Furnace Efficiency

1
Furnace Efficiency

• Bryce Cox
• Dallin Bullock

2
Problem

• My gas bill is very expensive
• My furnace claims an efficiency of 78 but it
  appears to be less efficient

3
Objective

• Using recorded high and low temperatures
  calculate the heat flux from my apartment in the
  month of March 2008
• Use information on gas bill to determine natural
  gas used for heating
• Compare calculated use to measured and compare
  efficiencies

4
Assumptions

• Radiation is negligible
• Furnace keeps temperature inside apartment a
  constant 70º F
• All neighboring apartments also at constant 70º F
• Heat transfer through only two walls

5
More Assumptions

• Average convective heat transfer coefficient of
  10 W/m2K
• Inside wall surface temperature is equal to
  temperature inside apartment

6
Set up
Material Material Thermal Conductivity (W/mK) Thermal Conductivity (W/mK) Thermal Conductivity (W/mK)
Brick Brick 0.72
Gypsum Gypsum 0.17
Hard Wood Siding Hard Wood Siding 0.094
Stud Stud Stud 0.16
Glass 1.4
Insulation 0.038

• Generate value for conductive resistance in walls
• Find values for thermal conductivity of wall
  materials

7
Solution

• Total resistance ofcomposite wall is1.054
  m2K/W
• Resistance of windowsis 0.105 m2K/W

8
Solution

• From recorded high and low temperatures we
  estimated average day and night time temperatures
• We then used the average temperatures to
  calculate heat flux for each day and night

9
Results

• We found the total energy lost by heat transfer
  for the month was 3,371,151,069 Joules
• Converted to British Thermal Units 3,195,234 BTU
• 3.195 DecaTherms (Unit used by gas company)

10
Results

• My gas bill states that I used 7.2 decatherms in
  March. Estimating that 1.5 decatherms a month is
  used by the water heater and oven then 5.7 DTH
  were used by the furnace

11
Results

• The furnace has a published efficiency of 78
• According to our calculations this means the
  furnace should use 4.1 DTH
• We found that it actually used 5.7DTH which is
  about 56 efficiency

12
Conclusion

• The discrepancy in efficiency is due to many
  possible factors
• Dirty filter
• Restricted air flow (poor duct arrangement)
• Dust buildup in combustion chamber

13
Recommendations

• Change filter every 3 months
• Clean ducts if needed
• Make sure vents are not obstructed

14
Appendix

• Resistance per area equations

15
Appendix

• Heat transfer equation

16
Appendix

• Thicknesses
• Brick 102mm
• Wood siding 8mm
• Studs 130 mm(40 mm wide, .65 m apart)
• Gypsum 12mm
• Glass 7mm

17
Appendix

• Total wall area 34.82 m2
• Total window area 5.63 m2

18
Appendix

• References
• BYU Geography Department Weather statistics
• http//www.pgjr.alpine.k12.ut.us/science/james/pr
  ovo2008.html
• Trane Heating Systems Furnace Information
• http//www.trane.com/residential/products/Furnaces
  /XR80.aspx