3. 2
Objective and Introduction:
Our objective was to design a system for fireplace heat recovery. In most wood-burning
fireplaces, much of the heat that is not directly blown into the room ends up being lost through
the chimney and to the outside. Because the heat convected from a fire is dependent only in
the direction it is felt, we felt that the most valuable way to recover heat was to place water
pipes around the back of the fireplace. The introduction of a new temperature sink has no
effect on the heat that convects into the interior of the home, so we found this concept to be a
minimalistic design change to the standard fireplace structure.
In our research, we have found that most wood-burning fireplaces can reach steady
temperatures of 1100o
F to 1500o
F. By running pipes through the system, we effectively create
a heat exchanger system that can take advantage of the large amounts of heat energy that is
normally lost. By utilizing thermally conductive pipes that can withstand such high
temperatures, we can heat the flowing water to nearly a boil, lightening the load on the
residential boiler.
Heat exchangers are systems that have two fluids flowing adjacent to each other at
different temperatures. Because of the Zeroth Law of Thermodynamics, the fluid of higher
temperature will convect its heat across the heat transfer surface area to the fluid of lower
temperature. This process will continuously occur until the system reaches a temperature
equilibrium for both fluids, but the flowing nature of the fluids allow the system to exchange
heat indefinitely.
Design Criteria and Assumptions:
Our assignment consisted of designing a heat recovery system for a fireplace. Due to
the excessive heat energy that is wasted during the process, we approached the task by
designing a heat exchanger that would attempt to recover the lost energy and use it to assist a
residence’s boiler system. By having a secondary water-heating system available, it is possible
to lighten the load on the boiler and save on energy costs.
In the proposal of our design, many assumptions had to be made in order to allow our
experience with thermodynamics and fluid dynamics to properly apply to the system. For
example, our water-flow input was assumed to be turbulent and fully developed right from the
start. For the Extended Bernoulli’s Equation to apply, we assumed our pipe system to be
perfectly sealed, allowing a steady, incompressible, flow of water to be analyzed with continuity
analyses.
Had we not made these assumptions, we would not have the tools necessary to perform
the accurate calculations on such a complex system.
4. 3
Design Procedure:
We started the design by analyzing the two fluids of the heat exchanger: the fire-heated
air surrounding the pump-controlled water. In order to acquire an overall analysis of the
system, it was necessary to find the Overall Heat Transfer Coefficient.
(Eq. 1)
To find the convection coefficient of the water being heated, we utilize the velocity of
the water and its fluid properties to find the Reynolds Number. The temperature at which the
fluid properties are found is the Bulk Fluid Temperature (Table A-9E).
(Eq. 2 & 3)
With the dimensionless Reynolds Number, we can find the Nusselt Number.
(Eq. 4)
Because the Nusselt number is the ratio of conductive to convective heat transfer, we can
utilize it to calculate the Convective Heat Transfer Coefficient of the internal water flow.
(Eq. 5)
The process to find the convection coefficient of the heated air is actually different. This
is due to the fact that the air around the fire was assumed to be ambient, so we modeled that
fluid to be under free or natural convection. The major differences in analysis are the
utilization of the Film Temperature and the addition of the Coefficient of Volume Expansion.
(Eq. 6 & 7)
These new variables are used to find the Rayleigh Number, which is necessary to find the
Nusselt Number for natural convection systems.
( )
{
( ) ⁄
[ ( )
⁄
]
⁄
} (Eq. 8 & 9)
5. 4
The equation to find the Free Convection Heat Transfer Coefficient is then the same as that for a
forced convection system.
(Eq. 10)
With these individual convection heat transfer coefficients, the Overall Heat Transfer
Coefficient of the entire system can then be represented.
(Eq. 11)
Using this coefficient, we can use the heat exchanger equations to fully analyze the system.
( )
(Eq. 12 & 13)
The pressure analysis of the system was performed using the Extended Bernoulli’s
Equation.
∑ (Eq. 14)
However, the two points of our analysis occurs before and after the pipes split and reattach, so
there is no need to include change in height. Also, because the diameter of pipe at both
analysis points are the same, there is no change in fluid velocity as well. This allows our
equation to be simplified to the following:
∑ (Eq. 15)
in this equation refers to the output pressure of the pump we have selected. The pressure
of a pump is determined using the horsepower and volume flow rate with the relations:
( )( )
(Eq. 16)
(Eq. 17)
The added terms shown on the Extended Bernoulli’s Equation refer to the frictional losses and
the minor losses, respectively. These terms contribute to pressure drop in the system caused
by fluid friction against the sides of the pipe and the dynamics of fluids flowing through joints
and manifolds.
6. 5
Design Phase
Figure 1: Fireplace Heat Exchanger Piping system with Pump
After extensive research, the material chosen for the pipe was copper. In addition to its
low cost and high thermal conductivity, it was a standard component in many heating systems.
This was a safe material choice because wood fires burn at 1100o
F to 1500o
F [1]
, but the
melting point of copper is upwards of 1900o
F [2]
. Because our elbow joints and manifolds
would consist of welded connections, their ability to withstand temperature usage could last
indefinitely. However, during our calculations, we assumed that fouling would not occur.
Realistically, corrosion may become an issue in this system, as it does in all piping systems. We
chose a standard inner diameter pipe size of 2.465 inches [3]
, making it easily accessible if
components ever needed to be replaced.
The single pipe travels through a manifold that divides the flow of water into 7
individual pipes of equivalent area. This is done to decrease the speed of the flow and increase
surface area exposure to the fire, thus allowing more heat absorption as the water passes.
After passing along the walls of the fireplace, the pipes reemerge from the “heat exchanger”
and enter a second manifold that rejoins the flow of all 7 pipes. We decided this to be the best
course of action in order to simplify our fluid analysis as well as reduce the heat loss of the
water to the surroundings. As previously stated, the pipes are all welded to each other rather
7. 6
than connected via gasket threaded to ensure temperature resistance and stave off water
leakages.
According to the New York City Plumbing Code, the maximum water pressure within a
building is 85 pounds per square inch. When exceeded, a water-pressure reducer must be
installed. Given this information, we found it acceptable to use a 2-horsepower pump that
would supply a pressure of 38.56 pounds per square inch.
Results & Discussion:
In order to perform a proper analysis on the system to calculate all the relevant
information, assumptions were made in regards to the simplicity of the system. It was
presumed that the water flow was fully developed and turbulent and moving through a
smooth, corrosion-free pipe. In order to use Bernoulli’s equation, it was required to accept that
the fluid flow was steady and incompressible as well.
The air outside of the pipes is assumed to be subject to no external forces, so the
buoyancy of hot air is assumed to be the only motion taking place. This allowed us to model
the “shell-side” fluid in this “heat exchanger” as a free or natural convection system.
The initial condition of the pipe fluid was assumed to be 60o
F water flowing at 0.6 ft/s.
In order for the water to leave the system at the desired 180o
F, heat energy from the cross-
flow air must transfer to the water. The ambient heated air adjacent to the pipes was assumed
to be 200o
F, and after calculations, the outlet temperature of the air was found to be 148o
F.
This was done by finding the convection heat transfer coefficients for both fluids (hH20 = 194.5
BTU/h·ft2
·R and hair = 0.99 BTU/h·ft2
·R) and determining the heat transfer surface area to be the
surface area of the exposed piping (AS = 4.1667 ft2
). The total heat transfer rate of the system
( ) was found to be 146.25 BTU/s.
With the system being powered by a 2-horsepower pump, it was determined that the
volume flow rate through the 0.205-inch diameter pipe was 88.9 gallons per minute; it followed
that the pressure offered by this pump was measured to be 38.56 pounds per square inch. The
utilization of the extended Bernoulli’s equation allowed us to calculate a total pressure drop
from the beginning to end of the heat exchanger was only 3.15 pounds per square inch.
8. 7
Cost Analysis:
As with all upgrades and installations, it must be determined whether or not it is
financially feasible to make such renovations. Assuming that the fireplace infrastructure is
already in place, the additional costs involved consist of the piping system, the pump itself, and
labor.
Using Plumbing Supply as reference [5]
, the cost of Type “L” Rigid Copper Pipe with a
diameter of 2.5 inches is approximately $35.00 per linear foot. The pipe cost, excluding the
manifold, would amount to $2065.00 for 59 linear feet and $928.48 for 28x 90o
elbows.
According to Water Pumps Direct [6]
, a 2-horsepower pump rated for 89 gallons per minute
would cost $400.
Thus, the total cost of the pump and copper piping, excluding the custom manifolds and
the copper piping required to reconnect the system back to the main plumbing infrastructure,
would come out to $3400.00 before labor.
Conclusion & Recommendation:
Our design uses a heat exchanger to capture some of the lost heat given off by the fire.
The water in the pipes is heated with this lost energy, which can then be fed directly into the
boiler, essentially lessening the load on the water heating system. This can directly lead to
reduced energy costs and a more environmentally friendly system. Though we may not
recommend going out of your way to perform such an installation, if the renovation of a
fireplace was already intended, this could be a fiscally responsible move. If installed properly
this system should last at least 50 years under normal operating conditions [7]
.
9. 8
Appendix
Detailed derivations and calculations regarding the Shell Fluid (Heated Air)
Detailed derivations and calculations regarding the Tube Fluid (Water)
Detailed derivations and calculations regarding the Heat Exchanger as a whole
Detailed derivations and calculations regarding the Fluid Pressure of the system
1. http://homeguides.sfgate.com/temperatures-woodburning-stove-48039.html
2. http://www.engineeringtoolbox.com/melting-temperature-metals-d_860.html
3. http://www.petersenproducts.com/Specifications/Pipe_Copper.aspx
4. http://www.nyc.gov/html/dob/downloads/pdf/plumbing_code.pdf
5. http://www.plumbingsupply.com/copperpipe.html
6. http://www.waterpumpsdirect.com/pumps/2-hp-sprinkler-pumps.html
7. http://colerepair.com/Copper%20Water%20Pipe.html
