Fireplace Heat Exchanger Project December 5, 2013

MEC 422 Group

Brandon Ye 107716055 Cade Dong 107747116 Christopher Cho 107806330

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Table of Contents

Objective and Introduction ………………………………..... Page 2

Design Criteria and Assumptions ………………………………..... Page 2

Design Procedure ………………………………..... Page 3

Design Phase ………………………………..... Page 5

Results & Discussions ………………………………..... Page 6

Cost Analysis ………………………………..... Page 7

Conclusion & Recommendation ………………………………..... Page 8

Appendix ………………………………..... Page 9

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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 1100oF to 1500oF. 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.

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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)

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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.

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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

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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.

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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].

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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