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Furnace Efficiency. Bryce Cox Dallin Bullock. Problem. My gas bill is very expensive My furnace claims an efficiency of 78% but it appears to be less efficient. Objective. Using recorded high and low temperatures calculate the heat flux from my apartment in the month of March 2008
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Furnace Efficiency Bryce Cox Dallin Bullock
Problem • My gas bill is very expensive • My furnace claims an efficiency of 78% but it appears to be less efficient
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
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
More Assumptions • Average convective heat transfer coefficient of 10 W/m^2·K • Inside wall surface temperature is equal to temperature inside apartment
Set up • Generate value for conductive resistance in walls • Find values for thermal conductivity of wall materials
Solution • Total resistance ofcomposite wall is1.054 m^2·K/W • Resistance of windowsis 0.105 m^2·K/W
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
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)
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
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
Conclusion • The discrepancy in efficiency is due to many possible factors: • Dirty filter • Restricted air flow (poor duct arrangement) • Dust buildup in combustion chamber
Recommendations • Change filter every 3 months • Clean ducts if needed • Make sure vents are not obstructed
Appendix • Resistance per area equations:
Appendix • Heat transfer equation:
Appendix • Thicknesses • Brick 102mm • Wood siding 8mm • Studs 130 mm(40 mm wide, .65 m apart) • Gypsum 12mm • Glass 7mm
Appendix • Total wall area: 34.82 m^2 • Total window area: 5.63 m^2
Appendix • References: • BYU Geography Department – Weather statistics • http://www.pgjr.alpine.k12.ut.us/science/james/provo2008.html • Trane Heating Systems – Furnace Information • http://www.trane.com/residential/products/Furnaces/XR80.aspx