Design, Prototyping, and Testing of an Apparatus for Establishing a
Linear Temperature Gradient in Experimental Fish Tanks
by
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
Romi Sinclair Kadri
AUG 15 20
Submitted to the
Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
LIBRARIES
Bachelor of Science
At the
Massachusetts Institute of Technology
June 2014
Q 2014 Romi Sinclair Kadri
All rights reserved
The author hereby grants to MIT permission to reproduce and to distribute
publicly paper and electronic copies of this thesis document in whole or in part
in any medium now known or hereafter created.
Signature of Author:
Signature redacted
7,
partment of Mechanical Engineering
February 5, 2014
Certified by:
Signature redacted
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Supervisor
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Accepted by:
Anette E. Hosoi
Associate Department Head for Education
Chairman, Undergraduate Thesis Committee
2
Design, Prototyping, and Testing of Apparatus for Establishing a Linear
Temperature Gradient in Experimental Fish Tanks
by
Romi Sinclair Kadri
Submitted to the Department of Mechanical Engineering
On February 5, 2014 in Partial Fulfillment of the
Requirements for the Degree of Bachelor of Science in
Engineering and Entrepreneurship
Abstract
Immunology researchers require a new type of fish tank that provides a
linear thermal gradient for experimental zebrafish in order to improve the
accuracy and validity of their research. Zebrafish require the ability to select
their surrounding water temperature in order to react to a simulated viral
infection with an optimized immune response. Although countless immunology
studies have been performed with zebrafish to date, their validity came into
question in early 2013 when it was demonstrated by MacKenzie et. at that the
immune response in fish is critically coupled with a form of environmental
temperature selection known as behavioral fever. Current research tanks
feature a uniform temperature throughout, preventing the fish from being able
to "choose" their surrounding water temperature in response to a simulated
viral infection. "Fish that are not offered a choice of temperatures and that
therefore cannot express behavioral fever show decreased survival under viral
challenge." (MacKenzie, et al., 2013)
In this study, a conceptual thermal-fluid system was designed, built, and
tested for its ability to establish a stable, linear thermal gradient in a standardsize 10L laboratory tank. The thermal profile of the volume of water contained
within the experimental tank was determined from temperature measurements
taken at incremental depths. The apparatus was found to produce a suitably
linear temperature gradient over a base-to-surface temperature difference of
19.6 0 C; far greater than the temperature difference of 8 0 C necessary for
unrestricted behavioral fever to be expressed in experimental zebrafish. As
such, it was determined that the approach taken is suitable for future use in
the development of aquaria for immunology research and water tanks for other
applications.
Thesis Supervisor: Anette E. Hosoi
Title: Professor of Mechanical Engineering
3
Acknowledgements
A great number of people have continually inspired and empowered me
during my undergraduate career at MIT, many of whom have helped to make
this project possible.
My upmost gratitude goes to Professor Peko Hosoi for her dedication to
providing students like myself with educational experiences that are tailored to
their interests and passions. Furthermore, she always makes time to provide
students with incredibly thoughtful, individualized advice and support. For me
this has included her supervision of this thesis, her support and facilitation of
an entrepreneurship concentration being formed within the mechanical
engineering program, her teaching in mechanical engineering classes, her
advice on numerous technical projects, and the creation of unique experiences
for students such as STE@M - the program for Sports Technology & Education at
MIT. It is safe to say that MIT simply wouldn't be the same without her.
I am extraordinarily grateful to my parents, stepparents, and
grandparents for funding and supporting my time here at MIT, and to Kenneth
Morse - founding Managing Director of today's Martin Trust Center for MIT
Entrepreneurship - for convincing them that MIT would be worth their money!
Without them, I would not have had the opportunity to be here.
Further thanks go to my father Sunil Kadri and our family friend Simon
MacKenzie for their funding and support of this project. In addition, my thanks
go to Adam Amsterdam of the MIT Zebrafish Facility and Professor Jacqueline
Lees for their enthusiastic support of the biological and practical requirements
of the system developed.
Many thanks to my friends and fellow MIT students Nikita Khlystov,
Nicholas Davis, and Athanasios Athanassiadis for their valuable advice on
various aspects of this project.
While the mechanical engineering department is home to many of the
world's most accomplished and esteemed academics, I find it hard to imagine
that the department would be able to function without the support of our
academic administrator, Brandy Baker. It's become a standing joke with her
that whenever I send an email to anyone at MIT requesting any piece of advice
whatsoever, it always comes back to me with Brandy cc'd and something in the
message body to the effect of "Ask Brandy! She knows all about this..". She's
up late every night to help her students beyond the day-to-day; she provides
invaluable personal advice to students on navigating MIT's courses, people, and
politics; she knows everyone and everything about this place, and I think that
most people in the department will share my feeling that we'd be lost without
her!
4
Every class I've taken at MIT has had a deep impact on my ability to
understand something about the world or to do something that I love, but one
in particular changed my perspective of everything I do: Engineering Innovation
and Design, taught by Blade Kotelly.
Through a systematic series of
experiential lectures and exercises, Blade's teachings allowed me to reach my
own conclusion that design is everything; that exceptional design is the most
critical element in converting new technologies into a form that will allow
them to make a meaningful impact on the world and its people. Moreover, I
realized that 'good' design is entirely contextual and therefore constantly
changing - not just in terms of people's ever-changing aesthetic tastes, but also
in the way that we perceive and interact with technologies across cultures and
time. Understanding this in way that I can apply to everything I do has been
one of the most critical learning experiences I've had, and I cannot thank Blade
enough for bringing it to me.
I also thank Professor Jacopo Buongiorno, Sanjay Sarma, Professor
Douglas Hart, Dr. Barbara Hughey, and Paul Ragaller for the learning
experiences they provided me in Thermal-Fluids Engineering, Manufacturing,
Engineering Systems Design, Measurement and Instrumentation, and Technical
Writing, respectively. These courses empowered me with the knowledge and
understanding required to solve technical challenges for scalability and impact.
Last but certainly not least, I thank Rosemary Sugrue for supporting me
through the past two years in every way possible. From the small things like
making me food as I write these acknowledgements to advising this project
with her knowledge and experience of thermal-fluids engineering and technical
writing, to sharing a home with me, to allowing me to set up an 'experimental
facility' in our bathtub, and to keeping me sane under the pressure of an MIT
education, she's always ready to help me with open arms.
Thank you all for making this project possible, for opening my eyes to
the world and helping me to understand my role in it, and for making my MIT
experience so extraordinary.
5
1. Introduction
Immunology researchers require a new type of fish tank that provides a
linear thermal gradient for experimental zebrafish in order to improve the
accuracy and validity of their research. This project involves the design,
prototyping, and testing of an apparatus for establishing and maintaining a
stable, linear temperature gradient in experimental fish tanks.
Zebrafish require the ability to select their surrounding water
temperature in order to react to a simulated viral infection with an optimal
Although countless immunology studies have been
immune response.
performed with zebrafish to date, their validity came into question in early
2013 when it was demonstrated by MacKenzie et. at that immune response in
fish is critically coupled with a form of environmental temperature selection
known as behavioral fever. Current research aquaria feature a uniform
temperature throughout, preventing the fish from being able to "choose" their
surrounding water temperature in response to a simulated viral infection.
"Fish that are not offered a choice of temperatures and that therefore cannot
express behavioral fever show decreased survival under viral challenge"
(MacKenzie, et al., 2013).
The target temperature range of the gradient to be established by the
system in development is 25*C - 33*C, as defined by the range of temperatures
in which behavioral fever is expressed among experimental fish under immune
challenge (MacKenzie, et al., 2013). The steady-state temperature gradient
should be approximately linear in order to promote freedom of behavioral
expression of thermal selection among the experimental fish. The desired flow
rate is 10% of tank volume per minute, as dictated by circulation requirements
related to fish health. Although the current project does not consider human
safety issues such as the presence of unprotected hot surfaces, these must be
identified and mitigated during any product development beyond this proof-ofconcept.
2. Experimental Tanks
An experimental system was developed in order to test the suitability of
various methods for establishing a temperature gradient in the current
application. To maximize versatility, a modular approach was taken. Figures
la-e show the various modules used in the experimental setup:
6
Figure Ib: AquaEuro USA
Max-Chill 1/ 13hp in-line
Chiller
Figure 1a: Cylindrical 2.5L
(1/4-size) tank with
inlet/outlet valves at top,
middle, and bottom, and
an aluminum base
Figure 1c: Hydor ETH201
200W in-line Heater
0
Figure Id: IceProbe Column fancooled base
Figure le: Intel STS100A Flat fancooled base
Clear PVC tubing connects the tank outlet to a centrifugal pump that
circulated water through the heater and chiller (when used) and back into the
desired valve at the top, middle, or bottom of the tank. When desired, either
of the two fan-cooled heatsinks shown in Figures d & le can be mounted to
the aluminum base of the tank in order to provide additional cooling. The
7
thermal gradient response of various system configurations is determined from
temperature measurements taken at incremental depths within the tank after
the setup is allowed sufficient time to reach a steady state.
Further information regarding the experimental setup, thermal
measurement equipment, system configurations, and measurement procedure
can be found in Appendix A, Section 1.
3. Results from Experimental Trials
Figure 2a shows the configuration used for Tank A, and Figure 2b shows a
graph of temperature as a function of depth:
31.0
30.0
F4
Ca&ler
29.0
28.0
A.
Pump)
E
ChIler
27.0
26.0
a' 25.0
24.0
3
23.0
0
Figure 2a: Tank A Configuration
with heater inlet at top, chiller inlet
at bottom, and outlet in the middle.
The arrows inside the tank represent
the approximate flow from each
inlet to the outlet.
20
Depth (cm)
10
30
Figure 2b: Graph of Temperature vs.
Depth for Tank A including error
bars. A sharp thermocline can be
observed between the two bulk
temperature regions above 15cm,
and below 20cm depth.
Although Tank A exhibits a reasonable temperature range of 5.6 0.2'C,
the flat regions at either end of Figure 2b indicate that a defined thermocline
is present somewhere between a depth of 15-20cm. The flow rate in Tank A is
higher than the other tanks tested, forcing the bulk temperature of the flowing
fluid to dominate over any thermal conduction that may be taking place. The
observed thermocline is likely present because of the hot and cool water
mixing near the outlet (at 15cm depth), and because the flow rate is too high
for any significant conduction to take place. As a result of the flow rate being
8
higher through the heater than through the chiller, the thermocline is present
slightly below the center of the tank.
Figures 3a-c show the configurations used and temperature vs. depth
graphs for Tanks B a C:
HWr
Hee
Pump]
Figure 3a: Tank B Configuration with
heater inlet at top, outlet in the
Figure 3b: Tank C Configuration with
heater inlet at top, outlet at the
bottom, and additional base cooling.
middle, and additional base cooling.
36.0 ;
-
-
-
-
35.0
34.0
33.0
GD
32.0
I4.'
31.0 ;
'U
IGD 30.0
a.
E 29.0
GD
I28.0
27.0
Tank B
in
Tank C
-
-
-
-
..
26.0
0
5
10
15
20
25
30
Depth (cm)
Figure 3c: Graph of Temperature vs. Depth for Tanks B
error bars.
a C including
Tank B exhibits a fairly flat temperature curve from the surface to a
depth of 20cm, and a steep linear gradient from 20cm to 30cm. The
temperature range is 8.7 0.2 C. As there is no inlet at the base of Tank B, the
cooling arises solely from the flat fan-cooled base. The base does not generate
any flow (besides some convective current that is assumed to be negligible).
Because there is no obvious flow in the lower region of Tank B, the region's
9
steep linear gradient is likely a result of Fourier's law for conductive heat
transfer dominating over any mixing of fluids. The direct flow from the heater
inlet to the central outlet creates the flat temperature curve from the surface
to 15cm, and the small drop-off from 15 to 20cm depth is likely due to the
mixing of the moving heated fluid and the top of the (assumed) stationary
chilled fluid in the lower 2 to 1/ 3 rd of the tank.
Tank C does not exhibit a notable thermal gradient. A slight drop in
temperature occurs near the tip of the cooling probe (between 20-25cm
depth), but the total cooling power does not appear to be sufficient to chill the
water as it flows down the tank to the bottom outlet.
Figures 4a-b show the configurations used and temperature vs. depth
graphs for Tanks D & E:
33.0 1
f A:::
-
32.0
U.31.0
Pump
n.Tank D
-
30.0
* Tank E
29.0
E
0 28.0
Linear (Tank E)
27.0
-
Figure 4a: Tank D & E
Configuration with heater inlet at
top, chiller inlet in middle, outlet
at bottom, and additional base
cooling. Tank D features a higher
flow rate through the heater than
through the chiller, and Tank E
features a higher flow rate through
the chiller than through the
heater.
-
26.0
0
10
20
30
Depth (cm)
Figure 4b: Graph of Temperature
vs. Depth for Tanks D & E including
error bars.
Tanks D & E are configured identically besides a variation in the
proportional flow rate between the heated and chilled water. The experiment
was initially performed with Tank D in an attempt to eliminate the presence of
a thermocline, as in Tank A, by forcing mixing between the chilled and heated
water, thus breaking down Fourier's law.
As shown in the temperature vs. depth graph for Tank D (Figure 4b), the
chilled water dominates and forces a mild thermocline from 10 to 20cm depth,
10
with a small amount of conductive cooling occurring above 10cm and a small
amount of additional cooling occurring below 20cm as a result of the flat fancooled base. Tank E is configured in order to further minimize the presence of
a thermocline while maintaining a temperature range similar to that of Tank D
(2.2 0.3'C). As shown in Appendix A, Table 1, the heater:chiller flow rate
ratio of Tank D is 2:1, while the heater:chiller flow rate ratio of Tank E is 1:2.
Although not completely straight, the temperature gradient of Tank E is
visually linear, with a temperature range of 2.4 0.1 *C. As the flow rate was
set to the minimum requirement of 10% of tank volume per minute, this
temperature range is assumed to be the maximum that can be attained with
the current experimental equipment.
&
It was determined that the following effects occur as a result of varying
system configuration. A variation in heater:chiller flow-rate ratio in Tanks D
E results in a change in mean temperature, as well as a change in the thermal
inflection observed at the center of the tank where hot and cool water is
assumed to be mixing. The placement of an outlet at the base of the tank
without any forced mixing (as in Tank C) results in very low system efficiency,
and almost no temperature gradient was observed with the current
experimental equipment. Because Fourier's law requires that the fluid is
stationary, it is inherently broken down by the presence of fluid flow as
observed in both halves of Tank A and the top 2/3rds of Tank B. Tank A proved
that a steep thermocline is formed in a tank when two fluids of different
temperatures flow towards each other and meet at an outlet, allowing them to
leave the tank before they have a chance to mix or transfer heat by conduction
as governed by Fourier's law.
A number of assumptions were used to generate the above conclusions
from the experimental results. In order to prove that the location of the
thermocline observed in Tank A was indeed offset from center by a higher flow
rate through the heater than in the chiller, further configurations would need
to be tested in which the heater:chiller flow-rate ratio is varied within the
same setup and the thermocline location is monitored in response. In order to
prove that Tank C was indeed ineffective at establishing a thermal gradient, a
much higher-power cooling column may be used, and that cooling column may
need to extend the entire height of the tank in order to account for the
breakdown of Fourier's law that occurs as a result of fluid flowing parallel to
the direction of heat transfer.
By extending the cooling column to the height of the tank, the heat
transfer would occur radially, i.e. perpendicular to the direction of flow, thus
Fourier's law would remain valid. However, a large visual obstruction (such as
that posed by a cooling column extending the height of the tank) is not suitable
for the research application, which relies on visual observation of the fish.
11
The suitability of the Tank E configuration comes into question when the
issues arise of: scaling to different sizes of tank with proportionally different
heights and diameters; and the further mixing of fluid due to the movement of
fish throughout the tank. The scaling issue may be addressed on a size-by-size
basis, but a CFD model would likely need to be developed in order to define
system parameters for each size of tank to be developed without the need for
further experimentation. Mixing of the fluid due to fish motion is likely to be
an issue, as a disturbance in the natural mixing of the fluid in a low-flow rate
system like this will likely have a substantial impact on the profile of the
temperature gradient. Because fish tend to be moving constantly, their motion
may impact the temperature gradient profile to such an extent that steady
state would not be reached. Furthermore, the control system in this case
would become rather complicated, as the temperature of the tank would have
to be continuously monitored, as opposed to a simpler control system in which
only the temperatures of the inputs and outputs are monitored. The effect of
fish motion on the temperature gradient profile could be quantified by further
experimentation in which a control (non-stocked) tank is configured identically
to a live (stocked) tank, and the thermal gradient is measured and compared
over time. This effect could also be estimated by CFD analysis.
Although the thermocline present in Tank A was not desirable in the
current experiment, it may be valuable to consider exploiting this
characteristic in future product development.
As realized in the current
experiment, Fourier's law breaks down quickly in the presence of fluid flow
parallel to the direction of heat transfer.
However, if flow occurs
perpendicular to the direction of heat transfer, Fourier's law holds true and a
linear temperature gradient can be established.
4. Design Concept
At present there is no common apparatus for establishing and
maintaining a stable temperature gradient in a fish tank. A fish tank is defined
as an open system consisting of: a contained body of water; an in-flow of fresh
water; and an outflow of wastewater. Laboratory fish tanks typically do not
feature any type of water heater or aerator inside the tank as the in-flow
water to all tanks in a laboratory facility is controlled for temperature, oxygen
content, and biological material by a system of centralized water processing
equipment. As such, the effects of in-tank aeration and heating that are
typical of ornamental fish tanks do not need to be considered.
As a thought experiment, Tank A' is created. By using the example from
Tank A (Figures 2a-b) and increasing the number of inlets and outlets (with
each of the inlets at incremental temperatures from bottom-to-top), it is
intuitive that a 'step-ladder' of temperature layers would form inside the tank.
12
Figures 5a-b show that each of these 'layers' would form between pairs of
outlets, and that a thermocline would be present between each layer.
f:
-
34
33
,32
-
4
31
30
29
28
E 27
26
25
24 i
I
I
I
0
10
20
30
Depth (cm)
Figure 5a: Theoretical Tank A'
Configuration with multiple heater
inlets (indicated by colored
arrows), each at incrementally
greater temperatures from bottom
to top. Outlets (indicated by gray
arrows) remove water between
each inlet causing a small
thermocline, thus creating a
stepped temperature gradient with
each step at the same temperature
as its respective inlet. The flow
rate would be identical from every
inlet in order to ensure even step
size across the entire gradient.
Figure 5b: Schematic of
Temperature vs. Depth for
theoretical tank A', based upon the
thermal response of experimental
tank A. Compared to Tank A, the
thermal 'steps' are reduced in size
as the number of inlets and outlets
increases. The thermoclines sit
over the outlet regions, and the
flats sit over the inlets.
Across a constant delta T of 250 C - 33*C from bottom to top, the size of
the steps is inversely proportional to the number of outlets. The principle
exploited for the design of the current device is that an infinite number of
evenly spaced inlets up the side of a tank with temperature evenly distributed
between them would create a perfectly linear temperature gradient by
reducing the step size to zero. This is analogous to the reduction of step sizes
in the use of the midpoint rule for the approximation of a definite integral.
13
5. Design Specifications
Of course it is not possible in practice to alternate an infinite number of
inlets and outlets up the side of the tank. Instead, the desired effect of an
infinite number of inlets can be achieved using a single long inlet running the
length of one side of the tank. If the inlet runs the entire height of the tank,
the outlet(s) must be placed at the opposite end of the tank.
The long inlet must be heated in such a way that the desired
temperature gradient of 25'C - 33'C from bottom-to-top is present in the fluid
flowing into the tank. The gradient should be visually linear at the tank inlet,
and the gradient breakdown across the length of the tank should be minimized.
In order to ensure gradient stability and linearity, the flow rate per unit height
must be constant along the entire length of the inlet.
A first prototype should be constructed to fit a standard-size 10L
laboratory test tank which can be custom fabricated to accommodate the new
inlet/heater element. Where practical, the tank shape should be optimized for
heat transfer while maintaining sufficient width so as to avoid excessive
restriction of zebrafish swimming space. For ease of manufacture, the 10L test
tank should be fabricated by assembling pieces of transparent polycarbonate to
form a 6" wide, 12" long, and 12" high cuboidal tank. To ensure compatibility
with the water circulation systems that are standard to zebrafish laboratories,
the intet/heater element must be able to accept a water supply at a constant
temperature from a 1/16" PVC hose. Furthermore, the tank outlet must drain
at an even flow rate at all points in the vertical axis to minimize breakdown of
the thermal gradient by fluid mixing, and the outflow should pass through a
hose that can be directed into the appropriate drainage system in use by the
test laboratory.
Standard laboratory health and safety regulations pertaining to the use
of electrical power and high-temperature heating elements must be adhered
to, however the primary safety consideration for the purposes of this proof-ofconcept is that of the welfare of any fish that may be used for live testing.
The tank and heater/inlet element must not pose any danger to the fish of
electrocution, burning, or poisoning by - for example - any use of corrosive
metals.
The proof-of-concept prototype must be easy to manufacture at low-cost
with readily available materials and resources. Off-the-shelf components
should be used where possible to simplify the manufacturing process. The
design should be scalable beyond the 1 OL prototype tank in order for the
system to be used - where practical - in applications beyond the optimization
of immunology research on the zebrafish model.
14
6. Theory of the Breakdown of a Linear Temperature Gradient in a
Cuboidal Fish Tank as a result of Conductive Heat Transfer
Although it is likely that some breakdown of the thermal gradient will
occur as a result of fluid mixing and convection currents, we can model
gradient breakdown as a function of flow rate across a rectangular fish tank by
In a fluid, conductive heat
its primary cause: conductive heat transfer.
transfer can be modeled by Fourier's law, which relates temperature gradient
to the heat flux across the length of a fluid body. Fourier's Law states that the
thermal conduction can be expressed as:
where qz is the heat flux (
),
-
dT
(1)
A is the thermal conductivity of the fluid (
dT i
)
qz =
K
and
is the temperature gradient across the section (-). Fourier's law
assumes that the fluid is static in the direction of heat transfer and maintains a
constant velocity in the direction perpendicular to that of heat transfer. Thus
in order for Fourier's Law to be a valid model for the current system it must be
applied to an infinitesimal slice of water as it passes from the inlet of the tank
to the outlet.
The expected heat flux qz can be calculated from the target
temperature range (25 0 C - 33 0C), the height of the experimental tank (0.3m),
and the thermal conductivity of water (0.614-f), as -4.64 -. By Fourier's law, a
linear temperature gradient can be established along the length of the tank
only if heat transfer is constant in the z-direction. Approximately constant
heat transfer between 'layers' of fluid can be attained in the current
application only if fluid mixing and vertical convection are minimized, thus the
current approach of reducing the layer-inducing thermal 'step size' to zero is
most likely to achieve the desired effect. Fluid mixing is considered negligible
based on the assumption that the flow exiting the heater outlet is of uniform
velocity and is perfectly parallel. Under this assumption, convection in the
vertical axis arises solely due to density-induced buoyancy forces across fluid of
different temperatures. The density at the 33'C surface of the tank is 2.4!3 (or
0.25%) less than the density at the 25 0 C base.
In any case, if vertical
convection were present as a result of the density-induced buoyancy forces,
the direction of the resulting motion of fluid within the tank would serve to
stabilize the temperature gradient. Higher density, cooler fluid at the bottom
of the tank would shift downwards, while warmer, lower density fluid would
move upwards; thus working against the vertical conduction due to Fourier's
law and transferring heat in the opposite direction. These buoyancy forces
(and therefore the extent of heat transfer due to convection) are assumed to
15
be negligible due to the low magnitude of the difference in the density of
water across a 250 C - 330 C temperature gradient.
Under this assumption, Fourier's law can be combined with the first law
of thermodynamics to determine the breakdown of an ideal thermal gradient in
the vertical z-axis over time. Assuming the thermal gradient remains linear at
all times although the total difference in temperature between the bottom and
top of the tank is decreasing, the breakdown of the thermal gradient as the
water translates across the tank can be approximated by the change in surface
temperature over time. Furthermore, this approximation assumes that: there
is negligible heat transfer between the water, the tank, and the surrounding
air; and that the temperature distribution is symmetrical around the mean
temperature of the inlet water, thus causing gradient breakdown to occur from
the bottom-up and top-down. This approximation remains true so long as the
temperature gradient at the water intet is truly linear. In practice, the change
in surface temperature over time was modeled in MATLAB (see Appendix C for
script) by iteratively solving for the absolute surface temperature per unit
time. The change in temperature in the z-axis per unit time can be expressed
by the heat equation:
dt
-a-
(2)
dzz
where z is depth within the tank (m), t is time after release from the heater
outlet (s), T is temperature as a function of z and t ( 0C), and a is the thermal
diffusivity:
a-
(3)
PCp
where A is the thermal conductivity of the fluid ( w),
p is the density of the
K)
fluid (!g-), and cp is the specific heat capacity (
for water, and p Et cp are set to
99 6 -4
). The constant A is 0.61 w
and
4.18 x 103
M3
kgK
respectively for water
at 25'C - 33"C. The constant a is then calculated as 1.47 x
The solution of Equation 2 can be found as:
T(z, t) = Teq - 4(ATO) Zo=1 , 3 ,s,...o
n=13,5...o fn
16
SC-ban
cos(-)e(4)
7r2
d
10-7 M
S
2
1rt
where Teq is the equilibrium temperature ('C), ATO is the surface-base
temperature difference at t=O (0 C), z is the vertical distance from the base of
the tank (m), d is the depth of the tank (m), t is time (s), and b is a fitting
parameter for the exponential decay.
In order for a stable gradient to be established over the length of a tank,
the ratio of the coefficients of diffusive heat transfer rate and convective heat
transfer rate (known as the P6clet number) should be much greater than 1.
The Peclet number is defined as:
Pe
= Tdiff
Tconv
(5)
where the coefficient of convective heat transfer rate is:
Tcon-
VX
(6)
where L, is the length of the tank (m) and v is the velocity of the water across
the tank ( S ). The coefficient of diffusion heat transfer rate is defined as:
Tdiff =Lz(7)
where Lz is 0.15m: the distance in z from the center of the tank (where the
temperature is the mean of the gradient at all times) to the water surface, and
a is the thermal diffusivity as defined above. For a theoretical flow rate of 1x
tank volume per minute, the Peclet number can be calculated as 2.55. As this
is greater than 1, the time for heat to diffuse in the vertical axis is greater
than the time for heat to convect from one end of the tank to the other.
Therefore, when ignoring effects of convection in the z-axis, the established
temperature gradient is expected to be sufficiently maintained along the
length of the tank for all flow rates above 1x tank volume per minute.
Due to the symmetry of a linear gradient, the increase in base
temperature over time is equal to the decrease in surface temperature over
time. Figure 6 shows water surface and water base temperatures as a function
of time after release from an ideal water inlet, as modeled in MATLAB:
17
34 -
mi Surface
i"Base
33 -
32
-
-31
-
30
-
29
ff
-
-
M.28
E
27
26
25
24
0
50
100
150
200
250
300
Time (s)
Figure 6: Graph of water temperature modeled as a function of time at the
surface (red) and base (blue) of the water contained within an experimental
fish tank. This assumes that an ideal inlet is used, featuring a perfectly linear
temperature gradient from bottom to top, even flow rate at all points from
bottom to top, and parallel flow from bottom to top. This also assumes that no
thermal energy is lost to the environment, that convective effects are
negligible, and that all flow across the tank is uniform, laminar and parallel.
The model predicts that the thermal gradient will have broken down
completely by around 275s. This means that with a flow rate of -0.2x tank
volume per minute or less, the model suggests that the gradient will have
broken down completely and the temperature will be uniform at the end of the
tank.
By correlating the flow rate through the tank with the time taken for an
infinitesimal slice of water to pass from the inlet to the outlet, the maximum
gradient loss can be estimated as a function of flow rate. Assuming that 1.5"
of the experimental tank's 12" length is to be used by the drainage system, the
distance between the inlet and outlet is 10.5" (0.27m). Assuming a flow rate
of Ix of tank volume per minute, the time taken for an infinitesimal slice of
water to pass through the tank is 1 minute (60s). As can be observed in Figure
6, it is estimated that the maximum thermal breakdown at the end of the tank
is 2.7*C from top and bottom with this flow rate, leaving a residual
temperature gradient of 27.7'C - 30.3'C; an acceptable gradient for the
zebrafish application. Figure 7 shows the modeled relationship between flow
rate and the residual gradient at the end of the tank, as governed by the Peclet
number for each flow rate:
18
32
-
-
33
-
31
j
30-w
2,0 -*Surface
29
"
27.
-
28V26
-w
Base
.*
.
0
E
C
27
26
25
0
0.5
1
2.5
2
1.5
Flow Rate (V-factor/min)
3
3.5
4
Figure 7: Graph of maximum thermal gradient breakdown as a function of
flowrate, modeled as the predicted temperature of the surface and base of the
water at the outlet-end of the tank. The units of flowrate are factors of total
tank volume per minute (i.e. "0.5" means that for a 10L tank, 5L of water
passes through the tank per minute). Thermal gradient breakdown decreases
as flow rate is increased.
While increasing the flow rate to a level that would maintain the desired
temperature gradient across the length of the tank would not pose any danger
to the fish, the energy demands of the system would increase dramatically.
This compromise comes as a result of the fact that standard zebrafish
laboratories can supply water only at a single, constant temperature. As such,
the only practical method by which to generate a linear thermal gradient
across the inlet with the available system inputs is to provide sufficient heat to
the inlet water (provided at base temperature) to achieve the desired deltaT.
By the first law of thermodynamics, the energy required to heat a flow of
water to a constant temperature (which is, in this case, the mean fluid
temperature of the tank) is directly proportional to the mass flow rate. Mass
flow rate is directly proportional to volumetric flow rate, thus in order to
maximize energy efficiency the desired flow rate should be set in accordance
with the maximum permitted thermal gradient breakdown over the length of
the tank, as defined by further behavioral experimentation with live zebrafish.
19
7. Proof-of-Concept Prototype
As a proof-of-concept, a prototype thermal gradient tank system was
designed and manufactured. The system consists of: a cuboidal polycarbonate
tank, 12" long, 12" high, and 6" wide; a heater manifold with gasket fittings
for tank sealing and thermal insulation; two strip heaters with electrical
connections; and an outlet mixing chamber shielded by a slotted grate to
minimize fluid mixing at the end of the 'live' area of the tank. The tank is
manufactured of " polycarbonate sheets, jointed and glued with epoxy and
sealed with silicon. The grate used to separate the live area of the tank from
the outlet-mixing chamber is made from a 1/8" polycarbonate sheet, with
horizontal slots cut out at incremental heights. This allows for fluid to flow up
towards the outlet valve behind the sheet, while minimizing fluid mixing in the
live area. Figure 8 shows a side-view of the tank layout, excluding the outlet
structure:
TEMPCO
Strip Hestms
Tank MWde/
Mantfhld Outlet
Tank-sealng pgkets
etther side of twnk
wall
-
Cold-water Inlet
Direction of fltw
Figure 8: Rendering of proof-of-concept prototype. The large blue arrow
represents the direction of intended water flow across the tank. The coldwater inlet features a threaded 1/16" hose fitting inserted into the heater
20
manifold to receive water from a standard laboratory circulation system.
Rectangular tank sealing gaskets are fitted on top of the heater manifold,
either side of the tank wall and compressed by a compression channel bolted to
the manifold outlet.
The heater manifold is designed around a type of strip heater
manufactured by TEMPCO, shown in Figure 9:
Figure 9: Illustration of a 120V 350W TEMPCO strip heater showing a crosssectional view of the internal heating coils and ceramic encasement. The
electrical posts are visible in the near-side of the illustration, and the mounting
holes appear can be seen at each end.
The heaters are designed to produce 350W as thermal energy when
connected to a 120V AC power supply. By the first law of thermodynamics, the
power required to raise the temperature of 2L of 25 0 C inlet water per minute
to the desired mean water temperature of 29*C is approximately 557W. By
using two of the TEMPCO strip heaters wired together in series and plugged into
a British 230V AC supply, the power drawn is approximately 670W. As the
thermal conductivity of air is around 1/ 2 0 th that of water, the power lost to the
environment is assumed to be negligible relative to the power of heat transfer
between the strip heaters and the water.
In order to maximize heat transfer, the heater manifold is designed to
be as thin as is practical for manufacture and operation. For ease of
manufacture, the manifold is made of three sheet metal plates, sandwiched
together and cold-welded. The cold water (25 0 C) inlet accommodates a
standard 1/16" hose by allowing a threaded hose fitting to be screwed into a
drilled and tapped hole that's concentric with a cold-water inlet channel
21
located towards the bottom of the manifold. The interior cavity of the heater
manifold is shown in Figure 10:
/coa
CalNCUctI tip
Mn
fwl
0(d-elng3~~~
heater
-
ho
Figure 10: Annotated rendering of the inner plate of the heater manifold. As
implied by the location of the clearance holes for the strip heater mountings,
the heaters will be mounted either side of the two surface plates that are coldwelded to the inner plate shown - one to the far side (into the page) and one to
the near side (on top of the page). The depth of the resultant cavity is equal
to the 1/16" thickness of the inner plate shown.
The cold-water inlet channel accepts chilled water from a 1/16" hose
fitting and passes it through the expansion funnel. The expansion funnel is
designed in such a way that the flow is directed evenly across the angular
space leading to the large opening that constitutes the manifold outlet.
Backpressure is required within the manifold in order to force the water to fill
the entire cavity. This backpressure is maintained by the presence of a dualpurpose gasket that is mounted to the manifold outlet, perpendicular to the
direction of fluid flow. The outlet gasket is manufactured by water-jet and
consists of overlapping flaps of rubber that act as a unidirectional flow control
valve. This valve is needed to prevent water from escaping the tank by
reversing direction of flow through the manifold if the water supply is turned
22
off. The inlet pressure required to open the flaps enough to allow water to
pass into the tank produces sufficient backpressure to fill the manifold cavity.
As water moves up the manifold cavity it also escapes through the outlet
gasket at an even rate, thus the flow distribution gradient must be present in
order to maintain even flow velocity at all points within the manifold cavity.
Even flow velocity is critical to the effectiveness of the manifold in its capacity
to produce a thermal gradient at its outlet, as the underlying principle of the
design is that the temperature to which a small volume of water is heated is
directly proportional to the time that volume of water remains in contact with
the heater element (i.e. the walls of the manifold). The coolest water exits
the manifold at the bottom as it has spent the least amount of time inside the
cavity. The water exiting the top of the manifold is hottest as it spends the
longest amount of time inside the cavity, and the directional correction lip
turns the upward flow sideways such that it stays parallel with the horizontal
flow exiting the rest of the manifold. Provided that the flow velocity is kept
constant at all points inside the manifold (beyond the expansion funnel), the
distribution of temperature along the length of the manifold outlet should
constitute a linear temperature gradient.
8. Test Method
The proof-of-concept tank was tested by the same method as the
experimental tanks: a thermocouple probe was marked at 5cm increments from
the tip and inserted into the water through the aluminum guide plate (see
Appendix A, Figure 2). A reading was taken at the marked 5cm depth
increments from the water surface to the bottom of the tank (see Appenix A,
Sections 1.1-1.2 & 1.4 for further info). While a 1-dimensional method was
used to test the experimental tanks, a 2-dimensional method was used for the
current system in which temperature measurements were taken at the inlet,
center, and end of the tank. This method was used in order to quantify true
gradient breakdown. Figure 11 shows a side-view of the tank with the test
measurement locations:
23
Outlet Mixing
Chamber
Water Surface
I
I= =
Outlet
Valve
Tank inlet/
Heater
I
I
w
WW
R
LU---
7I_=
I
I
I F
I 1 1,uw
.~~~
Surface
NI
5cm
I
10cm
I
I
JJ___
15cm
-
II
NI
20cm
II
NI
25cm
I
End
Base
-------------
Middle
-I4
Heater
Figure 11: Illustrated side-view of the proof-of-concept tank. Blue crosses
indicate the temperature measurement locations. The green lines represent
the axes along which the thermocouple probe is inserted into the tank during
testing. The heater axis measures the temperature gradient from the heater
outlet while the middle and end axes measure the breakdown of the thermal
gradient as the water flows across the tank from right-to-left. The heater
measurements are taken a few millimeters from the heater outlet, the end
measurements are taken 1" in from the outlet grate that separates the outlet
mixing chamber from the rest of the tank, and the middle measurements are
taken at an equal distance from the heater and end measurement locations.
All measurements were taken in the center of the tank in the axis
perpendicular to the page.
Measurements were taken at all points shown at various time intervals
after startup. Prior to startup, the tank was pre-filled with water at 14 0 C (the
uniform circulation temperature in use at the laboratory facility) and the
laboratory water supply was connected to the manifold's cold-water inlet. The
flow rate was calculated by measuring the volume of water that passed through
24
the tank outlet in a one-minute period. At startup, the heaters were
connected to a 230V electrical outlet, drawing 670W for heat generation.
9. Results & Discussion
-
The flowrate was measured at 0.43L/minute (4% tank volume/minute):
giving a Peclet number of 0.023 < 1. This flow rate significantly lower than an
optimal flow rate for minimizing gradient breakdown while also keeping energy
demand reasonable, as highlighted in Section 6 above. Unfortunately the
flowrate at the test facility was determined by the standard circulatory
equipment in use and therefore could not be altered. By the first law of
thermodynamics, 670W of thermal conversion at 100% efficiency equates to a
mean temperature increase of 22.4*C to the water at a flow rate of
0.43L/minute, thus at 100% efficiency, an inlet temperature gradient of 14 0 C
58.8'C would be expected in the prototype system. Figure 12 shows the actual
temperature gradient observed at the heater outlet:
60
0
0
0
55
0
0
0
=N&=22.5MINS
0
mqb e25MINS
0.
.,
-
50
20MINS
."
0
0
am"=070MINS
0.
45
0
U
40
0
0
**
0
0
0
*Target
1%
****
i
I
ncIy
E
0630
25
-
-
*.,
*0*
*00.
.0*
*****ee
,ol(
-
20
...
-
15
-
10
Surface
5
10
15
Depth (cm)
20
25
Base
Figure 12: Graph of temperature vs. depth at the heater outlet at set time
intervals after startup. The target temperature gradient for 14 0 C water input
is indicated by the dotted blue line. From 20mins - 25mins, the gradient
straightens out to become increasingly linear, however at 70mins the gradient
has distorted to some extent. The error on this graph is smaller than the
marker size.
25
The gradient observed at the heater outlet is significantly steeper
(AT=19.6 0 C) than the target (AT=8 0C) but it is much shallower than expected
at 100% efficiency. Analyzing the base measurements, it seems evident that
the water temperature in circulation increases by around 3 0 C between 25mins
and 70mins, thus an increase of 2.3C in the mean heater outlet temperature is
observed during that period. The true inlet water temperature was not
measured at 25mins or 70mins.
Furthermore, the small increase in
temperature between 25cm and the base of the tank at 70mins is likely due to
residual warming of the bulk fluid that sits in the pocket underneath the heater
outlet, as can be seen at the bottom-right of the tank in Figure 11 above.
For further development of the heater manifold, two key parameters
must be assessed. The first is the profile of the gradient established; the other
is the thermal conversion efficiency. Although advisors to the project have
identified that the gradient observed in Figure 12 above is sufficiently linear
for experimental fish to express behavioral fever, the linearity of the
temperature gradient profile could be improved in two ways. First, the
possibility of an uneven heat distribution from the strip heaters can be
compensated-for by adjusting the profile of the flow distribution gradient
indicated in Figure 10 above. By further experimentation, the heat distribution
across the strip heaters could be analyzed for 'warm' and 'cold' spots, and the
flow rate through the respective parts of the manifold adjusted by thinning or
thickening the cavity, thus increasing or reducing heat transfer as necessary.
Another consideration is that the water-jet used to manufacture the heater
outlet gasket may not have allowed sufficient precision so as to ensure even
release pressure up the inside of the manifold. Any pressure discrepancies
within the manifold result in an uneven flow rate, and therefore an uneven
gradient.
The thermal conversion efficiency can be calculated as the ratio of the
difference between the mean and lowest temperatures measured (assumed to
be equal to the inlet water temperature), and the difference between the
mean and base temperatures of the expected gradient at 100% efficiency. The
100% efficiency case does not consider any bulk fluid warming below the heater
manifold - rather it assumes the heater outlet runs from the base to the
surface of the tank. The mean heater outlet temperature measured at 70mins
is 25.7*C and the lowest (inlet) temperature is 17.5*C; the mean temperature
of the 100% efficiency case is 36.40C with a base temperature of 140 C. The
calculated thermal conversion efficiency of the current system is therefore
32.1%. This implies that 8.7kW would be required in order to establish a linear
temperature gradient of 250 C - 330 C with a flow rate of 1x tank volume per
minute, as the deemed necessary by the current model in order to ensure
sufficient gradient stability. The efficiency could be increased significantly in
future iterations by: thinning the manifold cavity in the axis perpendicular to
the page (relative to Figure 11 above) to increase conduction through the
26
water being heated; by encasing the outside of the strip heaters with a
thermally insulating material; by trimming the excess manifold material from
the right of the heaters as can be seen in Figure 11 above to reduce thermal
conduction and radiation into the surrounding air; by manufacturing the heater
manifold from a material with higher thermal conductivity; and by using
thinner material for the outer manifold plates.
Figure 13 shows the gradient breakdown in the tank, as represented by
temperature measurements taken at the middle and end of the tank 70minutes
after startup.
40 -Heater
OmPMiddle
35 -o
End
U
*
Middle/End (Modeled)
' 30
-
E
20
15
Surface
5
10
15
20
25
Base
Depth (cm)
Figure 13: Graph of temperature vs. depth measured at the heater outlet, the
middle, and end of the tank at 70minutes after startup. The dotted green line
represents the gradient predicted by the model used in Figure 6, as applied to
the larger deltaT produced at the heater outlet of the prototype system.
The predicted gradient at the middle and end of the tank is effectively
zero as the time for fluid to reach the middle of a 10L tank at a flow rate of
0.43L/min should be 698 seconds (assuming ideal laminar, unidirectional flow):
this exceeds the 600second breakdown threshold observed in the model
graphed in Figure 6. While the measured gradient is significantly different to
the modeled gradient, it is indeed 'steeper' and therefore more desirable for
use in the zebrafish application. Despite this, the mechanical implications of
the discrepancy observed must be considered.
27
There are a number of factors that may be contributing to the
difference between the measured and modeled gradients, and more thorough
experimentation would be required in order to identify the magnitude of the
exact causes. Looking closely at the Surface-5cm and 10-15cm regions of the
Middle and End gradients, there is a small reduction in temperature between
10-15cm from middle to end, and a small increase in temperature between the
Surface-5cm from middle to end. Assuming that the thermal energy is
transferred from the lower (10-15cm) region to the higher (Surface-5cm) one,
this is likely a sign of convective heat transfer. The flatness of the Surface5cm region could be another sign that warm fluid is moving to the surface as
the water translates across the tank. After rising water reaches the surface it
transfers some thermal energy to the air above it, thus lowers in temperature
and descends slightly. Over time, the mixing of air-'cooled' water and rising
warm water would be expected to produce a flattened temperature region
within close proximity to the surface.
Another factor to consider is the cuboidal shape of the tank itself. Since
the gradient breakdown does not match the conduction-based model, it may be
the case that the water is reaching the middle/end of the tank in far less time
than the 698seconds predicted. If that is the case, then the flow is most
certainly not unidirectional from one end of the tank to the other. If the flow
is indeed travelling at a higher velocity along the central plane of the tank
(along which the flow is ejected by the heater) than calculated for uniform
flow, then flow is likely to be occurring in the opposite direction along
perpendicular planes at the outer edges of the tank. Such a flow pattern could
be produced by reflection of the heater flow at the face of the outlet grate.
Assuming that the flow rate (and perhaps direction) does vary according to
location along the axis perpendicular to the page in Figure 10 (i.e. distance
from the central plane along which water is ejected), eddies are likely to form
in the corner of the tanks. If present, these are likely to have partial or
complete responsibility for the plateau cooling effect observed below 15cm
depth at the middle and end of the tank in Figure 13, and for the increase of
mean temperature of the tank over time as observed in Figure 12. Fluid is not
replaced in areas shielded by an eddy line, thus fluid of a 'new' temperature
cannot replace fluid of an 'old' temperature to change the thermal profile of
that region of water. Instead, variations in the temperature of these regions
are caused by conduction, and by convection to a small degree. If the bulk
volume of the tank is heated, yet a large portion of the water rests (cold)
behind eddy lines, the eddy water will have a net cooling effect on the tank
water as a whole - perhaps resulting in the flattened curve seen below 15cm at
the middle and end of the tank. Yet as more and more thermal energy is
conducted from the thermal gradient output into the eddy water, that water
increases in temperature (albeit slowly), perhaps contributing to the increase
in mean temperature shown over time in Figure 12.
28
In order to minimize the presence of gradient-degrading eddy water and
optimize the fluid pathway for uniform flow in future iterations of this system,
the tank used should be elliptical in shape. Eddy pockets are likely to exist in
the corners of the cuboidal tank used in this study, and the 6" width of the
tank was not ideal for promoting uniform flow. With an elliptical tank, the
corners would be eliminated such that no eddy pockets could form, and the
gradual expansion and re-contraction of the body would encourage uniform
flow. Furthermore, an increase in flow rate will reduce gradient breakdown
over time while increasing the power required for the same gradient to be
achieved.
10. Conclusion
A series of experiments were conducted in order to determine the most
suitable approach for establishing a stable, linear temperature gradient in
experimental fish tanks. Following thorough analysis of the observations from
these experiments, a design specification was produced that further defined
the goals for the development of this apparatus. The physics of establishing
and maintaining a thermal gradient were analyzed with respect to time, and
these findings were correlated with the flow rate through the tank such that
future design iterations can consider energy factors as they relate to gradient
A prototype was designed and manufactured, and a
sustainability.
temperature gradient of 19.6'C was established (far in excess of the 8 0 C
target) at the outlet of the heater manifold with 32.1% efficiency. The
gradient produced was observed to be sufficiently linear for the application of
enabling the expression of behavioral fever in experimental zebrafish. The
application of this technology will allow for a revision of current immunological
research approaches and methodologies, facilitating optimized immune responses
in experimental zebrafish. This will serve to further our knowledge of this allimportant building block of human medical research.
While the current design was found to meet the practical elements of
the design specification, a number of mechanical aspects such as ensuring even
flow rate along the length of the heater outlet have not been tested-for and
may account for some of the discrepancies between the modeled and measured
results. Further iterations and thorough testing are required in order to
perform sensitivity analysis on various aspects of the system design and inputs,
and to optimize the system for energy efficiency and thermal-fluid
performance. Future iterations may consider: altering of the heater manifold
to improve heat transfer; changing the shape of the test tank from cuboidal to
elliptical; varying the flow rate between experiments to assess breakdown
effects relative to the proposed model; using a higher-precision manufacturing
process for the heater outlet gasket; encasing the outer heater surfaces in an
insulated material; and quantifying the distribution of heat across the heater
surfaces such that flow rate adjustments can be made to compensate.
29
References
MacKenzie, S., Boltafia, S., Rey, S., Roher, N., Vargas, R., Huerta, M., et at.
(2013, June 14). Behavioural fever is a synergic signal amplifying the innate
immune response. (S. MacKenzie, Ed.) Proceedings of The Royal Society , 11.
30
Appendices
Appendix A - Extract from Measurement & Determination of Thermal
Gradients in Experimental Fish Tanks
1. Prototype System & Testing Configuration
Figure 1 shows the prototype system that consists of a cylindrical tank,
108mm ID x 330mm height, with valves located at 0,150, and 300mm from the
base.
Figure 1: Photograph of the assembled prototype system, consisting of the
chiller (bottom), tank (top-left), heater (top-right), pump (center), and clear
PVC tubing. The thermocouple probe and guide plate used to take
temperature measurements from the system are shown to the right.
31
As shown, clear PVC tubing connects the tank to a centrifugal pump, an
in-line water heater, and an in-line water chiller that comprise the thermofluid control system for the tank. Adjusting the tightness of a clamp across the
intermediary stages of tubing controls the flow rate through the heater and
chiller.
The heater flow rate for each experiment was measured by filling the
tank to just below the surface (hot water) inlet in order to provide
backpressure to the lower inlets/outlets, and filling a measuring jug from the
surface inlet for a period of 30 seconds. The volume of water captured was
then multiplied by 2 to give the volumetric flow rate in L. The total flow
rate was then measured by repeating the process for the pump output, and the
chiller flow rate was calculated by subtracting the heater flow rate from the
total flow rate.
Once the relevant flow rates were recorded, the full system was left
running for one hour to reach steady state. Thereafter, the temperature was
measured as a function of depth for a single system configuration by dipping a
temperature probe into the tank at incremental depths of 5cm.
The
temperature readings were logged in Microsoft Excel along with details of the
system configuration and a calibration offset. Temperature measurements
were performed four times for each experiment to ensure accuracy, and
experiments were performed in total - one for each system configuration.
1.1 Thermal Measurement Equipment
A long metal-encased Vernier TCA Thermocouple probe was used to
measure water temperature at a series of depths. Figure 2 shows a tighttolerance location plate that was manufactured and used to keep the probe
centered in the tank for all measurements.
32
Figure 2: Photograph of the machined aluminum plate used to center probe for
measurements. The plate was laid over the top of the tank and its straight
edges were aligned tangentially with the rim of the tank at all four sides. The
thermocouple probe was then inserted into the hole with a tight fitment so as
to ensure consistent radial placement as the probe was inserted deeper into
the tank. Although the current experiment called for measurements to be
taken only in the center of the tank (i.e. by dipping the probe through the
bottom hole shown above), the multiple holes could be used for taking
measurements at a range of radii such that a three-dimensional thermal model
of the experimental tanks could be determined.
A TCA type-K thermocouple reader connected to a LabPro interface
operated the Vernier probe. A laptop running Logger Pro software recorded
the probe's temperature reading via a USB connection to the LabPro. The
temperature readings were then copied into an Excel spreadsheet in which the
system configurations were logged and the data analyzed.
1.2 Thermocouple Calibration
A medical thermometer was used to calibrate the thermocouple prior to
each experiment. The medical thermometer and the thermocouple were
placed in a bowl of warm water and their readings were taken. The LabPro's
inbuilt calibration feature could not be used, so an offset was incorporated into
the Excel file in which the data were recorded.
33
1.3 System Configurations
Six system configurations were tested. Each system configuration is
defined by the total flow rate through the pump, the partial flow rate through
the heater and chiller (if used), additional cooling methods when used, the
inlet locations for the heated and chilled water into the tank, and the outlet
location to the pump. The heater inlet, chiller inlet, and outlet locations were
fixed by the three valves located at 0mm (bottom), 150mm (center), and
300mm (top) from the base of the tank. Table 1 shows the six configurations
tested:
Table 1: Experimental system configurations including flow rates, inlet/outlet
locations and additional cooling method where appropriate.
Figure 3 shows the inlet/outlet locations on the tank:
34
0mm
Top (HeaterInlet)
I
150mm
Center
300mm
Bottom
Base (AdditionalCooling)
Figure 3: Graphical representation of the experimental tank, showing the top,
center, and bottom valve positions and their respective depths. The
application of cooling to the tank base is also indicated.
Figures 4 & 5 show the two additional cooling methods used: the "flat fancooled base"; and the "column fan-cooled base":
Figure 4: IceProbe column fancooled base
Figure 5: Intel STS100A Flat fancooled base
35
Both the IceProbe and STS100A are comprised of an aluminum heatsink
and a DC fan.
The IceProbe applied its cooling to the water via a
probe/column that protruded through the tank base while the STS100A directly
cooled the flat base of the tank. In their respective system configurations, the
IceProbe is mounted to a polycarbonate tank base with a 1 " hole to house
the probe (column), while the Intel STS100A active heatsink is attached to a
flat aluminum base plate. Figure 6 shows the STS100A attached to the base of
the tank:
Figure 6: Experimental Tank with STS100A flat fan-cooled base attached
All configurations used a Hydor ETH201 200W external in-line heater and
a Hydor Seltz L20 11W pump, and the chiller used in some configurations was
an AquaEuro USA Max Chill 1 /13HP (57W) external aquarium chiller.
1.4 Tank Measurements
After setup and flow rate measurement, each experimental tank
configuration was left for one hour to reach steady state. The temperature
probe was then calibrated, and measurements taken.
36
The probe was inserted into the center hole on the aluminum location
plate (Figure 2) and markings on the probe at 5cm intervals from base to tip
were aligned with the aluminum location plate to ensure that measurements
were taken at repeatable depths. The temperature readout from Logger Pro
was copied into the 'measured temp' column of the Excel data spreadsheet and
adjusted according to the thermocouple calibration. A portion of the Excel
data spreadsheet is shown in Table 2.
Table 2: Excerpt of Excel data logging file, showing measured and adjusted
data for Tank C
Depth
(cm)
Measured Temp
2C.
Adjusted Temp
3C
5
26.2
30.7
15
26.2
30.7
25-
25.8
30.3
The "Measured Temp" is the readout from Logger Pro and the "Adjusted
Temp" adds the thermocouple's calibration offset to the Measured Temp value.
Each experimental configuration was measured four times at each
depth. After measurements were completed, the apparatus was re-arranged
for the next configuration and the process repeated.
37
Appendix B - Extract from Measurement & Determination of Thermal
Gradients in Experimental Fish Tanks
2. Recommendations
It is proposed that a further system is tested in which water is heated
from bottom-to-top in a thin thermal control chamber that extends the height
of the tank at one side. The thermal control chamber should contain a fluid
flow tube surrounded by a coiled resistance wire121 that produces constant
heating (i.e. constant radial heat flux, allowing Fourier's law to apply) from
the base to the top of the tank, into which water enters at the desired base
temperature of the tank (25 0 C). At a large number of regularly spaced
intervals from bottom-to-top, a small channel should be present between the
thermal control chamber and the tank to allow for water to flow in at the
appropriate temperature for the depth. Some amount of calculation would be
required in order to determine the fluid pressure profile within the thermal
control chamber necessary to counteract the pressure due to the depth of the
tank, as needed in order to ensure equal flow at every depth. On the opposite
side of the tank, a mirror-image of the tank inlet channels should be formed
allowing water to exit the tank into a drainage chamber at an equal flow rate
at every depth, thus ensuring that all flow remains perpendicular to the
desired thermal gradient in the tank. At the very base of the tank, a larger slit
should be formed along the downstream half to allow for biological waste to be
'scraped' off the bottom of the tank by the lateral flow.
3. Conclusions
A suitably linear temperature gradient of 2.4 0.1 C was established in
tank E, which was fed by a hot water intet at the top, a chilled water inlet at
the center to force mixing of the hot and cold water, and an outlet at the
base. Tank E received additional cooling from a flat fan-cooled base in order
to extend the gradient past the central mixing point of the hot and cold water.
Although the mean temperature was not high enough and the temperature
range was much lower than the 8*C requirement, it is assumed that a 250 C33*C temperature gradient could be established by further iterations on this
configuration, including a higher-powered heater and chiller, and a more
accurate method of flow rate regulation.
Moreover, it was determined that the stability and linearity of a tank's
thermal gradient response would be greatly improved if the fluid was flowing
perpendicular to the direction of the desired thermal gradient. By taking this
into consideration it is recommended that any future prototype tanks are
constructed such that horizontal flow is induced, eliminating the requirement
for heat transfer or fluid mixing in order to establish a vertical thermal
gradient.
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Appendix C - MATLAB Script for modeling the change in water surface
temperature over time as an approximation of thermal gradient breakdown as
water translates from one end of a fish tank fitted with a thermal-gradient
inlet to the other.
clear;
lambda=0.61; %thermal conductivity factor of water (W/m*K)
rho=996;
%density of water (kg/m^3)
c_water=4180; %specific heat of water at 25degC (J/g*K)
alpha=lambda/(rho*c water);
%thermal diffusivity of water (m^2/s)
z=0.3; %depth to be plotted (m)
d=0.3;
%depth of tank (m)
T_b=25; %base temperature of tank at t=O (degC)
T_s=33; %surface temperature of tank at t=O (degC)
T=[];
t=0;
t_max=600;
while t<=t max
n=1;
sum=O;
while n<=9 %generate series solution for n=1,3,5,7,9
sum = sum + ((1/(n^2*pi^2))*cos(n*pi*z/d)*exp(1000*alpha*nA2*pi^2*t/(d^2)));
n = n+2;
end
T(t+1)=Tb+((T_s-T_b)/2)-(4*(T_s-T_b)*sum); %absolute surface
temperature at time t
t=t+1;
end
t=[0:1:tmax];
plot(T)
39