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/m^2·K Inside wall surface temperature is equal to temperature inside apartment

6. Set up Generate value for conductive resistance in walls Find values for thermal conductivity of wall materials Material Thermal Conductivity (W/m·K) Brick0.72 Gypsum0.17 Hard Wood Siding0.094 Stud0.16 Glass1.4 Insulation0.038

7. Solution Total resistance of composite wall is 1.054 m^2·K/W Resistance of windows is 0.105 m^2·K/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 m^2 Total window area: 5.63 m^2

18. 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