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Flow boiling heat transfer in
microchannel
A preliminary final year project report submitted in partial fulfilment of the
requirement for the degree of
B.Tech. in Mechanical Engineering (2014-2018)
By
Aritra Chatterjee(Roll No. 20)
Debanjan Baksi(Roll No. 34)
Debanjan Paul(Roll No. 35)
Debtanu Maitra(Roll No.38)
Under the guidance of
Prof. Dibyendu Mondal
Mechanical Engineering Department
Academy of Technology
G.T. Road, Adisaptagram, P.O.: Aedconagar
Hooghly-712121, West Bengal
May, 2017
1
Certificate of Recommendation
This is to certify that the project entitled “Flow Boiling Heat Transfer
in Microchannel” which is being submitted by Aritra Chatterjee,
Debanjan Baksi, Debanjan Paul and Debtanu Maitra, in partial
fulfilment for the award of Degree of Bachelor in Technology in
Mechanical Engineering from Academy of Technology, Hooghly –
712121, under Maulana Abul Kalam Azad University of Technology
(MAKAUT, formerly known as WBUT) for the 2014-2018 session, is
the record of the following students’ work under my supervision.
________________ _________________
(Aritra Chatterje) (Debanjan Baksi)
(Roll No. 20) (Roll No. 34)
________________ _________________
(Debanjan Paul) (Debtanu Maitra)
(Roll No. 35) (Roll No. 38)
Prof. ________________
Supervisor, Dept. Of Mechanical Engineering. Examiners
________________
________________
Prof. ________________
Head of Dept. of Mechanical Engineering
2
Abstract
The following report is a brief overview of microchannels and the
concept of flow boiling. A literature review of flow boiling in
microchannels has also been included. This is just a premiliminary
work, a part of the actual project concerning “Simulation of flow
boiling heat transfer in a single horizontal microchannel”, as assigned
by our mentor Prof. Dibyendu Mondal. Hopefully this report will form
a proper basis for further work in the project.
3
Table of Contents
FLOW BOILING HEAT TRANSFER IN MICROCHANNEL ......................0
CERTIFICATE OF RECOMMENDATION .............................................1
ABSTRACT......................................................................................2
TABLE OF CONTENTS......................................................................3
INTRODUCTION..............................................................................4
HEAT TRANSFER IN MICROCHANNELS ............................................6
FLOW BOILING...............................................................................7
FLOW BOILING HEAT TRANSFER IN MICROCHANNELS (LITERATURE
REVIEW) ........................................................................................9
OBJECTIVES OF THE PRESENT WORK.............................................11
KEYWORDS ..................................................................................12
CONCLUSION ...............................................................................14
REFERENCES.................................................................................15
PAPERS.............................................................................................15
SITES ................................................................................................15
4
Introduction
Microchannels are essentially channels with hydraulic diameters less
than 1mm. Microchannels are being extensively used in the field of
fluid control and heat transfer. This project is concerned with the heat
transferring properties of microchannels, hence the ensuing
discussions will mostly relate to that.
As the scale of devices becomes small, thermal control and heat
dissipation from these devices can be effectively accomplished
through the implementation of microchannel passages. The small
passages provide a high surface area to volume ratio that enables
higher heat transfer rates. Smaller channel size in a heat exchanger
provides higher surface area to volume ratio and results in higher heat
and mass transfer rates and lower equipment size. Automotive and
aerospace industries embraced the use of smaller sized passages in
compact heat exchangers to meet the weight and size constraints,
while high performance requirements in cryogenic industries, for
example, necessitated the use of millimeter-sized passages in
equipment with relatively
large heat transfer rates
and higher effectiveness
requirements.
Research into
microchannels was initially
undertaken Tuckerman
and Pease in 1981, who Figure 1 – Publication histogram showing papers
related to single-phase liquid heat transfer and fluid
flow in microchannels.
5
demonstrated for the first time the high heat flux removal capability
of up to
800 W/cm2 achieved with microchannels in single-phase and two-
phase flows. After a slow start, research interest in microchannels has
increased significantly in the last decade, with numerous papers
published from the 90s to the late 2000s (see Fig. 1, 2).The main thrust
during this period was on understanding the fundamental
mechanisms. Research is now focused on further refining the
theoretical concepts, generating experimental data sets, enhancing
heat transfer performance while reducing pressure drop, and
extending the use of microchannels to new applications.
Figure 2 shows the various
papers published for flow
boiling heat transfer and
two-phase flow in
microchannels. In this brief
report, we will have a
overview of microchannels
and the various studies
conducted regarding flow
boiling heat transfer in
microchannels.
Figure 2 – Publication histogram showing papers related
to flow boiling heat transfer and two-phase flow in
microchannels.
6
Heat transfer in microchannels
Over the last decade, micromachining technology has been
increasingly used for the development of highly efficient cooling
devices called heat sink because of its undeniable advantages such as
less coolant demands and small dimensions. One of the most
important micromachining technologies is micro channels. Hence, the
study of fluid flow and heat transfer in micro channels which are two
essential parts of such devices, have attracted more attentions with
broad applications in both engineering and medical problems.
Microchannel heat transfer has the very potential of wide applications
in cooling high power density microchips in the CPU system, the
micropower systems and even many other large scale thermal
systems requiring effective cooling capacity. This is a result of the
micro-size of the cooling system which not only significantly reduces
the weight load, but also enhances the capability to remove much
greater amount of heat than any of large scale cooling systems. It has
been recognized that for flow in a large scale channel, the heat
transfer Nusselt number, which is defined as hD/k, is a constant in the
thermally developed region where h is the convective heat transfer
coefficient, k is thermal conductivity of the fluid and D is the diameter
of the channel. One can expect that as the size of the channel
decrease, the value of convective heat transfer coefficient, h,
becomes increasing in order to maintain a constant value of the
Nusselt number. As the size of the channel reduces to micron or nano
size, the heat transfer coefficient can increase thousand or million
times the original value. This can drastically increase the heat transfer
and has generated much of the interest to study microchannel heat
transfer both experimentally and theoretically.
7
Flow Boiling
Flow boiling occurs when all the phases are in bulk flow together in a
channel; e.g., vapor and liquid flow in a pipe. The multiphase flow may
be classified as adiabatic or diabatic, i.e., without or with heat addition
at the channel wall. An example of adiabatic flow would be oil/gas
flow in a pipeline, or air/water flow. In these cases the flow patterns
would change as the inlet mass flow rates of the gas or liquid are
altered or as the velocity and void distributions develop along the
channel. Boiling would not take place and phase change would only
occur if in a one component multiphase flow (e.g., steam-water) the
pressure decreases and flashing occurs. Examples of diabatic flow are
to be found in the riser tubes of steam generators and boiler tubes in
power plants or in the coolant channels between nuclear fuel
elements in a boiling water reactor. Boiling occurs on the walls of the
channels and the flow patterns change due to vapour production as
one observes the flow
downstream in the channel
due to vapour production.
The situation of interest in
nuclear reactors is flow
boiling. Consider a vertical
channel of arbitrary cross‐
sectional shape (i.e. not
necessarily round), flow area
A, equivalent diameter De,
uniformly heated (axially as
well as circumferentially) by a
heat flux q". Let Tin be the
inlet temperature (Tin<Tsat),
Figure 3 - Heat transfer and flow regimes in a vertical heated
channel
8
m the mass flow rate and P the operating pressure of the fluid (e.g.
water) flowing in the channel. We wish to describe the various flow
and heat transfer regimes present in the channel as well as the axial
variation of the bulk and wall temperatures. (Ref. Fig. 3)
At axial locations below the onset of nucleate boiling, the flow regime
is single‐phase liquid. As the fluid marches up the channel, more and
more steam is generated because of the heat addition. As a result, the
flow regime goes from bubbly flow (for relatively low values of the
flow quality) to plug (intermediate quality) and annular (high quality).
Eventually, the liquid film in contact with the wall dries out. In the
region beyond the point of dryout, the flow regime is mist flow and
finally, when all droplets have evaporated, single‐phase vapor flow.
9
Flow boiling heat transfer in
microchannels (literature review)
Flow boiling in microchannels was first studied by Tuckerman and
Pease in 1981, but it took more than ten years before a major effort
was undertaken by other researchers to explore this topic further. The
first major effort on understanding the thermohydraulic behavior of
flow boiling systems in microscale passages was presented by
Moriyama et al. in 1992. They used R-113 refrigerant in 35-110 μm
high and 30 mm wide rectangular passages. This geometry is
sometimes referred to as microgap in the literature.
In 1993, Peng and Wang reported one of the first studies with
subcooled flow boiling of water in minichannels. The fully developed
boiling region had little influence from subcooling or flow velocity.
These observations were helpful in determining the nature of flow
boiling in microchannels.
A more systematic study covering a large range of minichannel
diameters was conducted by Bowers and Mudawar in 1994. They
reported the average heat transfer, pressure drop and CHF data in
these channels.
In 2002, Serizawa conducted adiabatic flow experiments with steam-
water and air-water flows in microchannels and studied flow patterns,
which were affected by the surface roughness. He presented a flow
pattern map based on his experimental observations. The differences
between the adiabatic and diabatic flows were studied experimentally
by Hetsroni et al.
10
Figure 4 - Historical development timeline over 25 years highlighting advances in flow boiling in
microchannels.
11
Objectives of the present work
As is evident from our previous discussions, the study of flow and heat
transfer in microchannels is very important for the technology of
today and the near future as developments are following the trend of
miniaturization in all fields.
Our future work on the project will include:
I. Simulation of Flow Boiling Heat Transfer in a single horizontal
microchannel using commercial flow solver (ANSYS Fluent 13.0)
II. Validation of the CFD model by comparing the present simulated
results with the available literature.
III. The effects of various Reynolds No. on “volume fraction of
vapour”, “static temperature along the wall” and “heat transfer
coefficient” at the heated wall is evaluated.
IV. The Incipient Heat Flux is investigated as a function of fluid inlet
velocity and fluid inlet temperature.
12
Keywords
• CHF (Critical Heat Flux) describes the thermal limit of a
phenomenon where a phase change occurs during heating (such
as bubbles forming on a metal surface used to heat water),
which suddenly decreases the efficiency of heat transfer, thus
causing localised overheating of the heating surface.
• Flow regime is a description of the geometrical distribution of a
multiphase fluid moving through a channel. Many different
terms are used to describe this distribution, the distinction
between each one being qualitative and somewhat arbitrary. In
vertical or moderately deviated channels, the most common
flow regimes for gas-liquid mixtures are bubble flow, dispersed
bubble flow, plug flow, slug flow, froth flow, mist flow, churn
flow and annular flow.
• Heat sink is a passive heat exchanger that transfers the heat
generated by an electronic or a mechanical device to a fluid
medium, often air or a liquid coolant, where it is dissipated away
from the device.
• Hydraulic diameter, DH, of any channel, is defined as 4A/P, P
being the wetter perimeter and A being the cross-section area.
• Macrochannel is a channel with hydraulic diameter greater than
3mm.
Minichannel is any channel with hydraulic diameter varying
from 0.2mm to 3mm.
• Micropower system is a system that generates electricity, and
possibly heat, to serve a nearby load. Such a system may employ
any combination of electrical generation and storage
technologies (e.g. small scale generators) and may be grid-
13
connected or autonomous, meaning separate from any
transmission grid.
• Nucleate boiling is a type of boiling that takes place when the
surface temperature is hotter than the saturated fluid
temperature by a certain amount but where the heat flux is
below the critical heat flux.
• Nusselt number (Nu) is the ratio of convective to conductive
heat transfer across (normal to) the boundary in heat transfer at
a boundary (surface) within a fluid.
14
Conclusion
An initial foray into the topic of flow boiling heat transfer in
microchannels has showed that there is a lot of potential in
conducting research work in this area. Flow boiling microchannel heat
sinks are very promising for several applications, such as, the
computer and IT industry, high power semiconductor devices,
miniature vapour compression refrigeration systems. We notice
several papers have been published regarding microchannels and flow
boiling heat transfer since the late 20th century, making it a fairly new
topic of interest.
In this brief report, we familiarized ourselves with microchannels and
the concept of flow boiling. As part of the project, we will later work
on a simulation of flow boiling heat transfer using ANSYS software and
record suitable findings.
15
References
Papers
▪ “Flow Boiling Heat Transfer in Microchannels” – Dong Liu, Suresh
V. Garimella; Purdue University
▪ “History, Advances, and Challenges in Liquid Flow and Flow
Boiling Heat Transfer in Microchannels: A Critical Review” –
Satish G. Kandlikar; Rochester Institute of Technology
Sites
▪ Wikipedia: https://en.wikipedia.org/
▪ Case Study on Heat Transfer in Microchannel:
http://www.cpdlr.com/notes-articles-engineering/292-case-
study-on-heat-transfer-in-microchannel.html

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Preliminary report on flow boiling in microchannel

  • 1. Flow boiling heat transfer in microchannel A preliminary final year project report submitted in partial fulfilment of the requirement for the degree of B.Tech. in Mechanical Engineering (2014-2018) By Aritra Chatterjee(Roll No. 20) Debanjan Baksi(Roll No. 34) Debanjan Paul(Roll No. 35) Debtanu Maitra(Roll No.38) Under the guidance of Prof. Dibyendu Mondal Mechanical Engineering Department Academy of Technology G.T. Road, Adisaptagram, P.O.: Aedconagar Hooghly-712121, West Bengal May, 2017
  • 2. 1 Certificate of Recommendation This is to certify that the project entitled “Flow Boiling Heat Transfer in Microchannel” which is being submitted by Aritra Chatterjee, Debanjan Baksi, Debanjan Paul and Debtanu Maitra, in partial fulfilment for the award of Degree of Bachelor in Technology in Mechanical Engineering from Academy of Technology, Hooghly – 712121, under Maulana Abul Kalam Azad University of Technology (MAKAUT, formerly known as WBUT) for the 2014-2018 session, is the record of the following students’ work under my supervision. ________________ _________________ (Aritra Chatterje) (Debanjan Baksi) (Roll No. 20) (Roll No. 34) ________________ _________________ (Debanjan Paul) (Debtanu Maitra) (Roll No. 35) (Roll No. 38) Prof. ________________ Supervisor, Dept. Of Mechanical Engineering. Examiners ________________ ________________ Prof. ________________ Head of Dept. of Mechanical Engineering
  • 3. 2 Abstract The following report is a brief overview of microchannels and the concept of flow boiling. A literature review of flow boiling in microchannels has also been included. This is just a premiliminary work, a part of the actual project concerning “Simulation of flow boiling heat transfer in a single horizontal microchannel”, as assigned by our mentor Prof. Dibyendu Mondal. Hopefully this report will form a proper basis for further work in the project.
  • 4. 3 Table of Contents FLOW BOILING HEAT TRANSFER IN MICROCHANNEL ......................0 CERTIFICATE OF RECOMMENDATION .............................................1 ABSTRACT......................................................................................2 TABLE OF CONTENTS......................................................................3 INTRODUCTION..............................................................................4 HEAT TRANSFER IN MICROCHANNELS ............................................6 FLOW BOILING...............................................................................7 FLOW BOILING HEAT TRANSFER IN MICROCHANNELS (LITERATURE REVIEW) ........................................................................................9 OBJECTIVES OF THE PRESENT WORK.............................................11 KEYWORDS ..................................................................................12 CONCLUSION ...............................................................................14 REFERENCES.................................................................................15 PAPERS.............................................................................................15 SITES ................................................................................................15
  • 5. 4 Introduction Microchannels are essentially channels with hydraulic diameters less than 1mm. Microchannels are being extensively used in the field of fluid control and heat transfer. This project is concerned with the heat transferring properties of microchannels, hence the ensuing discussions will mostly relate to that. As the scale of devices becomes small, thermal control and heat dissipation from these devices can be effectively accomplished through the implementation of microchannel passages. The small passages provide a high surface area to volume ratio that enables higher heat transfer rates. Smaller channel size in a heat exchanger provides higher surface area to volume ratio and results in higher heat and mass transfer rates and lower equipment size. Automotive and aerospace industries embraced the use of smaller sized passages in compact heat exchangers to meet the weight and size constraints, while high performance requirements in cryogenic industries, for example, necessitated the use of millimeter-sized passages in equipment with relatively large heat transfer rates and higher effectiveness requirements. Research into microchannels was initially undertaken Tuckerman and Pease in 1981, who Figure 1 – Publication histogram showing papers related to single-phase liquid heat transfer and fluid flow in microchannels.
  • 6. 5 demonstrated for the first time the high heat flux removal capability of up to 800 W/cm2 achieved with microchannels in single-phase and two- phase flows. After a slow start, research interest in microchannels has increased significantly in the last decade, with numerous papers published from the 90s to the late 2000s (see Fig. 1, 2).The main thrust during this period was on understanding the fundamental mechanisms. Research is now focused on further refining the theoretical concepts, generating experimental data sets, enhancing heat transfer performance while reducing pressure drop, and extending the use of microchannels to new applications. Figure 2 shows the various papers published for flow boiling heat transfer and two-phase flow in microchannels. In this brief report, we will have a overview of microchannels and the various studies conducted regarding flow boiling heat transfer in microchannels. Figure 2 – Publication histogram showing papers related to flow boiling heat transfer and two-phase flow in microchannels.
  • 7. 6 Heat transfer in microchannels Over the last decade, micromachining technology has been increasingly used for the development of highly efficient cooling devices called heat sink because of its undeniable advantages such as less coolant demands and small dimensions. One of the most important micromachining technologies is micro channels. Hence, the study of fluid flow and heat transfer in micro channels which are two essential parts of such devices, have attracted more attentions with broad applications in both engineering and medical problems. Microchannel heat transfer has the very potential of wide applications in cooling high power density microchips in the CPU system, the micropower systems and even many other large scale thermal systems requiring effective cooling capacity. This is a result of the micro-size of the cooling system which not only significantly reduces the weight load, but also enhances the capability to remove much greater amount of heat than any of large scale cooling systems. It has been recognized that for flow in a large scale channel, the heat transfer Nusselt number, which is defined as hD/k, is a constant in the thermally developed region where h is the convective heat transfer coefficient, k is thermal conductivity of the fluid and D is the diameter of the channel. One can expect that as the size of the channel decrease, the value of convective heat transfer coefficient, h, becomes increasing in order to maintain a constant value of the Nusselt number. As the size of the channel reduces to micron or nano size, the heat transfer coefficient can increase thousand or million times the original value. This can drastically increase the heat transfer and has generated much of the interest to study microchannel heat transfer both experimentally and theoretically.
  • 8. 7 Flow Boiling Flow boiling occurs when all the phases are in bulk flow together in a channel; e.g., vapor and liquid flow in a pipe. The multiphase flow may be classified as adiabatic or diabatic, i.e., without or with heat addition at the channel wall. An example of adiabatic flow would be oil/gas flow in a pipeline, or air/water flow. In these cases the flow patterns would change as the inlet mass flow rates of the gas or liquid are altered or as the velocity and void distributions develop along the channel. Boiling would not take place and phase change would only occur if in a one component multiphase flow (e.g., steam-water) the pressure decreases and flashing occurs. Examples of diabatic flow are to be found in the riser tubes of steam generators and boiler tubes in power plants or in the coolant channels between nuclear fuel elements in a boiling water reactor. Boiling occurs on the walls of the channels and the flow patterns change due to vapour production as one observes the flow downstream in the channel due to vapour production. The situation of interest in nuclear reactors is flow boiling. Consider a vertical channel of arbitrary cross‐ sectional shape (i.e. not necessarily round), flow area A, equivalent diameter De, uniformly heated (axially as well as circumferentially) by a heat flux q". Let Tin be the inlet temperature (Tin<Tsat), Figure 3 - Heat transfer and flow regimes in a vertical heated channel
  • 9. 8 m the mass flow rate and P the operating pressure of the fluid (e.g. water) flowing in the channel. We wish to describe the various flow and heat transfer regimes present in the channel as well as the axial variation of the bulk and wall temperatures. (Ref. Fig. 3) At axial locations below the onset of nucleate boiling, the flow regime is single‐phase liquid. As the fluid marches up the channel, more and more steam is generated because of the heat addition. As a result, the flow regime goes from bubbly flow (for relatively low values of the flow quality) to plug (intermediate quality) and annular (high quality). Eventually, the liquid film in contact with the wall dries out. In the region beyond the point of dryout, the flow regime is mist flow and finally, when all droplets have evaporated, single‐phase vapor flow.
  • 10. 9 Flow boiling heat transfer in microchannels (literature review) Flow boiling in microchannels was first studied by Tuckerman and Pease in 1981, but it took more than ten years before a major effort was undertaken by other researchers to explore this topic further. The first major effort on understanding the thermohydraulic behavior of flow boiling systems in microscale passages was presented by Moriyama et al. in 1992. They used R-113 refrigerant in 35-110 μm high and 30 mm wide rectangular passages. This geometry is sometimes referred to as microgap in the literature. In 1993, Peng and Wang reported one of the first studies with subcooled flow boiling of water in minichannels. The fully developed boiling region had little influence from subcooling or flow velocity. These observations were helpful in determining the nature of flow boiling in microchannels. A more systematic study covering a large range of minichannel diameters was conducted by Bowers and Mudawar in 1994. They reported the average heat transfer, pressure drop and CHF data in these channels. In 2002, Serizawa conducted adiabatic flow experiments with steam- water and air-water flows in microchannels and studied flow patterns, which were affected by the surface roughness. He presented a flow pattern map based on his experimental observations. The differences between the adiabatic and diabatic flows were studied experimentally by Hetsroni et al.
  • 11. 10 Figure 4 - Historical development timeline over 25 years highlighting advances in flow boiling in microchannels.
  • 12. 11 Objectives of the present work As is evident from our previous discussions, the study of flow and heat transfer in microchannels is very important for the technology of today and the near future as developments are following the trend of miniaturization in all fields. Our future work on the project will include: I. Simulation of Flow Boiling Heat Transfer in a single horizontal microchannel using commercial flow solver (ANSYS Fluent 13.0) II. Validation of the CFD model by comparing the present simulated results with the available literature. III. The effects of various Reynolds No. on “volume fraction of vapour”, “static temperature along the wall” and “heat transfer coefficient” at the heated wall is evaluated. IV. The Incipient Heat Flux is investigated as a function of fluid inlet velocity and fluid inlet temperature.
  • 13. 12 Keywords • CHF (Critical Heat Flux) describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing localised overheating of the heating surface. • Flow regime is a description of the geometrical distribution of a multiphase fluid moving through a channel. Many different terms are used to describe this distribution, the distinction between each one being qualitative and somewhat arbitrary. In vertical or moderately deviated channels, the most common flow regimes for gas-liquid mixtures are bubble flow, dispersed bubble flow, plug flow, slug flow, froth flow, mist flow, churn flow and annular flow. • Heat sink is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device. • Hydraulic diameter, DH, of any channel, is defined as 4A/P, P being the wetter perimeter and A being the cross-section area. • Macrochannel is a channel with hydraulic diameter greater than 3mm. Minichannel is any channel with hydraulic diameter varying from 0.2mm to 3mm. • Micropower system is a system that generates electricity, and possibly heat, to serve a nearby load. Such a system may employ any combination of electrical generation and storage technologies (e.g. small scale generators) and may be grid-
  • 14. 13 connected or autonomous, meaning separate from any transmission grid. • Nucleate boiling is a type of boiling that takes place when the surface temperature is hotter than the saturated fluid temperature by a certain amount but where the heat flux is below the critical heat flux. • Nusselt number (Nu) is the ratio of convective to conductive heat transfer across (normal to) the boundary in heat transfer at a boundary (surface) within a fluid.
  • 15. 14 Conclusion An initial foray into the topic of flow boiling heat transfer in microchannels has showed that there is a lot of potential in conducting research work in this area. Flow boiling microchannel heat sinks are very promising for several applications, such as, the computer and IT industry, high power semiconductor devices, miniature vapour compression refrigeration systems. We notice several papers have been published regarding microchannels and flow boiling heat transfer since the late 20th century, making it a fairly new topic of interest. In this brief report, we familiarized ourselves with microchannels and the concept of flow boiling. As part of the project, we will later work on a simulation of flow boiling heat transfer using ANSYS software and record suitable findings.
  • 16. 15 References Papers ▪ “Flow Boiling Heat Transfer in Microchannels” – Dong Liu, Suresh V. Garimella; Purdue University ▪ “History, Advances, and Challenges in Liquid Flow and Flow Boiling Heat Transfer in Microchannels: A Critical Review” – Satish G. Kandlikar; Rochester Institute of Technology Sites ▪ Wikipedia: https://en.wikipedia.org/ ▪ Case Study on Heat Transfer in Microchannel: http://www.cpdlr.com/notes-articles-engineering/292-case- study-on-heat-transfer-in-microchannel.html