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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
2364
A Comparative Analysis of Flow Boiling in Micro-Gaps with
Internal Micro-Fins of Rectangular and Triangular Profiles
Shugata Ahmed
Department of Mechanical Engineering, Faculty of Engineering,
IIUM, Jalan Gombak, 53100 Kuala Lumpur, Malaysia.
Ahmad Faris Ismail
Department of Mechanical Engineering, Faculty of Engineering,
IIUM, Jalan Gombak, 53100 Kuala Lumpur, Malaysia.
Erwin Sulaeman
Department of Mechanical Engineering, Faculty of Engineering,
IIUM, Jalan Gombak, 53100 Kuala Lumpur, Malaysia.
Muhammad Hasibul Hasan
Department of Manufacturing and Materials Engineering, Faculty of Engineering,
IIUM, Jalan Gombak, 53100 Kuala Lumpur, Malaysia.
Abstract
Micro-gap heat sinks can be used for extensive evaporative
cooling of micro-electronic devices, micro-electro-mechanical
systems (MEMS) and micro-opto-elecro-mechanical systems
(MOEMS). Internal micro-fins may increase two-phase heat
transfer rate by extending surface area. However, excessive
pressure drop is one of the significant drawbacks of two-phase
cooling. Fin shapes play an imperative role in flow boiling
heat transfer rate and pressure drop penalty. The scope of this
paper is to estimate two-phase heat and mass transfer,
pressure drop, wall shear stress development and turbulent
characteristics of micro-gaps with rectangular and triangular
micro-fins by numerical simulation using water coolant.
Simulation has been carried out by FLUENT 14.5 release.
Volume of fluid (VOF) model along with Renormalization
Group Theory (RNG) k-ɛ turbulence model has been used for
fluid flow and heat transfer modeling. Governing equations
have been solved numerically by Finite Volume Method
(FVM). Simulation results demonstrate that thermal resistance
of triangular fin micro-gap is higher than rectangular fin heat
sink. Thermal resistance declines with pumping power
increment. However, for both of the heat sinks, decrement rate
drops-off after 0.004 W pumping power. In comparison to
triangular fin micro-gap, turbulent kinetic energy generation is
found higher for rectangular fin heat sink. Although
rectangular fin micro-gap shows superior heat transfer
performance, pressure drop penalty is also larger than
triangular fin micro-gap. Hence, it is recommended that
pressure drop should be minimized by optimizing geometrical
parameters and boundary conditions.
Keywords: micro-gap, micro-fin, thermal resistance, wall
shear stress, turbulent kinetic energy
Introduction
In modern world, miniature electronic devices have immense
popularity because of their light weight and carrying facility.
Beside civil applications, integrated devices are also used for
military and research purposes. These devices are densely
packed ICs, which produce high heat flux during operation.
Various micro-sensors are also embedded in these devices.
Some of these sensors are micro-electro-mechanical systems
(MEMS) or micro-opto-electro-mechanical systems
(MOEMS), which are extremely responsible for heat flux
generation. Due to the advancement of micro-fabrication
techniques, micro-electronic devices are becoming more
compact gradually, while speed and functionality are
increasing. As a corollary, dissipated heat flux from these
advanced devices is escalating. Thermal management of these
components is a major challenge for researchers.
Conventional air cooling technology is not sufficient for
future compact high speed devices.
Micro-channel heat sinks provide substantial cooling facility
for miniature devices. It was first introduced by Tuckerman
and Pease[1] for single-phase cooling of integrated devices by
water coolant. Beside high heat flux removal rate, they
noticed significant pressure drop in micro-channel because of
its small dimensions. Later researches were carried out on
evaporative cooling performance of micro-channels. Many
researchers reported that heat flux removal rate during flow
boiling is much higher than single-phase cooling[2][3].
However, some disadvantages of two-phase cooling were also
mentioned in the literature. Some of the drawbacks are higher
pressure drop, flow boiling instabilities such as temperature
and pressure fluctuations, flow reversal, exceeding critical
heat flux (CHF) and hot spot generation[4][5].
Recently, micro-gap heat sinks have been found potential to
reduce prevailing two-phase problems[4]. Alam et al.[5]
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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showed that micro-gap heat sinks reduce flow instabilities and
generate more uniform surface temperature than micro-
channels. According to Sheehan and Bar-Cohen[6],
temperature fluctuation in micro-gap heat sink depends on
vapor quality and wall heat flux. Again, Alam et al.[7]
revealed that convective heat transfer coefficient in micro-gap
heat sink is higher for smaller gap sizes. However, for smaller
gap sizes, pressure drop was reportedly high. In another
publication, Alam et al.[8] stated that below of gap
height, dry out takes place very early. Hence, it is not suitable
for cooling purpose. They showed that the gap size should be
between for effective cooling.
High heat transfer capability of micro-gaps can be achieved
by adding internal micro-fins[9][10]. Fins not only extend
surface area but also generate turbulence[11]. Hence,
convective heat transfer rate augments by rapid fluid mixing.
Yeom et al.[12] remarked that fluid dynamic effects are
dominant over surface area extension for heat transfer
enhancement using micro-fins. According to them, Micro-fins
also improve boiling and condensing surfaces. At the present
time micro-fins are used in heat exchangers, heat pipes, heat
sinks and many other high temperature applications[13].
Many researches were carried out on heat transfer
enhancement using micro-fins. Although micro-fins increase
heat transfer rate, most of the publications highlighted
significant pressure drop during flow over micro-finned
surfaces[14][15][16]. Fin shapes have critical role on heat
transfer and pressure drop characteristics of heat sinks[17].
Different opinions are found in the literature about impact of
fin shapes on cooling performance.
In a comparative study between micro-square pin-fin and
column pin-fin, Zhao et al.[18] accomplished that earlier one
shows better cooling performance. However, higher pressure
drop was also addressed for micro-square pin fin. Ricci and
Montelpare[19], Montelpare and Ricci[20] found that
triangular and rhomboidal micro-fins have higher convective
heat transfer rate than square and circular fins. However,
Hasan et al.[21] showed that in a nano-fluid cooled heat sink,
circular micro-fins have better thermal management capability
in comparison to square and triangular fins. Pressure drop is
related to friction factor. Higher friction factor results larger
pressure drop. In comparison to different fin profiles,
minimum friction factor was reported for triangular fins by
Zhao et al.[22].
Micro-gap heat sinks incorporated with micro-fins may
substantially elevate rate of evaporative cooling. Escalation of
two-phase heat transfer rate is susceptible to turbulent or
pseudo-turbulent nature of flow boiling influenced by micro-
fins. Recently, Ahmed et al.[23] elaborated the concept of
integrating rectangular micro-fins with micro-gap heat sinks
for two-phase heat transfer enhancement. A wide range of
simulation results revealed that micro-finned micro-gaps are
eligible for removing high heat fluxes if operated with high
Reynolds number. However, geometrical parameters are
greatly responsible for heat flux removal rate and turbulence
generation[24][25].
In Literature, efforts to estimate effects of using micro-fins of
different profiles in micro-gap heat sinks have not been
recognized. In this paper, a comparative study on flow boiling
characteristics of micro-gaps with internal micro-fins of
rectangular and triangular profiles have been carried out by
numerical simulation. Commercial CFD software FLUENT
14.5 release has been used for simulation purpose. Water has
been used as coolant. Evaporation rate, thermal resistance,
pressure drop, wall shear stress and turbulent kinetic energy
generation have been observed for varying heat flux and
pumping power.
Problem Description
Two micro-gap heat sinks of footprint area,
height and length have been considered in this
study. Channel material is aluminum. In both heat sinks, the
gap height is , upper and lower substrate thicknesses are
and 2 respectively. However, two heat sinks have
different shapes of internal micro-fins (rectangular and
triangular) with identical cross-sectional area. Due to variation
in fin shape, available surface area for convection as well as
hydraulic diameter of two heat sinks are distinct. Geometrical
parameters have been given in TABLE. 1. Geometries have
been created by ANSYS Workbench Design Modeler, which
are shown in Figure 1.
Table 1. Geometrical parameters
Parameters (unit)
Rectangular
fin gap
Triangular
fin gap
Cross sectional area,
21.8
21.8
Convective surface area,
Hydraulic diameter,
1.11
1.45
Figure 1: Geometry of micro-gaps with (a) rectangular micro-
fins (3D view), (b) rectangular micro-fins (cross-sectional
view), (c) triangular micro-fins (3D view), (d) triangular
micro-fins (cross-sectional view).
Liquid water enters into the micro-gap at a specific
temperature and flow rate. Heat is applied at the bottom of the
sink with a constant power. Applied heat energy transfers
through base metal and micro-fins by conduction and from
solid-fluid interface to fluid by convection. Liquid water
absorbs heat energy during flow through micro-gaps and
boils. As two micro-gaps have same cross-sectional area,
variation in heat transfer and pressure drop clearly take place
because of different surface areas.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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Mathematical Model
Flow Boiling and Heat Transfer
Volume of fluid (VOF) model[26] has been adopted for
modeling two-phase flow and heat transfer in micro-gaps.
Steady-state governing equations have been derived and
solved numerically for proper boundary conditions.
Continuity equation:
(1)
Here, is void fraction, is vapor velocity, is the density
of vapor and is mass transfer from liquid to vapor phase
due to evaporation.
Conservation of momentum equation:
(2)
Here is the density of liquid-vapor mixture, which is defined
as following:
(3)
In (2), is fluid pressure, is dynamic viscosity of fluid and
is surface tension force. Continuum surface force (CSF)
method[27] has been used to calculate surface tension. The
equation is the following:
(4)
Here, is surface tension coefficient. For water, .
is local curvature of liquid-vapor interface.
Conservation of energy equation:
(5)
Here and are enthalpy and temperature of vapor
respectively, represents effective thermal conductivity
and is the enthalpy of vaporization.
For solid domain, the energy equation can be written as:
(6)
Here represents temperature of the solid domain.
Turbulence modeling
As stated earlier, fins are responsible for generating
turbulence. Hence, a turbulence model is necessary for
complete flow modeling. Turbulent flow in micro-gaps with
internal micro-fins has been simulated using Renormalization
Group Theory (RNG) turbulence model[28]. Governing
equations for turbulence are given below:
(7)
(8)
In above equations, and are turbulent kinetic energy and
rate of energy dissipation respectively.
= generation of turbulent kinetic energy due to the mean
velocity gradients.
= generation of turbulent kinetic energy due to buoyancy.
= contribution of the fluctuating dilatation in compressible
turbulence to the overall dissipation rate.
and are inverse effective Prandtl numbers for and
respectively and and are source terms.
The model constants have following default values:
= 1.42, = 1.68
Modeling mass transfer
During boiling, mass transfer takes place between liquid and
vapor phases. Mass exchange between two phases is
calculated from evaporation-condensation model, proposed by
Lee[29]. Following equation is used:
(9)
Here, is the evaporation coefficient. Wu et al.[30], De
Schepper et al.[31] and Alizadehdakhel et al.[32]
recommended to maintain interfacial temperature
close to saturation temperature (.
Boundary conditions
Various boundary conditions are defined at inlet, outlet and
outer walls of the heat sinks, which are stated below:
Inlet: , , . In this study, inlet
temperature of water has been kept constant at 25 .
Turbulence intensity is also defined at the inlet. For fully
developed internal flow, turbulence intensity is calculated
from following formula:
(10)
Here, = root mean square of velocity fluctuations
= mean flow velocity
= Reynolds number
Outlet: . Atmospheric pressure is defined at the
outlet of the heat sink.
Solid-fluid interface: Heat transfer from wall to fluid is by
convection. Convective heat transfer coefficient is calculated
from following equation:
(11)
Here, is convective heat transfer coefficient, is heat
transfer rate by convection, is surface area, and are
temperature of solid and fluid respectively.
Channel bottom wall: Uniform heat flux is applied at the
bottom of the heat sink. Heat is transferred through solid wall
by conduction in the normal direction of bottom surface. Heat
flux transferred by conduction is calculated from following
equation:
(12)
Other channel walls: Other channel walls are considered as
insulated. Hence, . As a result, temperature gradient
at boundaries:
(13)
Subsidiary equations
Total thermal resistance, summation of conductive and
convective thermal resistance, is calculated to comprehend the
heat transfer performance of the heat sink. Following equation
is used:
(14)
Here, is the height of the micro-gap, which is the length of
heat conduction path, and represent available surface
area for heat transfer by conduction and convection
respectively.
Required pumping power is calculated using following
formula[33]:
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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(15)
Here, is the cross-sectional area and represents pressure
drop.
Mesh Generation and Simulation
Hybrid meshes have been created by ANSYS Workbench.
Number of elements should be optimized to minimize
computational time. Surface Nusselt number has been
observed for different numbers of meshing elements. It has
been determined that maximum can be obtained for
3633747 and 3737799 numbers of elements for rectangular
and triangular fin grids respectively.
Governing equations have been solved numerically by Finite
Volume Method (FVM). Semi-Implicit Method for Pressure
Linked Equations (SIMPLE) algorithm[34] has been used to
solve pressure velocity coupling equation.
Following assumptions have been made for numerical
analysis:
Flow is steady-state and fully developed.
Heat transfer by radiation is negligible.
Solid and fluid properties are independent of temperature.
All used properties of materials are given in TABLE. 2.
Table 2: Thermophysical properties of materials at
25C temperature
Results and discussion
Rate of evaporation
Mass exchange from liquid to vapor phase is calculated from
(9). In Figure 2 and Figure 3, rate of mass transfer from per
unit volume of fluid due to evaporation in rectangular
and triangular-fin micro-gaps have been plotted for
incrementing heat flux and pumping power
respectively. It is accomplished that rate of evaporation
escalates with ascending heat flux. However, for advancing
pumping power, a steeply decreasing trend of evaporation rate
is noted at the beginning, which diminishes after surpassing
0.004 W of pumping power for both heat sinks. Figure 2 also
exhibits that for same heat flux, evaporation rate in triangular
fin micro-gap is greater than rectangular fin heat sink.
Figure 2: Rate of evaporation from per unit volume vs.
effective heat flux for rectangular and triangular fin micro-
gaps
Figure 3: Rate of evaporation from per unit volume vs.
pumping power for rectangular and triangular fin micro-gaps
at heat flux
Heat transfer characteristics
From Figure 4, it is perceived that convective heat transfer
coefficient (h) of rectangular fin micro-gap is higher than
triangular fin gap. From (11), it is clearly observed that h
depends on surface area (A). Rectangular fin micro-gap has
larger surface area than triangular fin heat sink. Hence,
convective heat transfer coefficient is greater for earlier heat
sink.
Properties (unit)
Aluminum
Water
(liquid)
Water
(vapor)
Density,
2702
998.2
0.55
Thermal conductivity,
202.4
0.6
0.026
Specific heat capacity,
9030
4182
1859
Viscosity,
_
890.3
1.34×
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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Figure 4: Area-weighted average heat transfer coefficient of
upper and lower surfaces vs. effective heat flux for
rectangular and triangular fin micro-gaps
Again, it is seen that heat transfer coefficient of lower surfaces
decline with heat flux increment after onset of boiling (ONB).
However, h remains almost invariant with heat flux variation
for upper surfaces. As a net effect, total thermal resistance
of the heat sinks elevate after incipience of boiling,
which is shown in Figure 5. In literature, contradictory
opinions are found about influence of heat flux on heat
transfer coefficient. Zhao et al.[35], Lee and Lee[36] reported
that two-phase heat transfer coefficient is independent
of heat flux. On the other hand, Bertsch et al.[37] showed that
is strongly influenced by heat flux. In the present
simulation, upper and lower surfaces have shown different
behaviors regarding dependency of heat transfer coefficient on
heat flux. Because of higher heat transfer coefficient, total
thermal resistance of rectangular fin micro-gap is lower
than triangular fin heat sink. Gunnasegaran et al.[38] also
noticed that triangular microchannel heat sinks exhibit lower
thermal performance than rectangular microchannels.
In Figure 6, it is observed that diminishes with pumping
power increment. Declining characteristics of with
pumping power increment for rectangular and triangular fin
micro-gaps are quite similar. Descending rate is high for
lower pumping powers. After , decrement rate
drops-off for both of the heat sinks. Hence, increment of
pumping power is not always cost effective. A similar trend
was also reported by Hung and Yan[39], Manaf et al.[40] for
single-phase flow of water in microchannel heat sink.
Figure 5: Total thermal resistance vs. effective heat flux for
rectangular and triangular finned micro-gaps
Pressure drop
Pressure distribution in rectangular and triangular fin micro-
gaps is illustrated in Figure 7. It is seen that pressure
decreases in the flow direction.
From Figure 8, it is apprehended that for both of the heat
sinks, pressure drop is consistent with heat flux increment for
single-phase flow. However, as expected, it is found that
pressure drop ascends after onset of boiling (ONB) at
heat flux.
Although heat transfer performance of rectangular fin micro-
gap is superior to triangular fin heat sink, from Figure 8 it is
observed that pressure drop in rectangular fin micro-gap is
larger than triangular fin gap. As cross-sectional area of both
heat sinks are same , pressure drop
variation clearly occurs due to different surface areas.
Pressure drop in rectangular fin micro-gap is higher due to
larger surface area.
Figure 6: Total thermal resistance vs. pumping power for
rectangular and triangular finned micro-gaps at
heat flux
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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Figure 7: Pressure distribution on X-Z plane at Y=2.5 mm in
micro-gaps with (a) rectangular micro-fin, (b) triangular
micro-fin for heat flux
Figure 8: Pressure drop vs. effective heat flux for rectangular
and triangular fin micro-gaps
From (15), it is comprehended that pressure drop is influenced
by pumping power. Relation between pressure drop and
pumping power in micro-fin gaps is elucidated in Figure 9. As
expected, it is noticed that in both heat sinks, pressure drop
augments with pumping power increment. A similar trend was
also observed by Hung et al.[41] for single-phase flow in
double-layer microchannel heat sink.
Figure 9: Pressure drop vs. pumping power for rectangular
and triangular fin micro-gaps at heat flux
Wall shear stress
Wall shear stresses developed on upper and lower surfaces of
rectangular and triangular fin micro-gaps during flow boiling
have been plotted against pumping power increment in Figure
10. Similar to pressure drop, shear stress increases with
pumping power increment in both heat sinks. Almost equal
amount of shear stresses are developed on both surfaces in a
heat sink for a particular pumping power. However, shear
stress developed in triangular fin micro-gap is slightly higher
than rectangular fin heat sink.
Figure 10: Wall shear stress vs. Reynolds number for
rectangular and triangular fin micro-gaps at
heat flux
Wall shear stress development on lower surfaces of
rectangular and triangular fin micro-gaps are visualized in
Figure 11. Almost uniform shear stress distribution on
interfaces are noted. A slight variation can be perceived near
walls of the heat sinks.
Turbulent characteristics
Turbulent kinetic energy (k) distribution on X-Z plane in
rectangular and triangular fin micro-gaps are given in Figure
12. It is perceptible that turbulent kinetic energy increases in
the flow direction. However, it is observed that triangular fin
micro-gap is less capable of generating turbulent kinetic
energy in comparison to rectangular fin heat sink. Due to
higher pressure drop, higher velocity is obtained in
rectangular fin gap. As a result, greater turbulent kinetic
energy generation is observed.
Figure 11: Wall shear stress distribution on lower interface of
micro-gaps with (a) rectangular micro-fin, (b) triangular
micro-fin for heat flux
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 4 (2016) pp 2364-2372
© Research India Publications. http://www.ripublication.com
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Figure 12: Turbulent kinetic energy distribution on X-Z plane
at Y=2.5 mm in micro-gaps with (a) rectangular micro-fin, (b)
triangular micro-fin for heat flux
Further, contour plot of turbulent kinetic energy distribution at
the outlet cross-sections of the heat sinks are displayed in
Figure 13. In rectangular fin micro-gap, k is found higher
around fins. It attributes that rectangular fins are responsible
for turbulent kinetic energy production in micro-gap. On the
other hand, contribution of triangular fins in generation of
turbulent kinetic energy is not recognized.
Figure 13: Turbulent kinetic energy distribution on Y-Z plane
at the outlet in micro-gaps with (a) rectangular micro-fin, (b)
triangular micro-fin for heat flux
In Figure 14, it is perceived that for both of the heat sinks, Δk
increases after ONB. However, increment rate in triangular fin
micro-gap is much higher than rectangular fin heat sink. For
very high heat flux , Δk of triangular fin gap
is found higher than rectangular fin heat sink.
Figure 14: Turbulent kinetic energy vs. effective heat flux for
rectangular and triangular fin micro-gaps
Conclusion
Two-phase heat transfer and pressure drop in micro-finned
micro-gaps are significant issues for developing high
performance cooling systems with small pumping power
requirement. This paper concerns about characteristics of two-
phase flow in micro-gaps with rectangular and triangular
micro-fins. Rate of evaporation, thermal resistance, pressure
drop, wall shear stress development and turbulent
characteristics have been compared by numerical simulation.
Rectangular fin micro-gap shows better heat transfer
performance than triangular fin heat sink for larger pressure
drop and wall shear stress penalties. Pressure drop and shear
stress can be reduced by optimizing geometrical parameters
and boundary conditions.
In this study, a steady-state solver has been used. However, a
transient solver may provide more realistic results as relevant
literatures suggest that temperature and pressure fluctuate with
time during flow boiling.
Acknowledgment
The support of the Ministry of Education, Malaysia under the
grant FRGS 13-020-0261 is gratefully acknowledged. This
research was also supported by International Islamic
University Malaysia from Endowment Type B fund (EDW
B14-127-1012).
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