Table of Contents
1.
2.
3.
4.
5.
6.
7.
8.
Section
Executive Summary
Introduction
Design Objectives
Methodology
Governing Equations
Material Properties
Boundary Conditions
Geometry and Mesh
Mesh Convergence Study
Results and Discussion
Initial Results
Accuracy Check
Sensitivity Analysis
Final Results
Conclusion
Design Recommendations
Design Constraints
Appendix
References
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3
3
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4
4
5
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6
7
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9
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10
11
1|Page
Executive Summary
Knowledge of survival time for shipwreck victims in
cold water can greatly increase the effectiveness of
the safety measures taken to prevent hypothermia.
Hypothermia is a condition that occurs when the core
body temperature of a person drops below that
required for normal body functions. Hypothermia is
very dangerous, and is fatal if the core body
temperature of a person drops below 30 degrees
Celsius. This is a drop of only 7 degrees Celsius from
the normal core body temperature of a person that is
around 37 degrees Celsius. Survival suits can be used
to greatly decrease the rate of heat loss from
individuals exposed to cold water, and search and
rescue teams also greatly help out by trying to get the
victims out of the water as soon as possible. There
are many different proposed models that have been
developed for the purpose of determining survival
time. Existing models range widely from simple onedimensional analytical models utilizing basic heat
transfer equations, to models that are very complex
where individual body segments are modeled in
three dimensions. All of these models typically
incorporate fat, muscle, core, and skin regions of the
body as the predominant layers that inhibit heat loss.
These models typically take into account the
metabolic heat production of the body as well.
Finally, models typically always are able to predict
survival time by measuring the time it takes for the
body core temperature to drop to 30 degrees Celsius.
For our model we are using a geometry that is a
single cylinder to model the human body. The
cylinder consists of fat, muscle, core, and skin layers.
All dimensions and parameters of the model are
chosen corresponding to a statistically average adult
male. These parameters include amount of body fat,
muscle, and skin, as well as material properties such
as thermal conductivity of the different layers of the
body. The model is modeled in Comsol multiphysics.
With the software, an outer boundary conditions is
set corresponding to water flow around the body,
where a heat transfer coefficient is used
corresponding to the heat transfer coefficient around
the human body.
The model incorporates a
neoprene wetsuit layer to simulate the effects of a
survivor wearing a neoprene survival suit. The goal of
the study is to examine the effects of different
wetsuit thicknesses on the overall survival time of the
survivor. Also in the study, a study was conducted to
see how water temperature effects the survival time
of an individual.
Several accuracy tests were
conducted to ensure that the model is acceptable
and accurate. The tests confirm that the current
model performs similar to an analytical model and a
model conducted by other researches. The Accuracy
test was done by comparing heat loss rates from the
body over a range of different water temperatures. A
sensitivity analysis was done where a range of
metabolic heat production values were tested. The
study showed that the metabolic heat production
values greatly affected survival time. The final testing
of the model was done with a range of 3 to 11 mm
thick wetsuit thicknesses. The study found that
increasing the thickness from 3 mm to 11mm more
than doubled the survival time from 2.5 to around 5
hours in 5 degrees Celsius water. A test of how
different water temperatures effected survival time
for a 5mm wetsuit revealed that survival time greatly
increases with water temperature. The model in the
end is still considered very basic, but is very useful for
gaining a better understanding of the relationship
between wetsuit thickness and survival time. Further
progress needs to be made in order to consider the
model advanced enough to be used in real world
applications of modeling survival time. Some of
these advancements would include the incorporation
of multiple body segments in the model. Also, blood
perfusion should be included in the model.
2|Page
Introduction
Design Objectives
The development of the neoprene survival suit has
greatly
benefited
individuals
exposed
to
environments where cold water immersion is a
health and safety concern. Neoprene is a very good
insulator due to its low thermal conductivity, which
lessens the transfer of heat through the material.
When used as survival suits for ship wreck situations
where hypothermia is a concern, neoprene suits can
greatly extend survival time for individuals. In ship
wreck situations, it is particularly important to know
the amount of time an individual has to survive.
Predicting the extension of survival time that these
suits provide is advantageous for both specifying the
type of suit required for safety in certain situations as
well as in the aid of search and rescue teams. By
knowing beforehand how long a victim has to survive,
search and rescue teams are better able to
coordinate their missions.
By creating a simplified model of a human in
Comsol multiphysics, a finite element based software
program, we plan to simulate core body temperature
as a function of time to determine survival time. We
can then examine the relationship between wetsuit
thickness and survival time by varying the wetsuit
thickness in our model. The criteria for determining
survival time will be taken as the point at which the
core body region drops to a temperature of 30
degrees Celsius[2]. The human will be modeled as a
single cylinder with the cylinder being divided into
corresponding layers of the core region, muscle, fat,
skin, and the wetsuit layer. Body region proportions
and thicknesses, such as body fat to total body
weight ratio, will correspond to a statistically average
adult male
For individuals adrift at sea in cold water the
primary cause of death is hypothermia.
Hypothermia occurs when the body’s core
temperature drops to a level where normal muscular
and cerebral functions are impaired. It is generally
accepted that the core temperature at which
hyperthermia becomes fatal is 30 degrees Celsius. By
providing added insulation, survival suits limit heat
loss from the body, greatly slowing the drop of core
temperature. Determining survival time then is
based on the body core temperature drop. Many
analytical and finite element models have been
proposed that simulate the core temperature drop,
allowing predictions of survival time to be made.
Early models by Gagge et al[1] used analytical
methods and a single cylinder human analog to
predict survival time. Tikuisis, Tarlochan, and Fanger
all used single cylinder models. More advanced
models use a segmented multi-cylinder approach,
such as Ferreira et al. In these studies, survival time
was predicted by observing core body temperature
change for certain cases of water temperature and
biophysical parameters of the survivor.
The first part of the study focuses on validating the
Comsol model by comparing results with other case
studies and models. The later part of the study
compares results for survival time of different
thickness wetsuits, and results are discussed.
Methodology
Governing Equations
The basic energy balance used to determine heat
loss from the body is,
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦
= ℎ𝑒𝑎𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 − ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑡
𝑑𝑈
𝑑𝑡
= 𝑄̇𝑔𝑒𝑛 − 𝑄̇𝑙𝑜𝑠𝑡
1
In equation 1, the work term is not included. This is
because it is assumed that the subject is stationary,
and therefore not exerting any work. Heat produced
(𝑄̇𝑔𝑒𝑛 ) in equation 1 represents basal metabolic rate
as well as heat generated from shivering. Basal
metabolic rate, or BMR, is essentially the amount of
calories that a person burns in a given amount of
time. A rough estimate of about 100 Watts can be
used to start out with, but the research that we have
3|Page
seen indicates that a person’s BMR increases when
exposed to cold environments [3]. We can expect to
see heat production values reaching as high as 250
Watts[3]. Heat lost (𝑄𝑙𝑜𝑠𝑡 ) in equation 1 is dependent
upon the thermal resistance associated with the
various body layers and wetsuit which are depicted in
Figure 1. Heat loss is also a function of the
temperature of the water, and more specifically the
heat transfer coefficient around the human body due
to the water.
Equation 1 can be rewritten as,
𝑚̇𝐶𝑝
𝑑𝑇
𝑑𝑡
= (𝐵𝑀𝑅 + 𝐻𝑆) −
𝑇𝑐𝑜𝑟𝑒 −𝑇𝑤𝑎𝑡𝑒𝑟
𝑅𝑡𝑜𝑡𝑎𝑙
[Watts]
2
Where BMR is the basal metabolic rate, HS is heat
generated due to shivering, 𝑇𝑐𝑜𝑟𝑒 is the core
temperature, 𝑇𝑤𝑎𝑡𝑒𝑟 is the temperature of the water,
and 𝑅𝑡𝑜𝑡𝑎𝑙 is the total thermal resistivity associated
with the layers of body tissue, wetsuit, and water.
The value for BMR used in the current model is
debatable, as our sources are giving conflicting
information as to what this value should be. We have
discovered that it is somewhere in the range from
100 Watts to 500 Watts, as there are many factors
involved in heat production, such as metabolism,
blood perfusion, and shivering. Since equation 2
doesn’t take into account the changing core
temperature, to better understand the transient
conditions we can refer to the transient conduction
equation.
𝛿𝑇
𝛿𝑡
=
𝑘 𝛿𝑡𝑇
𝜌𝑐𝑝 𝛿𝑥 2
+
𝑄
𝜌𝑐𝑝
3
Material Properties
Important material properties here are thermal
conductivity, density, and specific heat capacity for
each body region as well as the wetsuit layer.
Material properties for each body region differ only
slightly when comparing sources. All properties used
in the model are listed in table 1. These properties
are held constant with respect to time, and any
variation in these values over time is negligible. This
includes changes in thermal conductivity of the
neoprene material due to soaking in seawater.
Compared to the neoprene fabric, water trapped
against the body from the wetsuit does not provide a
significant amount of added insulation.
Properties and Parameters used in the
model
k
cp
ρ
BM
[W m-1 K-1] [J kg-1 K-1] [kg m-3] [W m-3]
Core
0.49
3504
1080
3852
Muscle
0.51
3800
1085
684
Fat
0.21
2300
920
368
Skin
0.47
3680
1085
368
Wetsuit
0.15
1268
1400
0
Blood
3850
1059
0
Table 1. Properties and parameters used in the model. A
majority of values were taken from Ferreira[4]. BM is the basal
metabolic rate per unit volume.
Boundary conditions
Figure 1. Quarter cross section of the cylindrical geometry used
to simulate a human body.
Boundary conditions that pertain to the geometry
in figure 1 are as follows. The bottom and left
boundaries are lines of symmetry and are adiabatic.
The outer-most wetsuit boundary has a heat transfer
coefficient of 136𝑊⁄ 2 as well as an ambient
𝑚 𝐾
temperature
corresponding
to
the
water
temperature which depends on the conditions being
simulated. The heat transfer coefficient corresponds
to cold water flow around a human body at a velocity
of 0.25 m/s, determined experimentally [5]. All
4|Page
internal boundaries are continuous, allowing heat to
flow from the core to the surrounding water.
The model incorporates basal metabolic heat
production rates for not only the core, but the
muscle, fat, and skin regions as well.
Basal
metabolism rates for these regions were taken from
Ferreira [4] and can be found in table 1.
Geometry and mesh
testing. The parameter that was observed for the
study was the average temperature of the muscle
region of the model. This temperature was found by
observing a domain integration for the region where
values of temperature were plotted over the time
range that the problem was solved for. The study
started with a number of degrees of freedom(DOF) of
1279 and went up to 22191 DOF. A free mesh was
used in the model. Table 2 summarizes the data from
the convergence study.
DOF
1279
1534
2168
2556
4501
8427
9939
11813
22191
Figure 2. Free mesh generated for the geometry.
The geometry is a quarter cross section of a
cylinder. The model is not meant to be an accurate
model of the body’s ability to keep core body
temperature stable depending on the climate. Its
primary function is to model heat loss from the
human body, as well as predict the subsequent drop
in core temperature. The dimensions of the cylinder
were chosen according to the average surface area
and volume of a adult male. Values for average
surface area and volume, as well as the average
surface to volume ratio of a human were taken from
literature by F. Tarlochan and S. Ramesh as well as
papers by T.J. Nuckerton[5][6]. The value for body
surface area used is 1.8 m2. Body volume is taken to
be 66.4 Liters. Surface to volume ratio is 0.0282
m2/L.
Mesh convergence study
A mesh convergence study was performed to
ensure that the mesh was an appropriate size for
Average Muscle Temp at 2 hours [C]
23.1449
23.07895
23.0686
23.0588
23.108
23.1449
23.1326
23.0588
23.108
Table 2. Data from the convergence study showing little effect of
DOF on average temperature.
The results of the convergence study show a trend
indicating that the number of degrees of freedom has
little effect on the results if chosen above 1279
degrees. None of the data points deviate past one
tenth of one degree. For the model, we will be
working with temperatures significant to only one
decimal place. Therefore, as long as we stay above
1279 degrees of freedom, our results should be in the
range of mesh convergence.
For all of the
simulations, approximately 2500 degrees of freedom
were used.
Results and Discussion
Initial results
Initial results were compared with a similar one
cylinder model by Tikuisis where survival time was
estimated for various water temperatures [2]. The
study found that for an average sized male nude
5|Page
subject in zero degree Celsius water, survival time
was approximately two hours. These conditions were
replicated with our model by removing the wetsuit
region to simulate a nude subject and setting the
external temperature to zero degrees Celsius. A plot
was obtained of the core temperature seen in Figure
3.
Figure 4. Core temperatures for nude humans in zero degree
Celsius water, determined experimentally and plotted for a time
range of 30 minutes. Study was conducted by Hayward et al [3].
We replicated these conditions in our model and
observed the cooling rate, which is seen in figure 5.
Figure 3. Plot of core temperature at point (0,0) versus time in
seconds submerged in zero degree water for a nude subject. The
survival time is about 2 hours, as this is the point where the
temperature reaches 30 degrees Celsius.
In this test, our model agrees well with the model
used by Tikuisis, as both models predict a survival
time of 2 hours for the conditions given. Although
Tikuisis appears to be a credible author as we have
seen him as co-author in several studies concerning
human survival time in cold water, intuitively it is
hard to believe that a human can survive for two
hours with no clothing in zero degree Celsius water.
We suspect that our model may not hold true for
such low water temperature conditions, as the two
hour survival time seems unrealistic. To further
verify the model, the team decided to compare
results with a case study. In Thermal Balance and
Survival Time Prediction of Man in Cold Water[3],
core temperatures for humans in zero degree Celsius
water were measured experimentally for 21 test
subjects. Results from this study are summarized in
the following graph.
Figure 5. Core temperature at point (0,0) for a nude subject in
zero degree water plotted for a 30 minutes interval for our
model.
From the results of our model, it appears that
there is a drop of about 0.8 degrees Celsius for the 30
minute time span. For the model by Hayward, there
was a drop of about 2 degrees Celsius for the 30
minutes span. This works out to be a difference of
more than a degree between our results and theirs,
and so this comparison is inconclusive.
Accuracy check
The team chose to compare results with both an
analytical model as well as experimental data from a
6|Page
paper by Hayward et al [3]. The analytical model is a
steady state thermal resistance model referenced in
Incropera and DeWitt [7]. The model uses the
following thermal resistance equation.
𝑇𝑖 −𝑇𝑖𝑛𝑓
𝑞
𝑟
ln( 2)
𝑟
ln( 3)
𝑚
𝑓
𝑟1
𝑟2
𝑟
ln( 4)
𝑟3
𝑟
ln( 5)
1
𝑟
= 2𝜋𝐿𝑘 + 2𝜋𝐿𝑘 + 2𝜋𝐿𝑘 + 2𝜋𝐿𝑘4 + 2𝜋𝑟
𝑠1
5 𝐿ℎ
𝑠2
5
Here, 𝑇𝑖 is the core temperature which is set constant
at 35 degrees Celsius. 𝑇𝑖𝑛𝑓 is the water temperature,
𝐿 is the total length of the cylinder, and 𝑘 values are
thermal conductivity values for the different layers
listed in table 1. 𝑟 is the radius with the subscript
representing the different layers of the model, and ℎ
is the convective heat transfer coefficient of the
water, which is set at 136 W/m 2 K. A solution was
generated for the analytical model at five different
water temperatures. In the study done by Hayward
et al, body heat loss was measured experimentally for
different test subjects. Figure 6 shows the results
from the analytical, Comsol, and Hayward studies of
the heat loss rate of a human in varying water
temperatures. In Comsol, the heat loss rate was
taken
to
be
an
average
over
time.
Sensitivity analysis
Basal metabolic rate of a human varies greatly
depending on environmental and physical conditions
such as skin temperature, shivering rate, and physical
activity. BMR is an important value in the model
because metabolism and insulation are the two most
important factors in survival time. In order to better
understand the effects of BMR on survival time a
sensitivity analysis was conducted where survival
time was examined for several different rates of heat
production. The findings are plotted here.
Survival time vs. BMR
3
2.5
Body heat loss versus water
temperature
350
Heat Loss (Watts)
The results from Figure 6 show a general
agreement between our model and the analytical
solution, as well as the case study conducted by
Hayward et al. The data all have similar slopes and
intersect at around 30 degrees Celsius.
Survival time (hrs)
400
Figure 6. Body heat loss for various water temperatures for a
nude subject. Data for Hayward was taken from Thermal Balance
and Survival Time Prediction of man in Cold Water [3].
300
250
200
2
1.5
1
0.5
150
0
100
71.2
50
104.3
137.4
170.5
203.6
Total metabolic heat production (Watts)
0
5
10
17.5
25
37
Figure 7. Sensitivity analysis of survival time versus BMR. The
correlation is roughly linear.
Model
The results of this sensitivity analysis indicate that the
survival time prediction varies greatly with BMR. This
means that BMR must be chosen carefully for the
model.
Water Temperature (Celsius)
Hayward
Analytical
7|Page
Final Results
Survival Time for different wetsuit
thicknesses
6
Survival time(hrs)
5
8
7
Survival time(hrs)
The relationship between survival time and
wetsuit thickness was examined by obtaining a plot
of survival time versus wetsuit thickness with the
model at a water temperature of 5 degrees Celsius.
Survival time for different water
temperatures
6
5
4
3
2
1
0
4
0
2.5
5
7.5
10
12.5
Water temp(Celsius)
3
Figure 9. Survival time for different water temperatures for a
5mm thick wesuit.
2
1
0
0
3
4
5
7
9
11
Wetsuit thickness(mm)
Figure 8. Survival time for different wetsuit thicknesses at a
water temperature of 5 degrees Celsius.
The plot in figure 8 indicates that thick wetsuits
extend survival time. The graph appears to be
roughly linear. Next, the 5mm thick wetsuit was
tested in different water temperatures ranging from
zero to 12.5 degrees Celsius.
Figure 10. Core body temperature drop over a span of 5 and ½
hours for a 11mm thick wetsuit and a water temperature of 5
degrees Celsius.
It is interesting that the temperature is initially
increasing for a short time. This is the region where
the temperature distribution in the model is not in
equilibrium due to the initial temperatures of the
different body layers. Once the model is introduced
to the water (when you click “solve” in Comsol), the
model quickly reaches equilibrium where the core
temperature drop is approximately linear.
8|Page
The trends of both plots in figure 8 and 9 are what
one would expect for the given conditions in the test.
When wetsuit insulation thickness increases, survival
time increases. Also, water temperature greatly
affects survival time. Water temperature is in fact
the greatest factor in survival time. Looking at figure
9, the slope of the curve is clearly increasing in the
positive direction. This increase in slope is much
more profound than in figure 8 where the plot is
roughly linear. The fact that water temperature is a
great factor in survival time is not a surprise. Heat
transfer occurs across a temperature difference.
Reduce that temperature difference, and heat
transfer, or in this case heat loss from the body, is
greatly reduced, which is what is seen in figure 9.
The effect of wetsuit thickness on survival time is
slightly less profound than the effect of water
temperature. However, wetsuit thickness unlike
water temperature is a parameter that can be
controlled depending on the situation, and so this is
the parameter that is of interest. For a man wearing
a 3mm wetsuit in 5 degree water, survival time is only
around 2 hours 30 minutes. Wearing a thick wetsuit
of around 11 mm can approximately double this
survival time, as seen in the results in figure 8.
Conclusions
To restate, a human body can only sustain so much
cold before the hypothermia sets in. Wetsuits are
made to help a person resist the cold by reducing the
amount of heat lost to the water around him or her.
Our study focuses on how long an unconscious
person can survive in extremely cold waters before
death is inevitable by modeling the human body as a
cylinder and showing how the body reacts to the cold
water environment over time.
Design Recommendations
As stated previously, the survival time of a human
immersed in cold water is important for two reasons.
The first is for the specification of survival wetsuits
for individuals working in different environments.
The second is to aid in search and rescue missions
where knowledge of a victim’s survival time allows
people to make more informed decisions in planning
a rescue. As far as specifications go, the model sheds
light on the importance of different suits for different
cold water environments. Situations with very cold
waters will require suits that are significantly thicker
than situations where water is not as cold.
Specification of a suit for a certain situation cannot
be oversimplified as there are many factors beyond
water temperature that come into play. These may
include proximity to shore or a rescue vessel,
strength of the waters, size of the ship, and local
weather conditions.
For the search and rescue worker needing to know
survival time, this model confirms that survival time
can be estimated, and that suits provided for the
shipwreck victims must be taken into consideration.
As mentioned previously, wearing a wetsuit can easily
double survival time, depending on the thickness of
the suit. Rescue workers should take heed of this
when considering the risk-benefit factors of a
mission, such as situations where it may be beneficial
to hold off a rescue mission until a later time.
Design Constraints
Conclusions drawn from this study can have a
significant impact on matters of life and death.
Survival suits are called such because they do exactly
that, keep you from dying. Much discretion must be
used in the production and specifications of these
suits. There are currently several other much more
advanced models of the human thermoregulatory
system that can be used and have been used to
predict the survival time for humans adrift at sea.
Such models should be used in practice that have
been rigorously peer reviewed and approved of by
experts. Our model, while useful in understanding
the general relationship between wetsuit thickness
and survival time, as well as other factors such as
water temperatures, is not the most qualified model
for use in such important matters as saving a man’s
life. If future work were to be conducted building
9|Page
upon the current model, there are several steps that
could move the model into being one more worthy of
recognition and use for biomedical applications. The
first would be the move from a single to a multisegmented model. The human body is highly
complex even with regards to basic functions like
heat regulation. Arms, legs, head, torso and all other
parts of the body have differing insulative layers of
tissue as well as complex blood perfusion.
Incorporating multiple body segments will take this
into account. Shivering occurs in some areas more
predominantly than others as well. This would also
be taken into account with a multi-segmented model.
Comsol is a powerful tool that would allow great
detail to be taken if such a model were to be
pursued.
10 | P a g e
Appendix A. Mathematical Statement
A.3. Boundary Conditions
A.1. Geometry
Figure A.1.1 Quarter cross section used to simulate the
human body
A.2. Governing Equations
The basic energy balance used to determine heat loss
from the body is,
Figure A.3.1 – Numbering system for the different
boundaries of the geometry.
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦
= ℎ𝑒𝑎𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 − ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑡
𝑑𝑈
𝑑𝑡
= 𝑄̇𝑔𝑒𝑛 − 𝑄̇𝑙𝑜𝑠𝑡
In equation 1, the work term is not included. This is
because it is assumed that the subject is stationary,
and therefore not exerting any work. Heat produced
(𝑄̇𝑔𝑒𝑛 ) in equation 1 represents basal metabolic rate
as well as heat generated from shivering. Heat lost
(𝑄𝑙𝑜𝑠𝑡 ) in equation 1 is dependent upon the thermal
resistance associated with the various body layers
and wetsuit which are depicted in Figure 1.
Number
1
2
3
4
5
6
7
8
Equation 1 can be rewritten as,
Table A.3.1 – Boundary conditions for boundaries of the
geometry shown in figure A.3.1.
𝑑𝑇
𝑚̇𝐶𝑝 𝑑𝑡 = (𝐵𝑀𝑅 + 𝐻𝑆) −
𝑇𝑐𝑜𝑟𝑒 −𝑇𝑤𝑎𝑡𝑒𝑟
𝑅𝑡𝑜𝑡𝑎𝑙
Condition
Adiabatic(thermal insulation)
Adiabatic(thermal insulation)
Continuity
Continuity
Continuity
Continuity
Continuity
Heat flux: h=136W/mK, Tamb=water temp
[Watts]
Where BMR is the basal metabolic rate, HS is heat
generated due to shivering, 𝑇𝑐𝑜𝑟𝑒 is the core
temperature, 𝑇𝑤𝑎𝑡𝑒𝑟 is the temperature of the water,
and 𝑅𝑡𝑜𝑡𝑎𝑙 is the total thermal resistivity associated
with the layers of body tissue, wetsuit, and water.
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A.4. Input Parameters
Properties and Parameters used in the
model
k
cp
ρ
BM
[W m-1 K-1] [J kg-1 K-1] [kg m-3] [W m-3]
Core
0.49
3504
1080
3852
Muscle
0.51
3800
1085
684
Fat
0.21
2300
920
368
Skin
0.47
3680
1085
368
Wetsuit
0.15
1268
1400
0
Blood
3850
1059
0
Table A.4.1- Data from the convergence study showing little
effect of DOF on average temperature
Appendix B. Solution Strategy
B.1. Solver
Linear system solver: UMFPACK
B.2. Time Stepping
Time range: 1 to 14400 seconds
Type of mesh Triangular, free mesh
Number of elements: 2008
Degrees of Freedom: 4095
Table B.4.1 – Mesh statistics used in the final model.
B.5. Solution Convergence
DOF
1279
1534
2168
2556
4501
8427
9939
11813
22191
Average Muscle Temp at 2 hours [C]
23.1449
23.07895
23.0686
23.0588
23.108
23.1449
23.1326
23.0588
23.108
Table B.5.1. Data from the convergence study showing little
effect of DOF on average temperature.
Time step: 1 second
B.3. Tolerance
Relative Tolerance: 0.01
Absolute Tolerance: 0.0010
B.4. Type of Mesh
Appendix C. Additional Information
C.1. EES Code used for analytical solution
// Tom Barkley and Alexa Singer
// Analytical Analysis of Temperature vs. Heat Loss
// givens
r_1=0.02816 [m]
r_2=0.05816 [m]
r_3=0.068163 [m]
r_4=0.070163 [m]
r_5=0.070963 [m]
k_m=0.5 [W/m*K]
k_f=0.19 [W/m*K]
k_s1=0.45 [W/m*K]
k_s2=0.24 [W/m*K]
T_i=35+273.15 [K]
// T_f is changing for parametric study
L=4.19 [m]
h= 136 [W/m^2*K]
Figure B.4.1 – Mesh used in the model geometry.
// finding the natural logs
ln_1=0.605619
ln_2=0.158704
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ln_3=0.028919
ln_4=0.011338
// equation
(T_i-T_inf)/q= (ln_1/(2*pi*L*k_m)) + (ln_2/(2*pi*L*k_f))
+ (ln_3/(2*pi*L*k_s1)) + (ln_4/(2*pi*L*k_s2)) +
(1/(2*pi*r_5*L*h))
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Appendix D. References
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temperature scale based on a simple model of human
physiological regulatory response.” ASHRAE
Transactions. 77.1 (1971): 247-262.
[2] Peter Tikuisis. "Prediction of Survival Time at Sea
Based on Observed Body Cooling Rates." Aviation,
Space, and Environmental Medicine 68.5 (1997): 44148.
[3] J.S. Hayward, J.D. Eckerson, and M.L. Collis.
"Thermal Balance and Survival Time Prediction of
Man in Cold Water." Canadian Journal of Physiology
and Pharmacology 53 (1975): 21-32.
[4] Ferreira, M. S., and J. I. Yanagihara. "A Transient
Three-Dimensional Heat Transfer Model of the
Human Body." International Communications in Heat
and Mass Transfer 36.7 (2009): 718-24.
[10] Fanger, P.O. “Calculation of thermal comfort:
introduction of a basic comfort equation.” ASHRAE
Transactions. 73.2 (1997): III.4.1 – III.4.20.
[11] Ashim Datta, and Vineet Rakesh. An
Introduction to Modeling of Transport Processes:
Applications to Biomedical Systems. 1st ed. New
York: Cambridge University Press, 2010.
[12] P.F. Iampietro, et al. "Heat Production from
Shivering." Journal of Applied Physiology 15.4
(1960).
[13] D.S. Pal, and S. Pal. "Prediction of Temperature
Profiles in the Human Skin and Subcutaneous
Tissues." Journal of Mathematical Biology 28
(1990): 355-65.
[14] "Heat Capacity of Elastomers." Setaram
Instrumentation. . Setaram Instrumentation
K&P Technologies.
[5] F. Tarlochan, and S. Ramesh. "Heat Transfer
Model for Predicting Survival Time in Cold Water
Immersion." Biomedical Engineering Applications
Basis Community 17.4 (2005): 159-65.
[6] Nuckton, Thomas J., et al. "Hypothermia from
Prolonged Immersion: Biophysical Parameters of a
Survivor." Journal of Emergency Medicine 22.4
(2002): 371-4.
[7] Incropera, DeWitt et al. Fundamentals of heat and
mass transfer. 6th ed. International Edition. John
Wiley and Sons. 2007.
[8] C. Boutelier, L. Bougues, and J. Timbal.
"Experimental Study of Convective Heat Transfer
Coefficient for the Human Body in Water." Journal of
Applied Physiology 42.1 (1977): 93-100.
[9] Zolfaghari, Alireza, and Mehdi Maerefat. "A New
Simplified Thermoregulatory Bioheat Model for
Evaluating Thermal Response of the Human Body to
Transient Environments." Building and Environment
45.10 (2010): 2068-76.
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