This document outlines the design of a heated driveway system using a network of underground pipes, a heat exchanger, and pump. It analyzes using propylene glycol instead of water as the heat transfer fluid due to its lower freezing point. The system is designed to maintain the driveway surface at 40°F when the ambient temperature is 0°F with 10mph winds. Thermal and structural analyses were performed to size the pipe network and ensure the concrete slab does not fail under typical loads. An economic analysis found the system would cost $16 per square foot for installation and $0.20 per square foot annually to operate.

1.
Heated Driveway Slab
MEMS 1065
Analysis Performed by:
Never Slippin’
Engineers:
Matt Hilger
Taylor Koffke
Thomas Reuss
John Claudy

2. 1
Table of Contents
Abstract ………………………………………………………………………………….. 2
Problem Description …………..……………………………………………………….... 3
Design of Heat Transfer System ………………………………………………………… 4
Thermal Analysis of Piping Network …………………………………………………….6
Heat Exchanger Design ……………………………………………………………….... 20
Plate Heat Exchanger Analysis ……………………………………………………….... 21
Pump Analysis …………………………………………………………………………..31
Storage Vessel Selection ……………………………………………………………….. 37
Layout of Proposed Solution ……………………………………………………………38
Structural Analysis of Slab ……………………………………………………………...43
Economics …………………………………………………………………………….....47
Conclusion ………………………………………………………………………………54
Works Cited ………………………………………………………………………...….. 56
Appendix ………………………………………………………………………………...60

3. 2
Abstract
The purpose of this project is design a heat transfer system within a 20’X40’ driveway
that can melt away ice and snow during winter months. While full electrical heating systems for
driveways exist, they tend to have high yearly operating costs. The proposed solution will
involve a pump, heat exchanger, and a series of parallel tubes buried beneath the concrete that
will carry a 40% propylene glycol and water mixture. This fluid transfers heat through the
driveway and is continuously reheated by the heat exchanger to provide continuous heat to the
driveway for much lower yearly operating costs.
While these systems are becoming more common, they often require a hot water boiler
(180 ℉) to provide enough heat to the propylene glycol. A unique aspect of this proposal is
utilizing hot water from a standard hot water heater (140 ℉) to heat the glycol in the heat
exchanger. While this requires higher hot water flow rates, and more pipes within the driveway,
the total cost will be substantially less than if a boiler system had to be purchased and installed.
The governing requirement was that the driveway surface had to be heated to 40 ℉ in 0 ℉
ambient temperature with a 10 mph wind. From there, standard governing heat transfer equations
were utilized to calculate the heat transfer from the pipes to the driveway surface to ensure this
condition was met. A plate heat exchanger was designed based on heating the glycol back up to
its original temperature. Pipe lengths along with any needed valves and fittings allowed for the
calculation of pressure drop and the sizing of the pump. All calculations were performed using
Engineering Equation Solver (EES) so the process could be repeated multiple times for different
inputs.
The final recommended design includes a series of 27 parallel pipes laid lengthwise
within the driveway 3” below the driveway surface, a 60 plate compact heat exchanger, a ¾
horsepower centrifugal pump, and an additional five gallon storage vessel for the propylene
glycol. In addition a tankless water heater was required to boost the temperature of the hot water
from a traditional tank. In addition, it is highly recommended to install a control system that
adjusts hot water flow rate based on the glycol outlet temperature of the heat exchanger to save
hot water costs. A structural analysis was completed on the driveway slab to ensure that it would
not fail at the hole locations.
A full economic analysis was completed on both initial and operating costs. Overall, this
designed system will cost $16 per square foot for initial installation and an additional $.20 cents
per square foot of operating costs every year. These metrics fall well within the range of current
driveway snow melt systems, but the ability of this system to heat the driveway without a boiler
makes it the more impressive option.

4. 3
Problem Description
The purpose of this project is to propose a possible solution to the following problem
statement:
It is not uncommon to see concrete driveways laid out on an incline. Snow and ice
accumulate on driveway surface during winter months. If the snow and ice remain unattended, it
becomes difficult to control an automobile on the driveway. The owner can manually clear the
driveway or install a heating system within the slab when it is poured. A proposed heating
system is the subject of this project.
Consider a driveway that is 20 ft wide and 40 ft long. It is desired to embed within the
driveway a tubing system through which water is circulated. The water provides heat to the
concrete so that ice and snow melt and flow away. Embedded tubes must not detract from the
strength of the driveway.
To be designed, selected, or determined:
1. A layout for the tubes over which the concrete is poured, including braces if needed.
2. The tube material and size and joining method. (Should refrigeration tubing be used so
that fewer joints are needed?)
3. The method used to move water through the tubing. (Is a pump preferable?)
4. The source of the water. (Should water be pumped through and discharged to a drain, or
should water be pumped from and back to a sump tank?)
5. The heat source needed to warm the water, if any is necessary.
6. The appropriate fluid to use. (Water has been suggested above, but would a mix of water
and antifreeze be better? Is oil a better choice?)
7. Determine the total cost of the system, including installation.
To solve the problem statement, we broke the project into several different sections and
also added additional functional requirements. First, the thermal analysis of the piping layout
shown below was performed to determine: the concrete sizing parameters, pipe sizing
parameters, and necessary fluid parameters. After the appropriate dimensions were determined, a
structural analysis was conducted to make sure the slab would not fail under normal loading
conditions.
The function requirements are as follows:
1. The concrete slab must support the weight of the average large vehicle (25kN) with a
factor of safety of 5
2. The concrete slab is considered compromised if the holes in the concrete for the piping
fail
3. The entire project must be done in the least expensive fashion possible, while still
maintaining safe working conditions
4. The piping system must be able to melt snow when the ambient temperature is 0 degrees
F with a wind speed of 10 mph.

5. 4
Below is a simple layout of the proposed solution.
Figure 1: Simple Layout of proposed solution
Design of Heat Transfer System
Approach
There are three important components necessary to consistently transfer adequate heat
through the concrete to melt the snow: a network of pipes, a heat exchanger, and a pump. The
pipe network will be analyzed first to determine the flow rate, the number of pipes, the surface
temperature of the concrete, and the temperature loss of the fluid as it heats up the concrete.
From there, a heat exchanger can be selected to ensure that this temperature loss is recovered so
the fluid can re­enter the piping network at its desired initial temperature. Lastly, the pressure
loss through the piping network and heat exchanger, along with the losses due to fittings and
valves, can be calculated to find the total pressure loss. Then a pump can be selected to recover
this pressure loss at the desired flow rate.
Fluid Selection
Before any design takes place, a proper fluid for heating the driveway must be selected.
The choices came down to four options: water, oil, ethylene glycol, and propylene glycol. Water
was quickly disregarded due to the fact that it has a much higher freezing point than the other
options, which could lead to the pipes bursting and tremendous structural damage to the
driveway. In addition oil was briefly considered but eliminated as an option. While oil is an
excellent heat transfer fluid, it has to be treated exactly the same as the oil in a vehicle. The oil
would need to be filtered constantly, and changed on a regular basis. While there are ~5 quarts of
oil in a car, the total volume in the network will be many times that. Changing that amount of oil
in a residential household creates disposal problems, and would be very difficult as a do it

6. 5
yourself job. Most likely a professional would have to be hired. All these factors negate any
benefits of the improved heat transfer.
With water and oil now out of the picture, the two anti­freezes needed to be compared to
see which option would be better for this project. First, the freezing points of ethylene glycol and
propylene glycol water based solutions were compared. At various percentages of
ethylene/propylene glycol to water, the ethylene glycol had a slightly lower freezing temperature
than the propylene glycol, but this test was almost negligible in helping decide.
When comparing the heat transfer capabilities and efficiency of the two liquids, ethylene
glycol is clearly better. Since ethylene glycol has a lower viscosity than propylene glycol, its heat
transfer efficiency is better compared to propylene glycol. The only benefit that propylene glycol
has over ethylene glycol is that it has the higher specific heat. This means it will take more
ethylene glycol circulating in the pipes to produce the same amount of energy as the propylene
glycol. However, ethylene glycol is cheaper than propylene glycol, so even though more
ethylene glycol is needed it will probably cost the same amount as using propylene glycol.
The one issue with using ethylene glycol as opposed to propylene glycol is that ethylene
glycol is very toxic, while propylene glycol is not. When taken orally, ethylene glycol not only
attacks the kidneys, but can also affect the brain, heart, and lungs as well. If not taken care of this
can lead to death. Luckily, for this project no one would ever be in contact with the ethylene
glycol because it will be running through pipes underground. However, should the pipes ever
break or burst, something to consider would be how to properly dispose of the ethylene glycol
without it harming anyone.
Another aspect of ethylene glycol that needs to be considered, is if it will cause any
corrosion on either aluminum or copper piping depending on what is used. If copper experiences
high temperatures, the material can begin to weaken and the ethylene glycol will begin corroding
the material at a rapid pace. However, the temperatures at which copper’s strength begins to
weaken are at temperatures well over 120℉, so this can be neglected and not worried about. For
aluminum, corrosion from ethylene glycol occurs when aluminum is above 150℉ unless a
galvanized coating is applied to prevent corrosion. So, similarly to copper, corrosion for
aluminum should not be an issue because temperatures will most likely never reach that high and
if they do, there is a good chance people living in that area will not need this product. Propylene
glycol is often used as a corrosion inhibitor, and will actually protect both copper and aluminum.
After weighing all these options, propylene glycol is the safer choice. Although its heat
transfer capabilities are lesser, this system is designed for use in a household where children and
pets could be running around. The system is ultimately going to need a small supply tank to

7. 6
prime the pump. Most of the connections will be threaded and the pipes underneath the driveway
will see some significant stresses. It would be reckless to assume that not even a tiny leak will
occur throughout the lifetime of this system, and even a tiny amount of ethylene glycol can have
drastic consequences. 40% propylene glycol will be the fluid of choice, due to freeze protection
up to approximately ­8 ℉.
Thermal Analysis of Piping Network
The goal of the analysis of the piping network is to determine how much heat the fluid
moving through the pipe transfers through the concrete to the driveway surface. The transfer of
heat will allow for calculation of the surface temperature of the driveway, to ensure that it will be
above 40 ℉ to meet the functional requirements. In addition, the pressure drop will be analyzed
through the piping system to properly size the pump. At this point, the temperature drop across
the network is more important than knowing the exact inlet parameters. Thus, the calculations
were completed using Engineering Equation Solver (EES), and arranged in such a way that just a
few inputs are needed, and the program will output accurate values of heat transfer, pressure loss,
and surface temperature along the length of the driveway. A minimum inlet temperature to
satisfy the functional requirements will be found. Thus, the temperature drop can be found and
the heat exchanger will be appropriately sized.
Two piping networks were considered: a serpentine design where the pipes snake back
and forth across the driveway, and a parallel piping system as shown above in Figure 1. The
parallel piping system is much simpler, causes less pressure drop, and provides a more uniform
temperature across the driveway. The serpentine design, however, could be utilized to transfer
more heat if necessary. As seen through the calculations below, the parallel circuit proved to be
adequate for our design, and thus, will be the selected layout.
Cross Sectional View and Resistance Circuit
Some idealizations were made in the analysis of the network. The following shows a
visual of the cross­sectional view of the driveway to understand the idealizations.

8. 7
Figure 2: Cross­Sectional View of Driveway
As can be seen, the hot fluid flows through the piping network in the tubes embedded in the
concrete. The cold ambient air flows over the surface of the driveway. One of the difficult
aspects of this analysis is the different directions of heat transfer. The heat transfer from the fluid
through the pipes is radial, but the heat transfer to the surface can be looked at as a plane wall
conduction analysis. However, the heat transfer is not proceeding vertically up to the plane­wall,
it is leaving radially, thus turning this analysis into a 2­D heat transfer problem once the heat
leaves the pipes.
To convert the problem to one­dimensional, an idealization was made. Imagine, the
driveway as a series of overlapping concrete tubes surrounding the hot piping. If the hot piping is
able to heat the outer surface of the concrete tube to 40 ℉, than it can be safely assumed that the
piping will also heat the flat driveway surface to 40 ℉. The spacing is given by the geometric
relationships of the overlapping equivalent concrete pipes.
*It should be noted that every heat transfer equation listed in this report was taken from
Fundametals of Heat and Mass Transfer ​by Incropera and Dewitt [1].
Resistance Network
To calculate the heat transfer, the thermal resistance analogy was utilized. The resistance
network is shown below.

9. 8
Figure 3: Resistance Network and Heat Transfer Flow
As can be seen, the heat is transferred from the hot fluid through the pipe and concrete and
eventually lost to the air. The equivalent resistance of the system is given by:
(1)
In addition, the equivalent resistance up to the surface will be needed to calculate the surface
temperature.
(2)
Once, the equivalent resistance is found, the fluid and ambient temperatures are given design
parameters, so the heat transfer can be found by:
(3)
And since the heat transfer is the same through the circuit, the surface temperature will be given
by:
(4)
These basic equations will define the heat transfer through the driveway once the thermal
resistances are determined.
Note that there will be a contact resistance between the concrete and the piping, however,
there is no reliable experimental data to quantify this resistance. However, the idealizations make
this analysis inherently conservative, since the heat transfer is only being considered for one
concrete pipe at a time, but the adjacent pipes contribute heat as well.

10. 9
Convection Resistance of Internal Flow through a Pipe
The convection resistance for internal flow will be given by:
(5)
where ​h ​is the convection heat transfer coefficient and ​A​s ​is the surface area in contact with the
fluid. The convection heat transfer coefficient is a function of the thermal conductivity (​k​),
geometry of the pipe, and the Nusseldt number (​Nu​). The relationship is given as:
(6)
where ​D ​will be the inside diameter of the pipe. The Nusseldt number is a dimensionless ratio of
how the fluid convects versus conducts heat. The flow through the pipe networks will almost
certainly be turbulent, thus, empirical correlations for the Nusseldt number are required to
evaluate the convection coefficient. The most accurate empirical correlation for the Nusseldt
number for flow through circular ducts is given by the Gnielinski equation.
(7)
where ​f ​is the friction factor, ​Re​D​ ​is the Reynold’s number, and ​Pr ​is the Prandtl Number. The
friction factor is a dimensionless evaluation of the friction within the pipe and can be read off of
a typical Moody Chart. However, it is most accurately evaluated by iteration of the Colebrook
equation.
(8)
where ​e ​is the pipe roughness. The Reynold’s number is a ratio of inertial to viscous forces and is
calculated by:
(9)
where ​V ​is the flow velocity and ᵱ is the kinematic viscosity. The Prandtl number is a ratio of
momentum diffusivity to thermal diffusivity and calculated by:

11. 10
(10)
where ᵯ is the thermal diffusivity of the fluid. With the flow rate, internal diameter of the pipe,
temperature, and pressure of the fluid given as design parameters, working backwards through
the equations listed will allow for determination of the thermal convective resistance of the fluid.
Conduction Resistance through Pipe Walls
The following figure shows the standard cross section of a pipe with fluid flowing
through it.
Figure 4: Cross Section of a Pipe
For a pipe with this given cross­section, Length ​L, ​and thermal conductivity ​k​pipe ​the thermal
conductive resistance is given simply by:
(11)
Conduction Resistance through Concrete
The conduction resistance through the concrete of the system will add another resistor in
series with the convection and conduction of the fluid and the pipe. This resistance is modeled
by Equation 12:
(12)

12. 11
for the given concrete material length, L=r​2​­r​1​, conduction coefficient, k​concrete​, distance from
center of the pipe to the outer diameter of the pipe, r​1​, and the distance from the center of the
pipe to the intersection of adjacent conduction circles, r​2​. The radius, r​1 ​is constant, while the
outer radius, r​2​ changes along the surface of the driveway.
Convection Resistance of Air
In order to account for the natural convection of air that the driveway will experience on
any given day, the heat transfer needs to be calculated using the following equation:
AΔTQ = h (13)
where A is the area of the driveway, and ΔT is the difference in temperature between the air and
the driveway surface, and h is the convection heat transfer coefficient. The area of the driveway
has already been predetermined to be 40’x20’ and the range of temperature values for the air
have also been decided on. The range of temperature values for the air that is significant for this
project is any temperature that could cause the liquid passing through the pipes to freeze. As a
result the temperature range for the air will be from 0℃ to ­20℃. From the analysis on
conduction of the driveway, the surface temperature of the driveway is also known, which will
be used to solve for the difference in temperature between the air and the driveway. This leaves
the convection heat transfer coefficient (h) as the only variable that needs to be solved for.
To find the convection heat transfer coefficient for natural convection, the Nusselt
number (Nu) needs to be used. In order to solve for the Nusselt number the following
dimensionless parameters need to be calculated: Grashof number (Gr), Prandtl number (Pr), and
Rayleigh number (Ra). The first equation that needs to be solved for is the Grashof number,
which can be solved for using the equation below:
(14)
where β is the coefficient of thermal expansion for air, c​p​ is the specific heat, μ is the dynamic
viscosity, and L is the length of the driveway.
Next, the Prandtl number needs to be solved for, which is found using the following
equation:

13. 12
(15)
with k being the symbol for thermal conductivity of air. Once both the Grashof number and the
Prandtl number are solved for, they are multiplied together to get the Rayleigh number. Then to
get the Nusselt number, the Rayleigh number is then multiplied by a constant (C) and powered
by a certain value (n). These two variables depend on how the driveway is oriented and whether
the driveway is being heated or cooled. These two equations can be seen below:
(16)
(17)
Nusselt’s number does not only equal that equation, but it is also related to the convection
heat transfer coefficient by this equation:
(18)
As a result, once the the Rayleigh’s number is used to solve for Nusselt’s number that can be
taken and applied to the equation above. Since the length and the thermal conductivity of air is
already known, the convection coefficient can be solved for. This can then be taken and applied
to the heat transfer equation to find the heat transfer between the air and the driveway surface.
While the previous equations covers natural convection of air on a calm day, the
following can be utilized to calculate the forced external convection of flow over a plate, such as
our driveway. The Nusseldt number in this case is given by:
(19)
The reynold’s number is calculated similarly to equation 9, using the velocity of the air along
with the length of the driveway as the characteristic length. Once, the Nusseldt number is found,
equation 18 can be utilized again to find the convection heat transfer coefficient.

14. 13
Accounting for Temperature Changes
The resistance equations listed above are simple to use if the fluid and air remain at a
constant temperature. However, the fluid loses heat as it travels along the pipe network and
decreases in temperature. The air can be considered an infinite body whose temperature will not
change. As the fluid temperature decreases and the air remains the same, the temperature
difference decreases, meaning the heat transfer at the end of the network is less than the heat
transfer at the start of the network. In addition, as the temperature changes the heat transfer
convection coefficient of the fluid will also change. Thus, a method must be created to properly
evaluate the change in temperature of the fluid.
A valid approach to this problem is to break the length of the pipe into small segments
and analyze each segment. The following image shows the length of one pipe broken down into
5 segments.
Figure 5: Pipe broken up into Five Segments
T​i ​is given so the heat transfer for the first segment, ​q​1​, can be calculated using the resistance
analogy outlined above. In addition, the following equation is valid for the fluid at any point
along the length of the pipe.
(20)
where ​C​p​ ​is the constant pressure specific heat of the fluid. Rearranging, T​1​ can be found to be:
(21)
And now, using the new temperature, the resistances are recalculated so ​q​2​ can be found, and
then T​2​. This process is repeated until the outlet temperature is found. Obviously, the greater

15. 14
number of segments analyzed the more accurate the solution. EES was utilized to divide the
pipes into a large number of segments to approach an accurate solution.
Pressure Drop
The chosen layout was a parallel piping configuration and an example can be seen in the
figure below.
Figure 6: Sample Parallel Piping Arrangement
The direction of flow can be seen and the solid lines represent the pipes providing heat to the
driveway. Now, there will be pressure drops along the inlet and outlet manifolds, which will
cause slight pressure and temperature differences across the pipes as they run down the
driveway. This pressure drop will be accounted for in the minor losses section under the pump
design. But for the pressure drop through the network, it can be said that the pressure and
temperature is the same at any point in the pipes along the dotted lines, and the flow rate in each
pipe is simply the total flow rate divided by the number of pipes. The manifold pressure drops
will be taken into account for the final design.
The two causes of pressure drop in the piping network:
1. Losses due to friction
2. Losses due to gravity
The pump is utilized to overcome the frictional pressure losses and also pump it back up to it’s
original height to overcome gravity, so it is important to accurately quantify the pressure drops to
accurately size the pump.

16. 15
Since the pressure is the same along the dotted lines, essentially this means that the
pressure drop is equal in each pipe as they run down the driveway. So the pressure drop analysis
of one run of pipe will determine the pressure drop of the entire network.
The frictional losses can be quantified by the following equation:
(22)
where ​h​f​ ​is the head loss in units of length. The losses due to gravity is simply the change in
elevation, which in this case is simply dependent on the geometric properties of the driveway.
(23)
Note that any head loss can be converted to pressure loss as follows:
(24)
EES Results
The goal of the piping network was to have minimal pressure loss, maximum heat
transfer, minimum inlet temperature, and minimum price while meeting the necessary surface
temperature requirements for the driveway. From previous analysis heat transfer correlates
positively with larger pipe sizes and higher flow rates. Lower pressure drops correlates positively
with lower flow rates and larger pipe sizes. The minimum surface temperature requirement will
be more easily achieved as the number of pipes within the driveway increases. Cost obviously
increases with a greater number of pipes, and larger size pipes. Since the requirements listed
above often conflict with each other, an ideal balance must be found. Thus the following
analyses will keep the surface temperature requirement fixed, and vary flow rate and number of
pipes.
To determine the pipe size, the smallest diameter pipe that minimizes pressure loss and
transfers the most heat should be utilized. The holes within the concrete should be as small as
possible to minimize stress concentrations. The following shows the effect of changing the pipe
size for an inlet temperature of 50 ℃ and a flow of 3.0 gpm within the pipe.

17. 16
Figure 7: Frictional Pressure Losses and Heat Transfer vs. NPS
Looking at the figure, ¾” NPS pipe sizes create minimal pressure drops while still
transferring a good amount of heat.Now that the pipe size is determined, the inlet temperature,
number of pipes, and desired flow rate must be determined. The following table lists the
parameters utilized for the EES analysis. Aluminum was selected for initial analysis since it has
worse heat transfer ability than copper. If it is eventually decided that copper is the material of
choice, the analysis will not have to be performed again since it is already known to work for
aluminum.
Table 1: Inlet Conditions for Analysis of Runs of Pipes
Parameter Value
T​∞ 0 ℉
Wind Speed 10 mph
Fluid 40% Propylene Glycol
Pipe Size 3/4” NPS, Sch 40
Pipe Material Aluminum
To determine the required inlet temperature, the flow rate was held constant at 1.0 gpm and the
number of pipes was varied to acquire the 40 ℉ surface temperature requirement. The figure

18. 17
below shows the required number of pipes at each temperature to achieve the surface
temperature requirement.
Figure 8: Inlet Temperature versus Required Number of Pipes
A few things can be noted from the figure. The first is that 60 ℃ is equivalent to 140 ℉.
This temperature is generally the max temperature that a hot water heater can be set to for safety
reasons. Since water will be the heating fluid for the heat exchanger, the fluid must be
considerably lower than 60 ℃ so the heat exchanger can recover the lost heat. In addition,
greater than 30 pipes through the driveway starts to get a little crowded. Using these two
considerations, it can be seen that an inlet temperature of 40 ℃ with 24 pipes could prove to be
an adequate solution. Since the flow rate may have to be varied lower than 1.0 gpm, more pipes
may be needed so 27 pipes will be chosen.
Now the number of pipes can be held constant at 27 with an inlet temperature of 40 ℃
and the flow rate varied to see how the surface temperature is affected. The minimum surface
temperature requirement is also shown.
Figure 9: Surface Temperature versus Flow Rate

19. 18
It appears that a flow rate of about 0.50 gpm through each pipe will achieve the surface
temperature requirement. Recall that the design is conservative, so choosing 0.50 gpm exactly is
ok even if the calculated surface temperature is barely above 40 ℉. In addition, the flow rate
should be kept as low as possible to minimize pressure drops and reduce the load on the heat
exchanger. Lastly, the heat transfer and pressure drop (for one pipe) were plotted against the
flow rate for the same inlet conditions as above.
Figure 10: Heat Transfer and Pressure Drop versus Flow Rate for one pipe
The part of the graph where the data flattens out represents the transition region from
laminar to turbulent flow. While it would have been nice to have a flow rate that would exchange
more heat, the 0.5 gpm flow rate is still acceptable and will adequately heat the driveway up to
the surface temperature requirements.
One last consideration to be made is the fact that copper and aluminum will wear at high
flow velocities. The velocity of fluid moving through the pipes should be 5 feet per second or
less to prevent erosion. For 0.5 gpm per pipe, the flow velocity is well below 5 feet per second.
However, it has to be considered that each pipe will enter into a manifold which will have a
larger flow rate(0.5gpm*27 pipes=13.5 gpm). If the flow velocity calculations are performed it is
found that the flow velocity will be just over 4 feet per second, which is still within the required
range. But to slow down the flow a bit more and adhere to general manifold design, the manifold
pipe size will be increased to 1” NPS.
With all considerations above, along with the EES analysis, the following parameters are
acceptable and will heat the driveway surface up to a minimum of 40 ℉ with an ambient air
temperature of 0 ℉ and a wind speed of 10 mph.

20. 19
Table 2: Pipe Network Final Values
Parameter Value
Inlet Temperature 40 ℃ (104℉)
Flow Rate per pipe 0.50 gpm
Fluid 40% Propylene
Glycol
Parallel Pipe Size 3/4” NPS, Sch 40
Number of Pipes 27 pipes
Pipe Spacing 9.2”
Distance from Pipe to Surface 3”
Manifold Pipe Size 1.0” NPS, Sch 40
Pipe Material Aluminum
Minimum Surface Temp 40.05 ℉
Total Heat Transfer 88,500 Btu/hr
Pressure Drop 3.13 psi

21. 20
Heat Exchanger Design
Approach
For the design of the heat exchanger, some research was done into heat exchangers for
home use. While shell and tube heat exchangers are excellent for industrial process, it is
unreasonable to have such a large heat exchanger in a garage or basement. The most common
compact heat exchanger is a plate heat exchanger, which has a series of plates of which cold and
hot fluids travel past each other. A picture can of a plate heat exchanger can be seen below [2].
Figure 11: Layout of a Plate Heat Exchanger
The benefits of a plate heat exchanger is how small they can be, and their large areas of
heat transfer. The plates can be separated by as small of a gap as 2 mm which allows for a lot of
plates to fit in as small of a volume as possible.
The cold propylene glycol inlet temperature will be known based on the temperature drop
through the piping network in addition to any extra temperature loss from the network to the heat
exchanger inlet. The hot water inlet temperature is known to be 140 ℉ which is the max
temperature setting for hot water use. From there, the Log Mean Temperature Difference method
will be utilized to find the two outlet temperatures. If the brine outlet temperature is greater than
40 ℃ than the heat exchanger will be suitable for this service. In addition, the pressure drop will
be calculated to contribute to the pump head requirements.

22. 21
Note that the hot water demands of each household are very different. Lucky houses will
have a boiler system which can output 180 ℉ and makes reheating of the propylene glycol very
easy. However, standard houses may only have a 50 gallon hot water tank which can use up its
supply pretty quickly. This is the situation that will be designed for and most likely, an additional
water heat boost, such as a tankless water heater will be required to maintain the water inlet
temperature.
Inlet Propylene Glycol Temperature
The outlet temperature of the propylene glycol from the parallel piping network is known
from the analysis described in the previous section and is calculated through EES to be ~29 ℃.
In addition, the pipe has to travel back from the outlet manifold up through the length of the
driveway, plus through some additional piping to the heat exchanger inlet. The analysis of this is
exactly the same as the temperature drop outlined in the pipe network design. The extra length of
piping will be assumed to be ~50 ft and is uninsulated for a conservative estimate. Still there is
little temperature change, and the inlet temperature is found to be ~27 ℃.
Plate Heat Exchanger Analysis
Before an actual heat exchanger was selected, arbitrary dimensions were selected to
ensure that a plate heat exchanger will be a suitable design. A cubic plate heat exchanger of
length, height, and width 0.35 m with 100 stainless steel plates was selected for analysis.
Flow and Heat Transfer Geometry
To find the flow area of the fluids, the width (​a)​ of each gap must be known. It can be
calculated as follows by knowing the height of the heat exchanger along with the number of
plates.
a = h
Nplates
(25)
The velocity of each fluid is given as:
V = V˙
a w*
(26)
where ​w ​is the width of the heat exchanger and is the volumetric flow rate of the fluid. TheV˙
entire heat exchanger area is given as follows
L )(N )AHE = ( * w plates − 1 (27)

23. 22
Since the flow area of a plate heat exchanger is a rectangular cross section rather than a
circular cross section, an important quantity that needs to be defined is the hydraulic diameter.
DH = 4 Flow Area*
Wetted Perimeter ≈ 2 * a (28)
Flow Type Selection
Almost all heat exchangers can be designed to operate in parallel or counterflow mode.
The figures below show the difference in how they operate [1].
Figure 12: Counterflow Heat Exchanger Temperature Distribution
Figure 13: Parallel Heat Exchanger Temperature Distribution
The benefits of a parallel heat exchanger is that the largest temperature difference exists
at the beginning of the heat exchanger, where the hot inlet and cold inlet is transferring heat. This
allows the fastest transfer of heat. The benefits of a counterflow heat exchanger is that the
temperature difference stays more constant as the fluids travel through the heat exchanger. It is

24. 23
seen that an infinitely long parallel heat exchanger will converge to a temperature until there is
no temperature difference and thus no heat transfer. Since the outlet temperature is the most
important parameter for this system, a counterflow style plate heat exchanger will be necessary.
In this case, the outlet propylene glycol temperature can actually exceed the outlet hot water
temperature because there is still a temperature difference between the fluids at propylene glycol
exit, which is receiving heat from the hot water inlet. Thus a counterflow heat exchanger has the
best chance of recovering the lost heat to boost the propylene glycol temperature back to its
desired initial value.
Outlet Temperature Guess Values and Average Temperatures
Since the LMTD method requires knowledge of both the inlet and outlet temperatures for
both fluids, guesses for the outlet temperature must be made in this case since they are unknown.
A logical choice for the outlet temperature of the propylene glycol is 40 ℃. For the water, the
flow rate will most likely be smaller due to hot water system capacities, so the outlet water
temperature will probably be lower than the glycol so a decent guess is 30 ℃. Now that values
have been assigned for all temperatures, the average temperatures can be calculated as such.
Tave = 2
T + Tout in
(29)
The LMTD method will now be carried out utilizing these average calculations and an
actual outlet temperature will be calculated. If this outlet temperature does not equal the original
guess, the guess is changed and the calculations are repeated until the guess temperature and
calculated temperatures converge.
Fluid Properties
Now that the average temperature is known, the following properties for propylene glycol
and water must be found.
● Density (⍴)
● Specific Heat ( )Cp
● dynamic viscosity (ᵰ)
● Prandtl Number (​Pr)
● kinematic viscosity ( )ν = ρ
μ
● thermal conductivity ( ​)kf
Convection Coefficient Calculations
Before the convection coefficients are found a couple of dimensionless numbers are
required. The first is the Reynold’s number which is given by the following.

25. 24
eR = ν
V D* H
(30)
Next, the Nusseldt Number had to be calculated. The flow turned out to be turbulent, thus the
following equation is a relatively accurate empirical correlation to use for non­circular turbulent
flow regimes.
u 0.023 Re ) Pr )N = * ( 4/5
* ( n (31)
where for propylene glycol since it is being heated, and for the hot water since it.4n = 0 .3n = 0
is being cooled.
The convection coefficient for each fluid will be given by:
h = DH
Nu k* (32)
Heat Exchanger Performance
The total resistance is determined by the convection resistances in addition to the
resistances provided by the heat exchanger plates. The total resistance is given by:
RHE = 1
h Abrine* HE
+ 1
h Awater* HE
+
tplate
k Aplate* HE
(33)
The total resistance is related to the overall heat exchanger coefficient (​U​) by the following.
1
U A* HE
= RHE (34)
Thus, the heat exchanger area cancels out and the overall heat exchanger coefficient of a plate
heat exchanger is given by.
]U = [ 1
hbrine
+ 1
hwater
+
tplate
kplate
−1
(35)
Log Mean Temperature Difference
Referencing Figure 13, there are two temperature differences that are required to evaluate
a counterflow heat exchanger and they are shown below.
TΔ 1 = Twater,i − TPG,o (36)
TΔ 2 = Twater,o − TPG,i (37)
The log mean temperature difference is utilized for analysis of heat exchangers because the
temperature difference does not change linearly, so analyzing the temperature difference as a log

26. 25
mean is more accurate in describing the actual temperature difference. The log mean temperature
difference can be calculated as follows:
MTD L = ln( )ΔT2
ΔT1
ΔT −ΔT1 2
(38)
Total Heat Transfer
The total heat transfer of the counterflow plate heat exchanger is calculated as:
MTDqHE = U * AHE * L (39)
Note that there is no log mean temperature difference correction factor since the flow regime can
be assumed to be purely counterflow.
Calculation of Actual Outlet Temperature
Assuming the heat exchanger is kept well insulated, the heat transfer from equation 39
will be equal to the individual fluid heat transfers and thus the outlet temperature can be solved
for as follows:
C T )qHE = qc = ṁPG p,PG * ( brine,o − Tbrine,i (40)
C T )qHE = qh = ṁwater p,water * ( water,i − Twater,o (41)
All values are known except for the outlet temperatures so simple arithmetic yields the actual
outlet temperatures. As mentioned before, if this outlet temperature does not equal the initial
guess, the guess must be changed and the entire process must be repeated.
EES Iteration Process
To easily iterate, the process above was coded into EES. To change the guess value, a
portion of the difference between the inlet and outlet temperatures was added to the initial guess.
Thus, as the program ran, the guess slowly approached the actual answer. The equations are
shown below.
[i ] [i]Tguess + 1 = Tguess + 32
T [i]−T [i]actual guess
(42)
Thus, the guess value was changed by approximately 3% of the difference between the
actual value and the guess value. Although at times over 80 iterations were required for
convergence, the small temperature difference ensured that the most accurate solution was

27. 26
approached. In addition, larger changes to the guess values sometimes made equations 36 and 37
negative, leading to an error when the natural log had to be taken.
EES Analysis
For the cubic 100 plate heat exchanger as described above, the hot water flow rate was
varied until the propylene glycol outlet temperature was greater than 40 ℃. This required
approximately 9.2 gpm of hot water. For reference, the flow rate of a shower head is
approximately 2.5 gpm, so an addition to the existing hot water system will most likely be
needed and explained in a following section. Ultimately, this analysis shows that a plate heat
exchanger can effectively transfer enough heat to consistently cycle the propylene glycol until
the snow on the driveway has melted.
Heat Exchanger Selection
Bell and Gosset ​is a heat exchanger company that makes compact brazed heat
exchangers. Below is an example of their heat exchangers showing some of the intricate features,
along with highlighting their small size [3].
Figure 14: ​Bell and Gosset ​Brazed Plate Heat Exchanger
One of their recommended uses is for a snow melt application, and for the flow rate of propylene
glycol required in this system (13.5 gpm) they recommend their BP412 model brazed plate heat
exchanger. The following figure and table below show the dimensions of this heat exchanger.

28. 27
Figure 15: Drawing of Model BP412
Table 3: Dimensions of Model BP412 Heat Exchanger (All dimensions in mm)
Model # A B C D E F Max # of Plates
BP412 310 250 50 112 24 2 150
EES Analysis of Selected Heat Exchanger
Once again, EES was utilized to analyze the BP412 heat exchanger with listed
dimensions above. Again, the biggest factor that affected the outlet temperature of the propylene
glycol was the hot water flow rate. The number of plates could be varied to negate this effect, but
the price increases greatly as the number of plates increase.
Table 4: Final Selection for Variable Parameters
Hot Water Flow Rate (gpm) Number of Plates Height (mm)
8.0 60 240
The screen shot below shows the iterative calculations performed by EES and shows the
convergence of the outlet temperature guesses.

29. 28
Figure 16: Converging EES History
Note that and are the guess values and and are theTwater,o Tbrine,o Twater,out Tbrine,out
calculated values. It can be seen that the initial guess of the outlet temperatures were extremely
off, resulting in absurd calculated values. This is why the guesses were only changed by a small
amount. If the guesses were changed by a large amount, the water outlet temperature guess
would have been set to less than the brine inlet temperature, which would be impossible and
results in an error. 80 Iterations were calculated and the results converged to the following
performance parameters for the BP410 Heat Exchanger.

30. 29
(℃)TPG,out (℃)Twater,out U ( )/mW 2
* K LMTD (℃) q (Btu/hr)
40.8 28.3 2542 11.0 ~227,000
As a self check, ​Bell and Gosset​ rates this model heat exchanger for a maximum heat
transfer output of 400,000 Btu/hr when boiler supply water is utilized (180 ℉). Since lower
temperature water had to be utilized, it makes intuitive sense that the heat transfer output of this
particular design would be lower. The calculated heat transfer appears to be accurate and very
reasonable.
Pressure Drop
Since the flow regime within the plates of the heat exchanger turns out to be turbulent,
pressure drop calculations become difficult since friction factor methods break down for
turbulent regimes and non­circular flow areas. A calculation was ran utilizing the method of
pressure drop outlined in the pipe network section, but a pressure drop greater than 300 psi on
the brine side was calculated which is not accurate at all.
Luckily, ​Bell and Gosset​ has supplied tabulated information of pressure drops for all their
heat exchangers. For the BP412 model with 40 plates and 28.6 gpm of propylene glycol,
approximately 3.4 psi of pressure loss is expected. While there is less expected flow rate for this
particular design, there are more plates so 3.4 psi is most likely a decent approximation for the
pressure drop in this system. 4.0 psi will be selected as a conservative estimate.
Existing Hot Water System
As a point of reference, most household fixtures require less than 2.0 gpm so it is easy to
imagine how quickly the hot water would run out at 8.0 gpm, rendering the heat exchanger
useless. For houses without a boiler, it is absolutely recommended to install a tankless water
heater at the inlet to the heat exchanger to provide a boost of hot water.
Tankless hot water heaters heat water as you need it with high powered burners, rather
than store it continuously in a tank. Some homes have completely done away with traditional
water heaters and switched to complete tankless systems. However, for a traditional home with
the traditional water heater with a tank the tankless water heater will be used as a heat boost for
the snow melt application.

31. 30
Rheem ​is rated as one of the best tankless hot water heater companies and their RTGH95
model is rated for 8.4 gpm of water at a 45 ℉ temperature rise [4]. This essentially means that the
traditional hot water heater will heat water to a much lower temperature of 95 ℉ and the tankless
water heater will do the rest of the work. Essentially as long as the water flow rate stays at 8.4
gpm or lower, the tankless water heater will be able to provide continuous amounts of 140 ℉ inlet
water to the heat exchanger. A picture of the recommended model is shown below.
Figure 17: ​Rheem ​RGH95 Tankless Water Heater
Tankless Water Heater Considerations
The heating supply for the specified tankless water heater is natural gas, so additional
natural gas piping will need to be run from an existing line to the water heater. Water piping of
course will need to be ran from the existing water heater to the tankless heater inlet line. There
will be yearly costs associated with the tankless water heater from Natural gas pricing in addition
to the initial cost.

32. 31
Pump Analysis & Design
Approach
The pump is necessary in this cycle to overcome the pressure losses induced by the brine
simply flowing through the system. In this cycle, there are two major sources of pressure drop;
from the piping network and through the heat exchanger. In addition the minor losses induced
through the flow contacting valves and fittings must also be accounted for. Once all losses are
taken care of, the pump selection simply comes down to finding a pump that operates well at the
required flow rate and necessary head generation. The pressure drop of the pipe network and heat
exchanger have already been explained in their respective sections. The minor losses will be
explained in this section.
Minor Losses
Minor losses are calculated similar to frictional losses, except a modified version of the
friction factor is utilized called a ​K ​value. ​Crane Engineering ​has published an extensive and
widely accepted study on these ​K ​values. For example, a flow through the run of a pipe tee as
shown below will result in the following ​K ​value [5].
Figure 18: Flow through the Run of a Pipe Tee
0K = 2 * f (43)
where ​f ​is the previously defined friction factor. For this system, the minor losses will occur at
pipe bends, valves, tees, entrances, exits, expanders, and reducers. Once all ​K ​values are found,
the following formula can be used to calculate the head from minor losses.
Khm = Σ V 2
2 g*
(44)

33. 32
Manifold Pressure Drop
Ideally, the propylene glycol will enter the piping network through the manifold at the
top of the driveway and an equal amount of glycol will flow through each pipe in the piping
network. However, as outlined above, as the glycol enters the manifold and flows through tees a
pressure drop will occur. Thus, the pressure will be lowest at the last pipe in the piping network,
which also means the flow rate through the final pipe will be the greatest, since the flow will take
the path of least resistance. To find the max pressure drop through the system, the pressure drop
of the glycol following the path through the last pipe will be analyzed.
If equation 43 is evaluated, the ​K​ value for the manifold flow through a tee is 0.53. Now,
the flow hits 26 tees before reaching the final pipe so adding up the sum of the tee ​K​ values
allows for evaluation of equation 44. The total flow rate is 13.5 gallons per minute through 1”
NPS schedule 40 manifold piping giving a velocity of 1.5 m/s. Evaluation equation 44 and
converting to pressure utilizing equation 24 yields a 2.4 psi drop across the manifold due to
minor losses. Major friction losses cause an additional 1.1 psi drop across the manifold.
Considering the nominal pressure will be ~65 psig at the manifold, the total 3.5 psi pressure drop
across the manifold is small and will not cause unreasonable flow diversion.
Note that if there was a large pressure drop, a different method of supplying the piping
network would need to be considered since the flow rate is very critical to supplying the proper
surface temperature.
Summary of Minor Losses
The following table provides the minor losses that occur in the propylene glycol as it
follows the path of greatest pressure drop outlined in the previous section.
Type K­Value Number
90 Degree Bends 4K = 1 * f 9
Sharp Entrance .78K = 0 1
Sharp Exit .0K = 1 1
Ball Valve .0K = 3 * f 4
Tee ­ Through Run 0K = 2 * f 26

34. 33
Tee ­ Through Branch 0K = 6 * f 2
1”X2” Reducer .48K = 2 1
1”X2” Expander .06K = 6 1
*All ​K​ values calculated from Crane Engineering’s Report on Flow Through Fittings
Overall Pressure Loss
This section will walk through the path of largest pressure drop of the propylene glycol
and calculate the pressure drop along the way. Refer to the EES section of the appendix for
calculation details.
1. Leaves the pump and passes through a 90 degree elbow and 1 ball valve before entering
the expander into the heat exchanger. (0.43 psi)
2. Passes through the 1”X2” expander. (1.05 psi)
3. Passes through the heat exchanger. (4 psi)
4. Travels from the outlet of the heat exchanger through a 1”X2” reducer, four 90 degree
elbows, and approximately 25 feet of piping to the manifold inlet. (2.0 psi)
5. Passes through 26 tees and ~20 feet of piping to the last pipe in the network. (3.5 psi)
6. Enters the pipe through a 90 degree elbow. (0.0004 psi)
7. Travels through the run of pipe to the outlet manifold. (3.13 psi)
8. Travels through a tee branch before entering the outlet manifold. (0.0004 psi)
9. Flows through five 90 degree bends and approximately 80 feet of piping before
approaching the entrance to the glycol storage tank. (4.6 psi)
10. Flows through the sharp entrance and exit of the storage tank (0.31 psi)
11. Flows through one more 90 degree bend before entering the pump. (0.06 psi)
Adding up all the pressure drops at each stage, the total pressure drop is 19 psi through the
propylene glycol cycle. This corresponds to 42.7 feet of head required for the pump to generate.
Calculation of Required Horsepower
The most important parameter for properly sizing a pump is the horsepower that the
pump has to generate. The power in watts can be calculated through the following equation [1].
(45)

35. 34
where is the volumetric flow rate (m​3​
/s) and ​h​p​ ​is the required pump head. The required head
can be calculated in the pressure loss section of the piping analysis. The horsepower, the english
standard for power, of the pump can be found through the following relationship.
(46)
Using these two relationships and the results of the previous section, the required pump
horsepower is approximately 0.15 hp. Thus, the pump required will be a low horsepower pump
that functions efficiently at an operating point of 13.5 gallons per minute and 42.7 feet of
generated head.
Pump Selection
Cole Parmer ​has a great selection of small centrifugal pumps that would work excellent
for this application. Below is a pump chart of one family of stainless steel centrifugal pump [6].

36. 35
Figure 19: Pump Performance Curve from Cole Parmer
If the families of pumps are compared, it can be seen that type I and H could be good selections.
At 13.5 gpm the generated head of I will be very close to the minimum value of 42.7 feet. Thus,
type H (Model # 70761­02) with ¾ hp. At the desired capacity of 13.5 gpm, this pump can
supply approximately 55 feet of head of water. Since the density of brine (1026 kg/m^3) is
slightly greater than water, the expected head generation will be a little smaller at 53 feet of
head. The pump horsepower given in the table is essentially the inlet power required to power
the pump. So using the values from the pump curve, the expected efficiency can be calculated
through the following equation:
(47)
The efficiency of this pump is calculated to be only 25%. While this seems poor, there
were not many other great options available. The pump design for this problem is unique in that
such a low horsepower is needed but a lot of head generation is necessary. Options that were
more efficient were often 5x more expensive in terms of initial cost which will almost never be
worth the investment especially for a small residential application. Thus, pump type H will be
utilized for this operation, even though there will be some extra costs associated with running an
inefficient pump off of electricity. The pump can be seen below.

37. 36
Figure 20: Stainless Steel Centrifugal Pump from Cole Parmer, Model 70761­02

38. 37
Storage Vessel Selection
The last major piece of equipment needed before everything is connected together is a
small storage vessel for the propylene glycol. The storage vessel will mainly be used to prime the
system and the pump, as there is no other way to fill the pipes up with the amount of propylene
glycol needed. No analysis is really necessary for the storage vessel, as the two requirements are
listed below.
1. Can withstand the pressure of the propylene glycol (~65 psig max)
2. Has a small capacity of ~5.0 gallons
The capacity requirement should essentially be the smallest tank available that is easy enough for
the user to fill. An extra small tank would be difficult to pour large amount of propylene glycol
into, while a large tank would cause unnecessary extra volume within the system. Even though
propylene glycol is safe for residential applications, there should not be a ton of it sitting around.
McMaster Carr ​had a selection of small vertical tanks that can handle pressures up to 200
psig, well within the required pressure rating [7]. The tank and its dimensions are shown below.
Figure 21: Small Vertical Steel Pressure Vessel
Table 5: Dimensions of Selected Storage Vessel
Capacity Diameter Overall Height J L H
5 gallons 10” 19” ¾” ½” 1”

39. 38
Layout of Proposed Solution
This section shows the final design selected for the heated driveway. Details of the more
intricate features will also be explained. Throughout the drawings temperatures and pressures are
shown to visually show how these values change throughout the cycle. The drawing layout is
very accurate however not everything is to scale.
Below are the pictures of the main equipment which will sit in the driveway of the
residential household, and of the layout of the pipes beneath the driveway.
Figure 22: Layout of Major Equipment

40. 39
Figure 23: Layout of Driveway Piping Network
Control System
The first feature that needs to be explained is the control system with a zoom­in on the
important features shown below.
Figure 24: Control System

41. 40
So in this system, hot water leaves the hot water tank at 95 ℉ and enters the tankless water heater
where it is heated to 140 ℉. The propylene glycol enters the heat exchanger and leaves at 104 ℉
providing enough heat to the driveway as explained in the design sections. However, this is only
applicable for when the ambient temperature is 0 ℉ with a 10 mph wind. The necessary hot water
flow rate drops off considerably when the temperature is higher than 0 ℉. It is undesirable to heat
the driveway up well past 40 ℉ since that will add thermal stresses to the concrete.
There are two options for control here:
1. Constant propylene glycol outlet temperature
2. Variable glycol outlet temperature (as seen above)
For option 1, the temperature transmitter at the outlet of the heat exchanger on the glycol side
will read the temperature to the flow controller and adjust the hot water flow rate accordingly to
maintain 104 ℉. The theory behind this method is that as the ambient temperature heats up, the
propylene glycol temperature will not drop all the way to 69 ℉ so not as much hot water is
needed to heat the glycol back to 104 ℉ saving some money in hot water usage.
Option 2 is slightly more complicated but can result in higher savings. An additional
temperature transmitter reads the ambient temperature (along with the wind velocity) and adjusts
the desired outlet temperature accordingly. Now that the outlet temperature is set, the flow
controller adjusts the hot water flow rate to output this desired outlet temperature. The following
graph shows a possible calibration curve for a set­up like this. The outlet glycol temperature is
the required glycol temperature leaving the heat exchanger that will still heat the driveway up to
the required surface temperature requirements.
Figure 25: Possible Calibration Curve for Control System

42. 41
As can be seen, as the ambient temperature increases beyond 20 ℉, only about 2.0 gpm of
hot water is required which is about the same requirement for a standard shower. A true
calibration curve for the control system would be much more detailed and would include
variations in wind velocity. But, the reduction in hot water usage is very clear through option 2.
Additional Features for Hot Water and Heat Exchanger
Referring to the previous layout, there are a few troubleshooting features added in. There
are temperature gauges on both inlets to the heat exchanger to ensure that the temperatures are
what they should be. There is a 3/4”X2” expansion and 1”X2” reducer on the inlet and outlet of
the heat exchanger respectively. This is simply because the connections of the heat exchanger are
2” NPT and the pipes need to be adjusted accordingly. The outlet of the pump is ¾” NPT hence
the larger expansion versus the reducer. The outlet water from the heat exchanger can be
relatively hot (82 ℉ max ) so that water is circulated back to the inlet of the hot water heater. This
hotter inlet water temperature helps the hot water tank recover the heat back up to 95 ℉ more
easily.
Features of the Pump and Storage Vessel
A closer view of the pump and storage vessel is shown below.
Figure 26: Zoom­In of Pump and Storage Tank
Looking at the storage tank it can be seen that there are four connections. The bottom connection
“J” is a ¾” NPT and is what the propylene glycol will flow out of. There is a ¾”X1.25”
expansion into the inlet of the pump to accommodate the necessary 1.25” NPT pump inlet. The
propylene glycol will flow into the top of the storage tank which is a 1” NPT connection. There
is a ball valve on the inlet to block the inlet flow if needed. There are also two ¾” connections on
the tank. One connection will be for a pressure relief valve set for ~150 psig. The tank is rated
for 200 psig so the set pressure of the relief valve is safe for the tank design. The relief valve
simply drains to wherever the user desires. It is never expected to go off and even if it does
propylene glycol can be safely drained to most locations. The final ¾” connection will be

43. 42
utilized to initially fill the storage. The ball valve on the outlet of the tank will be kept closed
while filling the tank, and then opened to prime the system.
For the pump, there are pressure gauges on the inlet and outlet to monitor the
performance of the pump and ensure it is generating enough pressure. The temperature gauge on
the outlet of the pump reads off the propylene glycol entering the heat exchanger. The ball valve
on the outlet of the pump will be closed while the pump builds up pressure and slowly opened to
prime the rest of the system. The flowmeter on the outlet of the pump will read off the required
13.5 gpm flow rate. As the outlet valve of the pump is slowly opened, propylene glycol will
continue to be added until the desired flow rate is reached.
Features of the Piping Network
The piping network is quite simple and has been discussed at length in its respective
section. As seen in figure 23, the hot propylene glycol leaving the heat exchanger loops outside
of the garage and then enters the driveway. The reason for this is simply easy of construction. It
is probably easiest to drill a small hole through the side wall of the garage then it is too dig up
the driveway floor and have the glycol enter there. The inlet manifold itself is 1” NPS piping
with 26 1”X3/4” reducing tees to deliver the glycol to each pipe within the driveway. The final
pipe has a 90 degree bend rather than a tee.
The outlet manifold is the exact same layout as the inlet manifold. An extra feature is the
valve protruding out at the end of the driveway. This serves as two purposes. An obvious one is
to allow for complete drainage of the system. Another purpose is to allow the air to bleed off.
When the pump is started up and the propylene glycol is pushed through the pipes, it is pushing a
volume of air in front of it. This extra air negatively affects heat transfer can cause cavitation
within the pump. To bleed off the air, the valve should be slowly opened on startup until a small
amount of glycol leaks out. Once the glycol is leaking, it is known that no air is in the system and
the valve can be closed. Lastly, there is an extra ball valve where the glycol line re­enters the
garage in case the supply to the tank needs to be cut.

44. 43
Structural Analysis of Slab
The slab of concrete in the proposed design will see large stresses from vehicles driving
on it. Since one of the design criteria of the project is that the structural integrity of the slab must
not be compromised, we had to do an in­depth structural analysis. The holes in the concrete pose
the largest portion of stress for the slab, so they will be analyzed first.
The figure below shows a representation of the forces the slab will see when a car is
parked on it. The pink circles on either side of the hole shows the place where there will be a
stress concentration.
Figure 27: Stress Concentrations in the concrete
To account for this stress concentration, a factor is applied to the stress that is based off
of empirical material studies. The next figure shows how to determine the stress concentration in
a thin slab with a hole in it. The only problem with this proposed structural analysis of the slab is
that the slab cannot be considered a thin plate. The solution to a thick plate with a hole through it
is beyond the scope of undergraduate engineering, so instead we decided to use the finite element
analysis found on Solidworks to determine if the slab would be within safe working conditions
[8].

45. 44
Figure 28: Stress concentration on a thin slab with a hole
Solidworks allows the user to create 3D models and then run finite element analysis to
determine the stresses on the object. To allow for rapid model testing, we took advantage of the
DesignTable found on Solidworks, which allows the user to enter different sizing parameters to
see different versions of the model. The slab was sized to be 480”x240” (40’x20’) in the problem
statement. The problem statement also calls for a sloped driveway to allow the melted snow to
run away from the house, so we assumed a 10 degree slope for our project. It was also decided
that the concrete should be 5” in thickness, and the rest of the dimensions were dictated by the
thermal analysis. The final dimensions are depicted in figure 29. Not seen in the figure is the
number of holes in the slab for the tubes, which ended up being 28.
Figure 29: Dimensions of holes and their spacing

46. 45
After working with the model and entering the parameters the thermal analysis allotted for, we
were able to use the SimulationExpress Study program in Solidworks to test how the structure
will be affected by different forces. Concrete data was pulled from EngineeringToolbox [9] for
typical strength concrete, allowing us to accurately portray how the driveway would react to
vehicle being on it. Also, a “tire” was added to the piece as seen in figure 30. This ‘tire’ piece
allotted for the angle of the slope, and allowed the driveway to see a more appropriate version of
the 25kN max is would see from a typical heavy truck. The angle was built to see the typical area
a tire has in contact with the ground, to accurately portray the force the tire would press onto the
concrete.
Table 6: Properties of normal strength Portland cement concrete
Density 2400 kg/m​3
Compressive Strength 40 MPa
Flexural Strength 5 MPa
Tensile Strength 5 MPa
Modulus of Elasticity 41000 MPa
Poisson’s Ratio 0.21
Shear Strength 17 MPa
Figure 30: Angle to represent slope and tire

47. 46
The simulation shows a deformation so the user knows if they are receiving the desired stress.
The deformation of the concrete driveway with a 25kN force applied to the tire gives us figure 31.
Figure 31: Deformation of driveway
Figure 31 shows the desired deformation, so we go on to see if the stresses cause a failure in the slab or
not. Figure 32 shows the von Mises stresses calculated by the simulation.
Figure 32: Von Mises stresses on the driveway
As we see in this deformation, the highest point of stress is 6.652x10​5​
N/m​2​
​which is well below the
compressive strength of the concrete. A factor of safety of 5 was chosen for the analysis to check for, and

48. 47
figure 33 is the Solidworks representation of this. The factor of safety for this part of the project actually
ends up to be around 20, because of the assumption that the full weight of the car is on only one tire, but
that’s not really how the weight of a car is distributed.
Figure 33: Factor of Safety for the concrete slab
Economics
After all this analysis, it is important to quantify how much this system will cost a
homeowner. There are a few different layers to the overall cost of the system.
1. Initial Cost of the System
a. Pipes, Valves, Fittings
b. Heat Exchanger, Pump, Storage Vessel
c. Control System
d. Pressure and Temperature Gauges
e. Initial propylene glycol supply
2. Installation of the System
a. Plumber costs to run new water and natural gas lines
b. Tearing Up Driveway and Laying Pipes
c. Connecting each component together
d. Rebuilding Driveway
3. Yearly Costs
a. Electrical costs of hot water from tankless and tank water heater
b. Natural Gas costs
c. Electrical Cost of Pump

49. 48
4. Maintenance Costs
a. Propylene Glycol resupply
b. Any yearly repairs needed
5. Future Worth
a. Increases value of residence
Each of these points will be evaluated. Note there is really no yearly savings for this type of
system. It can be associated as a luxury item or necessary for safety but having this system will
not save money over time versus not having this system. There are small cost benefits such as
not needing any rock salt each winter. There are also larger benefits in that the driveway will not
deteriorate as quickly since it is being kept clear of salt, snow, and ice. However, these savings
are either small or difficult to quantify so they will not be included in the analysis.
Initial Cost
All piping for this system will be aluminum. The amount needed and costs are outlined
below. Lengths were calculated based on actual length plus a small additional amount in case
any extra was needed. The prices were gathered from ​Metals Depot​ [10].
Table 7: Prices of Necessary Piping
Type Length Needed
(ft)
Price per
Unit
Total Price
¾” NPS ­ Sch 40 1100 $31.60/ 20 ft $1738
1” NPS ­ Sch 40 200 $51.60/ 20 ft $516
1 ¼” NPS ­ Sch 40 4 $23.20/ 4 ft $23.20
2” NPS ­ Sch 40 10 $68.20/ 10 ft $68.20
The prices for the major equipments were all received from the vendors themselves.
Table 8: Major Equipment Pricing
Unit Price
BP412­60 Heat Exchanger $1105.14 [11]
316 SS Centrifugal Pump Model #: 70761­02 $495.00 [6]
ASME Code Small Vertical Pressure Tank $354.55 [7]

50. 49
The pricing for valves and fittings is included below. Note that for the reducers, more
than one will have to be placed in series. For example, to go from ¾” to 2”, a ¾”X1”, 1”X1.5”,
and 1.5”X2” reducer will be needed. A short piece of piping will be placed in between each
section. Note that steel was chosen as the material of choice for the reducing tees because they
were extremely cheap and there are so many tees. Aluminum reducing tees of the same size were
approximately 5 times greater. The conductivity of steel is much lower than aluminum, but the
area of heat transfer of the tees is miniscule compared to the aluminum that no difference in heat
transfer will be noticed.
Table 9: Prices of Pipe Fittings and Valves
Type Material Required
Number
Price per
Unit
Total Cost
¾” Brass Ball
Valve
Brass 2 $15.83 [12] $31.66
1” Brass Ball
Valve
Brass 3 $24.24 [12] $72.72
¾”X1” Reducer Aluminum 2 $9.42 [13] $18.84
1”X1.25”
Reducer
Aluminum 1 $14.36 [13] $14.36
1”X1.5” Reducer Aluminum 2 $19.26 [13] $38.52
1.5”X2” Reducer Aluminum 2 $25.73 [13] $51.46
1”X3/4” Inline
Reducing Tee
Steel 53 $6.46 [14] $342.38
The control system involves a variable flowmeter, a flow controller, and a couple
temperature transmitters.

51. 50
Table 10: Prices of Control System
Equipment Quanity Price per Unit Total Price
Multifunction Flow Computer 1 $815.00 [15] $815.00
Magnet Mount Thermocouples 2 $65.00 [16] $130.00
¾” Variable Area Flowmeter for water
up to 10.0 gpm with Analog Output
1 $430.00 [17] $430.00
There will also be a few extra temperature, pressure, and flow gauges for the system.
Table 11: Prices of Extra Gauges
Equipment Quanity Price per Unit Total Price
¼” NPT Standard dial Pressure Gauge
(100 psi max)
2 $23.00 [18] $46.00
Magnet Mount Thermocouples 2 $65.00 [16] $130.00
Clear in­line Flowmeter (up to 15 GPM) 1 $161.00 [19] $161.00
For the propylene glycol estimated cost, the total volume of glycol needed was estimated
by calculating the total volume of the piping system (from table 7) and adding it to the capacity
of the tank. An extra 5% was added to account for the capacity needed in the heat exchanger.
Overall, the system will need approximately 48.6 gallons of 40% propylene glycol and water
mixture. Thus approximately 20 gallons of that mixture is propylene glycol while the remaining
volume is water.
Table 12: Propylene Glycol Cost
Item Amount Price per Unit Total Cost
Food Grade 99.5%
Propylene Glycol
20 gallons $341.50/ per 15
gallons [20]
$455.33
Simply adding up the costs 7 through 12 yields an initial equipment cost of $7037.36.

52. 51
Installation Costs
This is a very labor intensive installation job and the labor costs will reflect that. The
person installing the system will have to add piping, dig up a driveway, bend and form the
piping, thread piping, and weld if necessary. It will be assumed that three skilled employees
making $20/hour for a residential piping specialist company will perform the work over the
course of 10 eight hour work days. The digging up of the existing driveway and laying of the
aluminum pipes will take the most time. This yields $4800 in laboring expenses. In addition
supervision and extra fees to the installation company will be 20% of the laboring expenses.
Overall, this is a $5760 installation procedure. This is approximately 80% of the initial
equipment cost which makes sense for the difficulty of the job.
Overall Initial Cost
The initial cost of the installation and equipment purchases is approximately $12,797.
Maintenance Costs
Since propylene glycol is a corrosion inhibitor, it will actually protect each component in
the system. For this reason, it is not necessary to flush the system and replace with new
propylene glycol each year. If the homeowner would prefer the glycol is not left stagnant in
pipes for long periods of time, it is recommended that the glycol is pumped into a storage
container at the end of winter and then recharge the system the following winter. Otherwise, it is
quite expensive to replace the fluid while also unnecessary.
In terms of maintenance, the system operates at relatively low pressure and temperature
and is constructed of high quality material. Thus only 0.5% of the initial investment will be
designated as the maintenance cost per year. This cost come out to $63.90 per year.
Yearly Operating Costs
The yearly operating costs will be estimated based off of the average run time for the
system which will vary based on location. Pittsburgh for example averages almost 40 days per
winter when there is snowfall. However, if it only snows for one hour on a certain day it will get
counted so the days of snowfall is difficult to judge the exact length of snowfall. If we assume

53. 52
that the system is needed for approximately 10 hours a day on these days that equates to 400
hours of operation each year.
Electrical Costs
Electrical costs were taken from Duquesne Light’s energy pricing ($7.97 cents per
kW*hr [22]). The following table shows the estimated costs of each component. The Hot Water
heater pricing here is the extra costs associated with owning this system, not the total cost of the
hot water system.
The pump is powered off of ¾ horsepower which can be simply converted to watts and
the price can be calculated. The standard hot water heater tank was not analyzed in this project.
The energy costs associated with the hot water tank were assumed to be $585 year. based on the
average for a 50 gallon electric water heater. The extra costs associated with pre heating the
water for the driveway were then based off of the 400 extra hours of necessary run time. The
flow computer and miscellaneous gauges requiring electricity were assumed to require
approximately 100 W of power each and calculated accordingly since there was no specific data
on the power that these will draw.
Table 13: Electricity Costs
Unit Total Price
per year
Pump $17.83
Hot Water Heater $26.71
Tankless Water
Heater (Display
Only)
$3.20
Flow Computer $3.20
Analog Flowmeter $3.20
Natural Gas Costs
The Tankless Water Heater receives its fuel from natural gas. While it is difficult to
predict how much natural gas the tankless water heater will use, there are industry standards for
calculating the yearly estimated energy cost [23]. That formula is given by the following:

54. 53
ost 365 1045 ost of Fuel/EFC = * 4 * C (48)
The cost of fuel is given in dollars per btu and the energy factor (EF) is determined by the
manufacturer which is an indication of how much hot water the heater can produce per unit of
fuel. Current natural gas prices are approximately $2.63 per million Btus. The energy factor for
the selected tankless water heater is 0.94 [4]. Using equation 46, the cost per year of the tankless
water heater will be approximately $42.
Total Yearly Costs
Including the maintenance and operating costs, the total yearly costs is approximately
$159.95.
Comparing to Current Systems
The average costs associated with snow melt driveway systems, and the total costs of this
system are compared in the following table.
Metric Our System Average
Initial Cost per Square Foot $16 $14­24 [25]
Yearly Cost per Square Foot $.20 $0.12­0.25 [26]
Comparing the expected costs of our design versus typical average values, our system was within
the range for both metrics. Some other considerations is again that there was no boiler utilized
for our driveway system. Many companies would have recommended an electrical heating
system however the yearly operating costs of full electrical systems are much higher. In addition,
the outline of a usable control system for our system was included in the pricing, which is not
always included with snow melt systems such as these. Overall, the system designed here is a
very cost effective design that does not sacrifice quality.
Present Worth Calculations
There is very little information on standard payment plans for snow melt systems since
they are still relatively uncommon. The most accurate way to estimate the payment plans would
be through a similar type of luxury residential application such as a pool. Pool loans are available
up to $50,000 at 3.99% interest rate [27]. For this calculation, it will be assumed that the
homeowner was able to pay 20% of the initial cost as a down payment and then took out an

55. 54
approximately $11,000 loan at a 4% interest rate. The homeowner is planning to pay off the loan
within three years.
In addition, there is an additional salvage cost associated with this system. It can be
assumed that the system will last for 20 years at which point the homeowner sells his house. It is
estimated that the snowmelt system will add 20% of the initial cost of the system to the selling
value of the home.
The present worth factor and series present worth factor are given by the following
equations. is given by:
1 )f
P
= ( + i
m
m n*
(48)
a
P
= i (1+ )*
i
m
m n*
(1+ ) −1i
m
m n*
(49)
The annual operating costs is $159.65, the salvage value is $2560, the monthly payment to meet
the 3­year loan deadline will be $306, and the initial down payment is $2560. The following
calculation details the present worth of the system:
W − 2560 159.65 ( , 0 years) 306 ( , years) 2560 , 0 years)P = $ − $ * a
P
12
4%
2 − $ * a
P
12
4%
3 + $ * f
P
* (12
4%
2
­$38,118WP =
So with the rates set as shown above, the present worth of this system is an expense of
approximately $38,000.
Conclusion
In conclusion, an efficient and cost effective heated driveway slab has been designed.
The driveway has been proven feasible to work even with standard hot water being used to heat
the propylene glycol. The driveway surface is expected to reach 40 ℉ in a varying range of
ambient conditions. A cost effective heat exchanger and pump have been selected to
continuously cycle the propylene glycol through the system. There are troubleshooting features
in the form of pressure and temperature gauges throughout the line to help the user dissect any
performance issues. There are also a number of block valves to immediately shut off the system
if necessary.

56. 55
The initial and operating costs are in­line with currently designed systems. A control
system has been proposed to lower operating costs even further than the expected values.
Research has shown that the heated driveway will increase the future value of the home if it is
ever planned to be sold.
Overall, this heated driveway system would be a cost effective method to improve safety
in any residential home. No longer will homes be forced to require a boiler to install an effective
snow melt system. This design will function for the majority of household and would make an
excellent addition anywhere cold winters are expected.

57. 56
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