuts are sections removed from fins perpendicular to airflow to disrupt boundary layer development. The project will test various cross-cut configurations and validate correlations from a previous study. A plate-fin heat sink will be compared to designs with one and two cross-cuts. The goal is to validate that a single cross-cut provides the best thermal performance improvement of 4-13% over the base design within a pumping power range of 0.01-1W.

1. Jamie Fogarty - 10100598 M.Eng. Research Project 2015/2016
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Thermal Enhancement of a Forced Convection Fin Array Heat Exchanger Using Secondary
Structures
Jamie Fogarty and Dr. Jeff Punch
Department of Mechanical, Aeronautical and Biomedical Engineering
University of Limerick, Limerick, Ireland
Abstract
Increasing circuit density, coincided with electrical device miniaturisation renders thermal management a priority concern.
A common solution is a designed heat sink with air-cooling fan. This project entails the thermal enhancement of a plate-fin
heat sink through use of secondary structures. The secondary structures are cross-cuts which segment the plate-fin, aimed
to interrupt boundary layer development and boost thermal performance. A plate-fin heat sink is compared to 3 other
configurations, 2 of which contain a single cross-cut, while the other contain two cross-cuts of equivalent length,
equidistant along the plate-fin. Results show that a single cross-cut is superior to multiple, with thermal enhancement of 4-
13% in the pumping power range of 0.01-1W. A previous study by Kim & Kim [1] on cross-cut heat sinks is validated,
along with cross-cut correlations for friction factor and thermal resistance.
Keywords: Heat sink, Cross-cut, Thermal Enhancement, Segmented.
Nomenclature
A Area ε Porosity
Cp Specific heat capacity (J/Kg-K) η Fin Efficiency
D Diameter (m) μ Dynamic viscosity (Pa-s)
f Friction factor ρ Density (Kg/m3)
H Height (m) Subscripts
h Heat transfer coefficient app Apparent
K Contraction/expansion coefficient b Base
k Thermal conductivity (W/m-K) bm Bulk mean
L Length (m) c Cross-cut
N Number ch Channel
Nu Nusselt Number cx Contraction
Pp Pumping Power (W) ex Expansion
Pr Prandtl number f Fins
𝑸̇ Volume Flow rate (m3/s) h Hydraulic
q Heat load (W) h s Heat sink
R Thermal Resistance (K/W) max Maximum
Re Reynolds number o Orifice
v Velocity (m/s) tot Total
Greek Symbols w Wall
α Thermal expansion coefficient (/K) Superscripts
β Diameter Ratio + Dimensionless variables
ΔP Pressure drop (Pa) * Dimensionless variables
1. Introduction
Heat transfer is an important process, playing a
dominant and controlling role in industrial and
manufacturing processes, and limiting the size and
capacity of technological components. Due to the
advancement of the semi-conductor industry in recent
decades, the size of electronic devices is reducing, while
their performance increases significantly. The trend of
increased circuit density and the miniaturisation of
electrical devices results in high heat concentrations,
creating a considerable amount of heat loads on chips and
their substrate. Without appropriate cooling, heat
generated detrimentally affects the performance of these
components, reducing the stability and life span of the
working device. Consequently, the effective thermal
management of electronic devices has become a priority
concern.
It is herebydeclared that this report is entirely my own
work, unless otherwise stated, and that all sources of
information have been properly acknowledged and
referenced. It is also declared that this report has not
previouslybeen submitted, in whole or in part, as part
fulfilment of any module assessment requirement.
Signed: ______________________ Date: __________

2. Jamie Fogarty - 10100598 M.Eng. Research Project 2015/2016
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The proceeding sub-sections discuss thermal
management methods. Section 1.1 introduces heat sinks
and characterises how their thermal performance is
affected, Section 1.2 introduces two methodologies for
optimising heat sinks, Section 1.3 takes one of these
methods and analyses its practises in literature to finally
arrive at Section 1.4; the objectives of the present study.
1.1 Heat Sinks
A common thermal solution is the installation of
a designed heat sink with an air-cooling fan. A heat sink
is a heat exchanger that transfers the heat generated by an
electronic device into a coolant fluid in motion. Then-
transferred heat leaves the device with the fluid in motion,
therefore allowing the regulation of the device
temperature at physically feasible levels [2]. The
functionality of a heat sink is based on the conduction of
the generated heat into the heat sink, and the convection
of the heat into the working fluid. The addition of an
extended surface onto the primary surface of a heat sink is
generally implemented to increase the convective surface
area per unit volume and to promote turbulence, resulting
in enhanced heat dissipation. Air is mainly used as the
working fluid as it is the least expensive cooling medium
and associated parts require minimum maintenance
requirements. Among the various types of heat sinks, the
two most common types are the plate-fin heat sinks and
pin-fin heat sinks, illustrated in Figure 1. Both are highly
applicable due to the benefits of easy fabrication and high
thermal performance achievable. Plate-fin heat sinks have
a simple design and low fabrication costs, while pin-fin
heat sinks have an advantage of hindering the
development of the boundary layer in a unidirectional
flow, at the expense of an increased pressure drop [3].
Owing to their merits, both heat sinks are commonly used
as cooling solutions for electronic components [3].
Figure 1: Plate-fin heat sink (Left), Pin-fin heat sink (Right).
Generally in forced convection heat sinks,
thermal performance is improved by increasing the
thermal conductivity of the heat sink materials, increasing
the surface area (usually by adding extended surfaces,
such as fins) and by increasing the overall heat transfer
coefficient (usually by increase fluid velocity, such as
adding fans, pumps, etc.) [4]. The employment of these
concepts is highly dependent on the relative weightings
placed on cost and pressure drop characteristics [5]. The
overall objective of the heat sink design is significant
enhancement of convective heat transfer with minimal
increases in the streamwise pressure drop penalties [6].
For a given flow condition and heat sink material, the
thermal performance of a heat sink is primarily influenced
by pressure drop and boundary layer development.
Considering the flow of air between two flat plates, as the
air progresses in the axial flow direction, a boundary layer
forms on each plate, eventually merging to form fully
developed flow. Figure 2 schematically presents this
concept. This restricts the thermal performance of the heat
sink as the distance from the leading edge increases, as
resistance to heat flow is proportional to boundary layer
thickness [7] due to the associated velocity profile
reducing convective performance.
Figure 2: Developing flow in the entrance region of the duct formed
between two parallel plates [8].
1.2 Heat Sink Optimisation
This problem may be diminished through the
employment of one of two heat sink fin optimisation
methods. The first one is to geometrically optimise the fin
arrangement i.e. thickness, height & spacing, with scope
to minimise pressure drop while maximising thermal
performance. This method is well understood, practised,
and for a given heat sink volume and flow condition, the
optimal heat sink design is well defined. The heat sink fin
spacing is configured as to allow the boundary layer to
merge just as the air flow exits the channel [9], while the
optimal fin geometry is determined through fin efficiency.
Although many geometrical optimisation studies have
been carried out for plate fin heat sinks, the employment
of these methodologies is limited by the fact that air flows
smoothly through the heat sink channels, due to the
parallel arrangement [6], thus limiting the achievable heat
transfer rates as a result of boundary layer development.
The latter optimisation method aims to determine, or
modify, a fin profile in order to minimises boundary layer
development, pressure drop and/or maximise the heat
transfer area without any penalty on the weight of the heat
sink. This method often entails the use of abstract fin
profiles, such as elliptical pin fins, segmented plate fin,
and perforated plate fins, and will be further discussed in
Section 1.3.
1.3 Literature Review
With aim to maximise thermal performance and
minimise material, various authors have employed
perforations to the fin profile. These perforations
maximise convective surface area and decrease the
pressure drop. Shaeri & Jen, Shaeri & Yaghoubi and
Ismail et. al. [10-12] all numerically investigated the
convective heat transfer from an array of solid and
perforated fins cooled by air. The perforations are
rectangular, through the length of the fin, in the

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streamwise direction, vary in quantity and size, and
subject to laminar and turbulence conditions. Note; Ismail
et. al. [12] included circular perforations in their analysis.
The authors use fin effectiveness to compare the
perforated fins to conventional plate fin heat sinks. Fin
effectiveness is defined as the ratio of heat transfer with
the fin, to the heat transfer if the fin was removed. All
cases report significant reduction in fin weight, and
increases in heat transfer area and fin effectiveness, with
perforated fins having up to 80% more effectiveness over
solid fins in the laminar regime and 65% in the turbulent
regime. Perforations are also shown to have a minimal
effect on total drag under laminar conditions, and
significantly less pressure drop (up to 24% less) at
turbulence conditions, resulting from the reduction in
wake behind the fin due to flow passing through the
perforations, thus reducing separation. Shaeri et. al. [13]
report from a numerical analysis that perforations on the
lateral surface of the fins (with perforation vectors
perpendicular to the flow direction) increase fin
effectiveness by 65% over the solid fin counterparts.
Apart from perforations, other investigators have
experimented with augmenting the design of the fins in
aim to retard boundary layer development. Soodphakdee
et. al. [14] compare plate fins and round, elliptical and
square pin fins heat sinks at moderate laminar air
velocities. The plate fins can be continuous (parallel
plates) or segmented staggered plates. Note the pin fins
configurations were inline and staggered arrays. The
investigators state that in general the staggered plate-fin
geometry showed the highest heat transfer for a given
combination of pressure gradient and flow rate. However,
the pressure drop for the staggered plate array was
considerably higher than the parallel plate. This inclines
higher pumping costs, and the authors conclude that the
geometries with the highest heat transfer characteristics
do so at the expense of pressure drop.
Sparrow and Liu [15] numerically compared an
array of inline and staggered plate fin segments over plate
fin heat sinks, under constant pumping power, heat
transfer area and laminar conditions. Segments were both
of inline and staggered array. Both segmented arrays yield
better thermal performance in comparison with the
parallel plate channel, at the expense of substantially
higher pressure drop, with the staggered array exceeding
both configurations. Despite the high pressure drop, the
authors state that the higher heat transfer per unit
exchanger length of the segmented array can prove highly
advantageous.
In 2009, Kim & Kim [1] experimentally
investigated the effects of cross-cuts on the thermal
performance of heat sinks. Cross cuts are sections
removed from the fin perpendicular to the axial direction,
analogous to segmented plate-fins, presented in Figure 3.
The authors determined that a single cross-cut is superior
to many, with single cross-cut heat sinks performing
better than the equivalent plate-fin heat sinks in most
experimental ranges, with the best cases showing better
thermal performance by 5-18%. The improvement in the
thermal performance of cross-cut heat sinks is greater as
the pumping power increases, in spite of poor flow
characteristics of cross-cut heat sinks in high pumping
power regions. This implies that the advantage of heat
transfer enhancement caused by the cross-cut far
outweighs the disadvantage of the pressure drop
increment [1].
Figure3: Conventional plate-fin heat sink (Left), Cross-cut heat sink
(Right).
In comparison to the other fin profile
augmentation designs presented, the optimised cross-cut
heat sink proposed by Kim & Kim [1] induces minimal
fabrication costs (due to the simplicity of the cross-cut
geometry), while enhancing the thermal performance of
the heat sink. This simple concept proves effective in
disrupting boundary layer development and reducing the
mass of the heat sink.
This project aims to investigate the use secondary
structures (cross-cuts) to enhance the thermal
performance of a forced convection fin array heat
exchangers, for application such as electronic cooling.
Note that heat sinks will be as geometrically similar as
possible to heat sinks used by Kim & Kim’s [1] and
experimentation will be representative to conditions used
by the authors. The project will feature experimentation
on various arrangements of cross-cut parallel plate
geometries over a range of Reynold’s numbers.
Experimental results from Kim & Kim’s [1] analysis will
be used to validate experimentation executed and in turn
validate correlations proposed by the authors for
predicting the Nusselt number and friction factor of single
cross-cut heat sinks.
1.4 Objectives
The main objective of this project is to validate an
experimental study on cross-cut heat sinks conducted by
Kim & Kim [1]. The effect of cross-cuts on the thermal
performance of a plate-fin heat sink will be investigated
and correlations proposed by Kim & Kim [1] will be
validated. The scope of the project is as follows:
 Acquire suitable heat sinks for experimentation.
 Design a wind duct to facilitate the experimental
testing of various heat sink configurations.
 Validate correlations proposed by Kim & Kim [1] for
Nusselt number and friction factor.
 Conclude the effects of the cross-cuts on the thermal
performance and pressure drop of plate-fin heat
sinks.
2. Experimental Apparatus and Procedure
2.1. Heat Sinks
Two plate-fin heat sinks were purchased fromAavid
Thermalloy – Europe. These heats sinks were fabricated

4. Jamie Fogarty - 10100598 M.Eng. Research Project 2015/2016
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using a bonded fin technique and have part number
416233. The heat sink base was fabricated using
Aluminium Alloy 6060 (k=200 W/mK [16]) and the fins
fabricated using Aluminium Alloy 1050A (k=229 W/mK,
[16]). The fins are positioned 1mm from the leading and
trailing edge of the heat sink. A detailed drawing of the
unmodified plate-fin heat sinks is present in Appendix A.
Details of the heat sink dimensions are presented in Table
1. The heat sinks were sent for secondary machining
during the experimentation process, as to allow for the
necessary configurations to generate the desired data for
comparison.
Table 1: Heat sink fixed dimensions (mm).
Base Height (Hb) 6
Base Width (W) 50
Base Length (L) 60
Fin Height (Hf) 30
Fin Length (Lf) 58
Fin Thickness (wf) 1
Channel spacing (wch) 1.5
Taking from Kim & Kim’s [1] experimentation,
the data indicates that the most effective cross-cut length
is when Lc
*=0.0833 (Lc
*=Lc/Lf), in this case
corresponding to a cross cut length of 4.8mm. Therefore,
one heat sink will contain a cross-cut to the equivalent
length. The study also signifies that the cross-cut position
has minimal effect on thermal resistance and pressure
drop. The cross cut will be positioned 17.9mm (Figure 4
(b)) from the leading edge and when the heat sink is
reversed, 37.2mm (Figure 4 (c)). The second heat sink
will have two 4.8mm cross-cuts. This is carried out as
literature suggests that segmented heat sinks have
heightened thermal performance. The cross-cuts were
positioned equidistant along the fins (Figure 4 (d)).
Figure4: Conventional plate-fin heat sink (a) alongwith other cross-cut
heat sink configurations tested.
2.2. Experimental Apparatus
The wind tunnel duct was designed and fabricated to
facilitate the experimentation of different heat sink
configurations, and is presented schematically in Figure 6.
The wind tunnel duct consisted of three sections: The fan
section, the convergence section and the working section.
The fan section housed two fans in series, which were
used to drive the necessary flow rates. The fans used were
a Muffin XP - MS12K3 and a Galaxy DC - GL48R7. This
section also housed honeycomb and wire mesh to
eliminate the swirl from air driven by the fans, ensuring a
uniform flow profile. The convergence section facilitated
the convergence from the fan section (127mm x 127mm
I/D) to the working section (50mm x 30mm I/D). The
working section is where the heat sinks were positioned.
This section solely encloses the heat sink fins and is flush
with the upper surface of the heat sink base plate. There is
no clearance between the top of the fins and the wind
tunnel. There exists 1⅓ channel width (wc) between the
fins and the two sides of the wind tunnel. The entire wind
tunnel was fabricated using 10mm thick polycarbonate
plates.
A flexible silicone heater (SRFG-202/*-P), which
has an etched foil design insulated with fiberglass, was
attached to the bottomsurface of the heat sink base plates
using a pressure sensitive adhesive. These heaters play the
role of a heat source as it was connected to a DC power
supply.
Note that in total, four power supplies were used to
give the necessary power to drive the fans and heat the
silicon heater. These were a Thurlby Thander TSP32222,
PSM 2/2A, Sorensen DCS 60-50 and a Digimess
PM3006-2. In order to measure the voltage and current to
determine the power supply to the silicone heater a Fluke
37 Multimeter was used.
Beneath the silicone heater and heat sink base plate,
30mm thick expanded polystyrene was used to ensure
minimal heat loss from the heating pad, ensuring
maximum heat transfer between the heating pad and the
heat sink. It should be noted that heat loss through the
expanded polystyrene was neglected in the calculation of
both theoretical and experimental heat sink thermal
resistance.
There are two pressure tappings on the top plate of
the wind tunnel duct in the working section to measure
the pressure drop over the heat sink in the flow direction.
The first is positioned one heat sink length (L) upstream
of the heat sink, while the other is two heat sink lengths
downstream of the heat sink. The positioning of the
pressure tappings is to ensure straight streamlines and
accurate readings. The pressure drop over the heat sink is
the difference in pressure between these two tappings.
3 Type K thermocouples (TCDirect 401-321) were
used for temperature measurement. In order to measure
the maximum temperature of the heat sink base plate,
three 1mm holes had been drilled into the heat sink base
plate to allow the thermocouples to be positioned along
the centreline, 15mm, 30mm and 45mm from the leading
edge. Another thermocouple was used to measure the
inlet air temperature. The thermocouples have an
uncertainty of approximately ±0.75%. A SR630
Thermocouple Monitor was used to convert the electrical
signals of the thermocouples into temperature readings.

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Figure6: Wind tunnel duct schematic. [TCM-Thermocouple Monitor, PSU-Power Supply Unit].
In order to determine the volume flow rate
through the wind tunnel duct, three concentric circle
orifice plates were manufactured. 3 orifice plates were
required to ensure a differential pressure difference
reachable by the fan series configuration at all flow rates
The orifice plates were interchangeable and positioned at
the inlet of the wind tunnel duct. The orifice plates
designed to the specifications in ISO 5167-1:2003, ISO
5167-2:2003 and ISO 5801:2007 [17-19] and had holes of
diameters; 35mm, 70mm and 90mm corresponding to a
diameter ratio (β) of 0.28, 0.55 and 0.71 respectively.
The specifications of the ISO standards outline
that orifice plates are to be used in circular conduits,
however in the conduction of this study the orifice plates
were fixed to a rectangular duct. A study partaken by
Bradford [20] investigates the difference in frictional
losses between circular and non-circular conduits,
concluding that the use of equivalent diameter under
turbulent flow gives satisfactory results for all sizes and
shapes of rectangular pipes. Additionally, Massey [21]
states that the use of equivalent diameter gives reasonable
results for conduits whos longer side is not greater than
about 8 times the shorter. The majority of experiments
conducted were in the turbulent regime. If one considers
the laminar friction factor for a circular conduit which is
64/Re [22] and the laminar friction factor for a square
section (such as the fan section 127mm x 127mm) which
is 56.92/Re [22]. This results in a 6.84% difference, when
compared to a circular conduit, for the full range of
laminar Reynolds numbers experimented, however for the
purposes of comparison of heat sink thermal resistances,
the percentage difference is minimal and is on a
comparable scale.
The air volume flow rate through the wind tunnel
duct and the pressure drop over the heat sink were
measured using a FCO 510 micro-manometer. The micro-
manometer has a full range of 0-200 Pa and an
uncertainty of ±0.025%.
2.3. Experimental Procedure
The fans were initiated and the micro-manometer
was positioned to read the ambient to inlet orifice plate
pressure drop. This was carried out to manipulate the
voltage on the fans to acquire the desired flow rate. Once
the desired flow rate was achieved the silicone heater was
powered on giving a heat load (q) of 23.33W, checked by
the multimeter, and was allowed to stabilise. Once the
heat load was fixed the base temperature of the heat sink
was monitored until the change in temperature was ±1 °C,
this indicated that a steady state had been reached. With
steady-state conditions the tubes of the micro-manometer
were positioned to read the pressure drop across the heat
sink and the maximum temperature of the heat sink base
plate was noted. The thermal resistance was calculated
from;
𝑅 =
𝑇 𝑤,𝑚𝑎𝑥−𝑇𝑏𝑚,𝑖𝑛
𝑞
[1]
3. Theory and Equations
3.1 Pumping Power
By measuring the volume flow rate through the wind
tunnel duct and the pressure drop over the heat sink, the
associated pumping power may be calculated from the
following equation:
𝑃𝑝 = 𝑄̇ 𝑥∆𝑃 [2]
3.2 Cross Cut Correlations
Kim & Kim [1] proposed correlations for predicting
the friction factor and the Nusselt number of a single-
cross-cut heat sink based on experimental results. The
correlations are founded on the basis that single-cross-cut
heat sinks have similar shape to plate-fin heat sinks
except for the cross-cut region. Therefore, semi-empirical
coefficients were added to the pre-existing plate-fin semi-
empirical correlations proposed by Teertstra,[23] and
Muzychka and Yovanovich [24] for Nusselt number and
friction factor respectively. These semi-empirical
coefficients account for the effect of the cross-cut region.
3.3 The Friction Factor Correlation
The friction factors for parallel plates are suitably
reported in the composite model form of the two limiting
cases involving hydrodynamically developing and fully
developed flows [24]. These limits are asymptotically
connected. This correlation is modified for cross-cut heat
sinks through the addition of two semi-empirical
coefficients α and β [15];
𝑓𝑎𝑝𝑝 𝑅𝑒 𝐷ℎ
= [(
3.44
√𝐿+
)
2+𝛼
+ (𝑓𝑅𝑒 𝐷ℎ
)
2+𝛽
]
1
2
[3]

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Where,
𝐿+
=
𝐿
𝐷ℎ 𝑅𝑒 𝐷ℎ
[4]
𝑓𝑅𝑒 𝐷ℎ
= 24 − 32.527(
𝑤 𝑐ℎ
𝐻
) + 46.721(
𝑤 𝑐ℎ
𝐻
)
2
−40.829(
𝑤 𝑐ℎ
𝐻
)
3
+ 22.954(
𝑤 𝑐ℎ
𝐻
)
4
− 6.089(
𝑤 𝑐ℎ
𝐻
)
5
[5]
𝛼 = 𝐿 𝑐
∗
𝜀(88− 304𝜀 + 267𝜀2)x exp(−0.5(
𝐿 𝑐
∗ −(0.1−0.06𝜀)
−0.12−0.32𝜀
)
2
[6]
𝛽 = 𝐿 𝑐
∗
{
(0.1 + 0.4𝜀) + (170 − 621𝜀+ 533𝜀2)
𝑥 𝑒𝑥𝑝(−0.5 (
𝐿 𝑐
∗ −(0.06−0.11𝜀)
−0.01−0.09𝜀
)
2
)
} [7]
The friction factor may be converted to a
pressure drop thru the following equation;
𝛥𝑃 = (𝐾𝑐𝑥 + 4. 𝑓𝑎𝑝𝑝.
𝐿
𝐷ℎ
+ 𝐾𝑒𝑥). 𝜌.
𝑣2
2
[8]
Where,
𝐾𝑐𝑥 = 0.42(1 − 𝜎2) [9]
𝐾𝑒𝑥 = (1 − 𝜎2
)2
[10]
σ is the ratio of the area of the flow channels to that of the
flow approaching the heat sink.
3.4 The Nusselt Number Correlation
A Nusselt number correlation for cross-cut heat sinks
was also developed based on a composite model of the
two limiting cases of thermally developing and thermally
developed asymptotes [23]. Addition of the empirical
coefficients γ and δ [15] modifies this pre-existing
correlation to account for the cross-cut region.
𝑁𝑢 =
[
1
(
𝑅𝑒
𝐷ℎ
∗
𝑃𝑟
2
)
3+𝛾 +
1
(0.644√ 𝑅𝑒 𝐷ℎ
∗
𝑃𝑟
1
3
√
1+
3.65
√ 𝑅𝑒
𝐷ℎ
∗
)
3+𝛿
]
−
1
3
=
ℎ𝐷ℎ
𝑘 𝑓
[11]
Where,
𝑅𝑒 𝐷ℎ
∗
= 𝑅𝑒 𝐷ℎ
.
𝑤 𝑐ℎ
𝐿
[12]
𝛾 = 𝐿 𝑐
∗
𝜀(399 − 1254𝜀 + 971 𝜀2)(−955 + 3500𝜀 −
3140 𝜀2)x exp(−0.5 (
𝐿 𝑐
∗
−(3.6−11.3𝜀+8.5𝜀2
)
−2.2+7.4𝜀 −5.8𝜀2
)
2
[13]
𝛿 = 𝐿 𝑐
∗
𝜀(26 − 82𝜀 + 65𝜀2)
𝑥 {
(−292 + 958𝜀 − 772𝜀2) + (498 − 1680𝜀 + 1387𝜀2)
x exp(−0.5 (
𝐿 𝑐
∗
−(2.7−8.8𝜀+7.3𝜀2
)
−0.55+1.97𝜀−1.6𝜀2
)
2 }
[14]
As for a plate-fin heat sink, for a single-cross-cut
heat sink the thermal resistance is given by,
𝑅 =
1
ℎ( 𝐴 𝑏+𝜂𝐴 𝑓)
+
𝐻−𝐻 𝑓
𝑘 𝑏.𝑤.𝐿
[15]
When the dimensionless length of a cross-cut becomes
zero, the empirical coefficients α, β, γ and δ converge to
zero. This results in the proposed correlations reverting to
the standard correlations for Nusselt number and friction
factor of conventional plate-fin heat sinks. These standard
correlations where used in the theoretical calculations in
section 4.1.
4. Results and Discussion
4.1. Validation
In order to validate the functionality of the designed
experimental apparatus and the validity of the present
study, experimental data from the tested plate-fin heat
sink were compared to existing correlations for heat sink
thermal resistance and pressure drop. Figure 6 (a) show
that the measured thermal resistance correlates closely
with the correlation proposed by Teerstra et. al. [23],
within an average of 17% difference. Additionally, the
measured pressure drop shown in Figure 6 (b) is in good
agreeance with the correlation proposed by Muzychka
and Yovanovich [24], with an average of 8% difference.
Taking from the comparisons, the experimental apparatus
is functional and the experiments were properly executed.
4.2. Discussion
This section is divided into 3 sub-sections. Section
4.2.1 discusses the effects of a single cross-cut and its
positioning on thermal resistance and approach velocity,
while Section 4.2.2 discusses the effect of two cross-cuts.
The results for the various heat sink configurations tested
are normalised against the results obtained for the
conventional plate-fin heat sink. This provides a ratio to
quickly determine if a variable is above or below that of
the plate-fin heat sink. Figure 7 (a) and (b) present the
normalised results obtained for thermal resistance and
approach velocity respectively. Section 4.2.3 discusses
the validity of the modified correlations proposed by Kim
& Kim [1], based on the experimental results found in
Figure 8 (a) and (b) for thermal resistance and pressure
drop accordingly.
4.2.1 Single Cross-Cut Heat Sink
It is evident from the thermal resistance ratio plot
(Figure 7 (a)) that one cross-cut is more effective than
multiple, with a thermal enhancement in the range of 4-
13%. At low pumping power, the approaching velocity
ratio (Figure 7 (b)) of the single cross-cut heat sinks is
above 1, due to the reduction in skin friction proportional
to the reduction in fin surface area in contact with the
moving air. This corresponds to a lower pressure drop in
than that of the plate fin heat sink, which would generally
induce a higher thermal resistance. However, despite flow
separation and secondary flow effects being negligible
terms of pressure drop, the combination of the
aforementioned and the increased flow velocity prove
effective in enhancing the thermal performance.

7. Jamie Fogarty - 10100598 M.Eng. Research Project 2015/2016
7
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
0.01 0.1 1
Rhs/Rhs,plate
Pumping Power (W)
CC_CLE
CC_FLE
2CC
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0.01 0.1 1
V/Vplate
Pumping Power (W)
CC_CLE
CC_FLE
2CC
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
0.010 0.100 1.000
PressureDrop(Pa)
Pumping Power (W)
Theory
Experimental
Error Bar 10%
ErrorBar 20%
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.010 0.100 1.000
ThermalResistance(K/W)
Pumping Power (W)
Theory
Experimmental
Error Bar 10%
Error Bar 20%
0
10
20
30
40
50
60
70
80
90
100
110
120
130
0.01 0.1 1
PressureDrop[Pa]
Pumping Power [W]
Theory
CLE
FLE
Error Bar 10%
Error Bar 20%
0
0.2
0.4
0.6
0.8
1
1.2
0.01 0.1 1
ThermalResistance[K/W]
Pumping Power [W]
Theory
CLE
FLE
Error Bar 10%
Error Bar 20%
Error Bar 50%
(b)(a)
(a) (b)
Figure6: Validation ofexperimental results. (a) Thermal Resistance and (b) pressure drop.
Figure7: Ratio of cross-cut heat sinkto plate-fin heat sink for (a) thermalresistance and (b) approach velocity. Note CC=cross-cut, CLE=closest to leading
edge, FLE=furthest from leading edge.
Figure8: Validation ofcross-cut correlations. (a) Thermal resistance and (b) pressure drop.
(a) (b)

8. Jamie Fogarty - 10100598 M.Eng. Research Project 2015/2016
8
As the pumping power increases, the effect of
poor flow characteristics caused by the cross-cut region
become prominent as the approach velocity ratio
decreases below 1; consequently, the thermal resistance
ratio is seen to increase. With a further decrease in
approach velocity ratio (increase in pressure drop) the
secondary flow effects of the cross-cut region prove
advantageous due to the decrease in thermal resistance
ratio. This trend is seen to continue past Pp=0.05W and
becomes more dominant as the pumping power increases
with a maximum enhancement of 13% at Pp=1W.
The positioning of the cross-cut does have a
noticeable effect on the thermal performance of the cross-
cut heat sinks. According to the approach velocity ratio
plot, when the cross-cut is positioned further away from
the leading edge, there is a direct decrease in the approach
velocity that is seen to digress from its counterpart i.e.
cross-cut closer to the leading edge. When the cross-cut is
situated further away from the leading edge, the thermal
resistance is enhanced by 2.5%, at Pp=1W, then if the
cross-cut where positioned closer to the leading edge.
4.2.2 Double Cross-Cut Heat Sink
In terms of the double-cross cut heat sink, the
thermal performance of this heat sink is worse than all
other configurations for the majority of experimental
ranges tested. At a pumping power of 0.01W, the
approach velocity is considerably above 1, loaning to the
reduction in material and in turn a reduction in skin
friction; giving a lower pressure drop and in turn a higher
flow rate. The thermal resistance at this pumping power is
seen to match that of the plate fin heat sink.
As the pumping power increases, the approach
velocity ratio decreases while the thermal resistance
increases. The fact that the boundary layer has to reattach
twice gives a higher pressure drop, that outweighs the
potential thermal enhancement advantage of boundary
layer redevelopment. A further increase in pumping
power above Pp=0.1W reduces the thermal resistance, as
the approach velocity ratio is seen to drop considerably
below 1. At Pp=1W there is a 6% thermal resistance
improvement over the plate-fin heat sink, however this is
below that of the single cross-cut heat sink.
4.2.3 Cross-Cut Correlations
Figure 8 (a) and (b) present the modified cross-cut
correlations for thermal resistance and pressure drop
respectively, proposed by Kim & Kim [1]. The thermal
resistance correlation predicts the cross-cut heat sink
within 27.7% averaged discrepancy, while the friction
factor (converted to a pressure drop in Figure 8 (a)) within
12.4%. The pressure drop is particularly accurate,
however there is a larger discrepancy between the thermal
resistance correlation and the experimental results. This
may loan to the fact that the heat sinks are bonded fin, and
a thermal contact resistance at the fin base may cause a
higher thermal resistance. Other factors may play reason
here; however, the correlation is sufficient in predicting
the thermal resistance within an estimation range.
5. Conclusions
Overall, the single cross-cut heat sinks are seen to
better preform when compared to the plate-fin heat sink,
in terms of thermal resistance. The most significant
findings of this project are as follows;
 A single cross-cut is superior to multiple
 A thermal enhancement between 4-13% is
achievable in the pumping power range 0.01-1W
 Cross-cut position has a noticeable effect, and is
seen to improve thermal resistance by 2.5%
when situated further away from the leading
edge, then closer.
 Cross-cut heat sinks experience a lower approach
velocity and higher pressure drop than plate-fin
heat sinks, due to friction drag and reattachment
of the boundary layer.
 In this experimental case, thermal resistance and
friction factor of cross cut heat sinks may be
predicted by modified correlations proposed by
Kim & Kim [1] within an average discrepancy of
27.7% and 12.4%, respectively.
Thermal enhancement was achieved, and plate-fin heat
sinks may decrease their size, while holding the same
thermal resistance through use of an individual cross-cut.
This in turn will aid the increasing problem of heat
concentrations due to increased circuit density with devise
miniaturisation.
6. Recommendations for future work
At higher pumping powers, approaching 1W, the
airside to orifice plate pressure drop tended to fluctuate
minutely. As a result, some experiments took longer than
others, as the pressure reading had to be sampled and
averaged until it converged onto one value. Having more
pressure tappings proceeding the orifice plate would
diminish this effect and give better resolution in readings.
Heat sinks tested in this project had small channel
widths, the effects of cross-cuts on plate-fin heat sinks
with larger channel widths should be tested to determine
if thermal enhancement is still achievable.
Acknowledgements
I would sincerely like to thank Dr. Jeff Punch for his
guidance and help throughout the project, Dr. Joseph
Leen & Brian Nestor for fabrication of the wind tunnel
duct and other associated parts, and finally my friends and
family for their support.
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9
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10. Appendix A
A-1
Appendix A – Plate-fin heat sink drawing.
FigureA1: Unmodified plate-fin heat sink from Aavid Thermalloy –Europe (part #416233). Dimensions are in mm.