1. By: Matthew Irvine and Cristina Belew

3. Origination and Goals  Partnership with Habitat for Humanity  Their goal is to lower the overall cost to owner  Studied the effect of insulation on energy costs  Looked for the effects of different insulations and insulating methods  Recommend the insulations with the lowest cost to owner

4. Four Different Areas  Wall insulation types  Framing dimension selection  Attic insulation  Duct Insulation

6. Design Modeling Assumptions  h and k values  No thermal contact resistance  Siding geometry  No radiation in attic, theoretical venting

7. Decision of appropriate options  Wall Insulation  Stud Sizing  Duct Insulation

8. Modeling Techniques  We began with a square foot section  Moved to a larger section with other elements included  Completed our analysis by simulating an entire house (Woodruff House)

9. Studied Design Description  Small and large wall section for 2X4 and 2X6  Attic Section  Duct Section

11. 2 x 4 Stud, 1 x 1 m 2 Section: Overview  Equation for heat flux Q = (T 2 – T 1 )/R total  Studied 3 times during the year January – 2.778 ºC April – 15.56 ºC July - 27.2 ºC  Desired inside temperature- 22.2 ºC Drywall Insulation Plywood Air Pocket Hardiboard

12. 2 x 4 Stud, 1 x 1 m 2 Section: R- values  R of Convection – 1/h*A h- convection coefficient (W/m·°C) A- area of convection (m 2 )  R of a certain material – L/k*A k- thermal conductivity L- thickness of material (m) A- area of material (m 2 )  R total = R outside,convection + R drywall + R insulation + R hariboard + R air pocket + R siding + R inside,convection R (W/m·°C) RiRi R january R april R july R hardiboard R plywood R insulation R drywall R air pocket R-Total January R-Total April R-Total July 0.042 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1062.120.07130.1562.6362.6422.651 0.03 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1062.960.07130.1563.4833.4893.497 0.046 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1061.930.07130.1562.4522.4582.467

13. 2 x 4 Stud, 1 x 1 m 2 Section: Theoretical vs. Simulation Heat Flux  Heat flux for each insulation and temperature difference was calculated next with Solidworks and compared to the theoretical calculations done. Heat Flux (W-theoretical) JanuaryAprilJuly 0.042 W/m 2 ·°C7.3672.513-1.886 0.03 W/m 2 ·°C5.5771.904-1.430 0.046 W/m 2 ·°C7.92002.701-2.027 Heat Flux (W- simulation) JanuaryAprilJuly 0.042 W/m 2 ·°C 7.42972.5393-1.8999 0.03 W/m 2 ·°C 5.61231.9192-1.4372 0.046 W/m 2 ·°C 7.99252.7312-2.0429 Error (%)JanuaryAprilJuly 0.042 W/m 2 ·°C0.84%0.63%0.91% 0.03 W/m 2 ·°C0.76%0.79%1.11% 0.046 W/m 2 ·°C0.73%0.50%0.78%

14. 2 x 4 Stud, 1 x 1 m 2 Section: FEA (January) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

15. 2 x 4 Stud, 1 x 1 m 2 Section: FEA (April) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

16. 2 x 4 Stud, 1 x 1 m 2 Section: FEA (July) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

17. 2 x 6 Stud, 1 x 1 m 2 Section: R- values  Next Step: How does the heat flux change when more insulation is added with a 2 x 6.  The R-values were calculated again when a thicker insulation. R (W/m·°C) RiRi R january R April R july R hardiboard R plywood R insulation R drywall R air pocket R-Total January R-Total April R-Total July 0.042 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1063.330.07130.1563.8463.8523.860 0.03 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1064.660.07130.1563.4833.4893.497 0.046 W/m 2 ·°C 0.1000.02940.03530.04410.05670.1063.040.07130.1562.4522.4582.467

18. 2 x 6 Stud, 1 x 1 m 2 Section: Theoretical vs. Simulation Heat Flux  Here are the heat flux numbers for the SolidWorks simulations compared to the theoretical calculations done: Heat Flux (W-theoretical) JanuaryAprilJuly 0.042 W/m 2 ·°C7.3672.520-1.886 0.03 W/m 2 ·°C5.5771.904-1.430 0.046 W/m 2 ·°C7.9202.701-2.027 Heat Flux (W- simulation) JanuaryAprilJuly 0.042 W/m 2 ·°C7.42972.5393-1.8999 0.03 W/m 2 ·°C5.61231.9192-1.4372 0.046 W/m 2 ·°C7.99252.7312-2.0429 Error (%)JanuaryAprilJuly 0.042 W/m 2 ·°C0.61%0.80%0.51% 0.03 W/m 2 ·°C0.47%0.69%0.38% 0.046 W/m 2 ·°C0.65%0.85%0.55%

19. 2 x 6 Stud, 1 x 1 m 2 Section: FEA (January) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

20. 2 x 6 Stud, 1 x 1 m 2 Section: FEA (April) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

21. 2 x 6 Stud, 1 x 1 m 2 Section: FEA (July) 0.042 W/m 2 ·ºC0.03 W/m 2 ·ºC0.046 W/m 2 ·ºC

22. Conclusions from Theoretical and SolidWorks Studies of 1 x 1 m 2 Section  Based upon this data, fiberglass is the insulation to choose. The heat flow through the section of wall is the lowest compared to the other insulation choices.

23. 3 Sections of Wall with 2 x 4 Studs: Overview  The next step: A bigger section of wall with studs included.  The R-values had to be calculated for the sections of wall next to the studs and next to the insulation. Drywall Insulation Studs Plywood Hardiboard

24. 3 Sections of Wall with 2 x 4 Studs: R-values RiRi R January R April R July R hardiboard R plywood R insulation R drywall R studs 1/R-Total January 1/R-Total April 1/R-Total July 0.042 W/m 2 ·°C 0.0380.01130.01360.01700.06490.0410.810.02751.0020.98330.9966 0.03 W/m 2 ·°C 0.0380.01330.01360.01700.06490.0411.140.02750.75450.75430.7524 0.046 W/m 2 ·°C 0.0380.01330.01360.01700.06490.0410.740.02751.0771.0761.073 Studs0.27640.08130.09750.12180.46630.29250.19721.75510.32590.32410.3216

25. 3 Sections of Wall with 2 x 4 Studs: Heat Flux Comparisons Heat Flux (W-simulation) 0.042 W/m 2 ·°C0.03 W/m 2 ·°C0.046 W/m 2 ·°C January 25.7920.9827.24 April 8.6807.1619.300 July -6.590-5.370-6.971 Heat Flux (W-Theoretical) 0.042 W/m 2 ·°C0.03 W/m 2 ·°C0.046 W/m 2 ·°C January 25.8521.5727.57 April 8.8807.4149.414 July -6.685-5.585-7.138 Error (%)0.042 W/m 2 ·°C0.03 W/m 2 ·°C0.046 W/m 2 ·°C January 0.21%2.73%1.20% April 2.25%3.41%1.21% July 1.43%3.85%2.34%

26. 3 Sections of Wall with 2 x 4 Studs: FEA (January) 0.046 W/m 2 ·ºC 0.03 W/m 2 ·ºC 0.042 W/m 2 ·ºC

27. 3 Sections of Wall with 2 x 4 Studs: FEA (April) 0.046 W/m 2 ·ºC0.03 W/m 2 ·ºC 0.042 W/m 2 ·ºC

28. 3 Sections of Wall with 2 x 4 Studs: FEA (July) 0.046 W/m 2 ·ºC0.03 W/m 2 ·ºC0.042 W/m 2 ·ºC

29. Duct Insulation: Overview  Next step: Determine what size fiberglass insulation is best  Assumptions: Air flowing through is 22.2 °C Air surrounding duct is the temperature of the outside since placed in attic  Three fiberglass insulation size choices of 2 inches, 4 inches and 6 inches.  The analysis in Solidworks was performed on a three foot section of duct. Reflective Barrier Fiberglass insulation Aluminum Core Air Flow

30. Duct Insulation: R-values  For a cylinder, the equation for the total r-value changes. It is dependent on the radius of each section of material. R-Values R convection, inside R aluminum R fiberglass R reflective barrier R ouside,convection 2 inch 0.13710.00070763.5290.000024530.1523 4 inch 0.13710.00070765.7143121.69064E-050.1054695 6 inch 0.13710.00070767.2980.000012190.08072

31. Duct Insulation: Heat Flux Heat Flux- SimulationJanuaryAprilJuly 2 inch 5.0741.7351.3057 4 inch 3.30251.13230.8393 6 inch 2.5840.8830.6652 Heat Flux- TheoreticalJanuaryAprilJuly 2 inch 5.0901.7441.304 4 inch 3.2601.1150.8492 6 inch 2.62020.898350.67376 Error (%)JanuaryAprilJuly 2 inch -0.31%-0.52%0.13% 4 inch 1.30%1.55%-1.17% 6 inch -1.38%-1.71%-1.27%

32. Duct Insulation: FEA Simulation (January) January Analysis: Temperature flow through the center at 22.2 ºC and the surrounding temperature 2.778 ºC 2 inches 4 inches6 inches

33. Duct Insulation: FEA Simulation (April) 6 inches4 inches 2 inches April Analysis: Temperature flow through the center at 22.2 ºC and surrounding temperature at 15.56 ºC

34. Duct Insulation: FEA Simulation (July) July Analysis: Temperature flow through the center at 22.2 ºC and the surrounding temperature 27.2ºC 2 inches 4 inches6 inches

35. Attic Insulation: Overview  Next Step: Which insulation is the best choice for the attic  Assumptions: Attic temperature is the outside temperature Inside temperature is 22.2 °C Drywall Insulation

36. Attic Insulation: R-values R-Values R inside R january R april R July R insulation R drywall R- Total January R- Total April R-Total July 0.042 W/m 2 ·°C 0.108 0.1632.120.07132.407 2.518 0.03 W/m 2 ·°C 0.108 0.1632.960.07133.247 3.358 0.046 W/m 2 ·°C 0.108 0.1631.930.0713 2.217 2.328

37. Attic Insulation: Heat Flux Heat Flux- TheoreticalJanuaryAprilJuly 0.042 W/m 2 ·°C 8.0682.758-1.986 0.03 W/m 2 ·°C 5.9812.045-1.489 0.046 W/m 2 ·°C 8.7592.995-2.148 Heat Flux- SimulationJanuaryAprilJuly 0.042 W/m 2 ·°C 8.08842.7731-1.9886 0.03 W/m 2 ·°C 5.98162.0508-1.4877 0.046 W/m 2 ·°C 8.75923.003-2.1457 Error (%)JanuaryAprilJuly 0.042 W/m 2 ·°C 0.25%0.55%0.13% 0.03 W/m 2 ·°C 0.01%0.28%-0.09% 0.046 W/m 2 ·°C 0.00%0.27%-0.11%

38. House Model: Overview  Next Step: Move from a small section of wall or attic to a full wall or ceiling.  Each section of wall was simulated separately and then the heat flux of all were added together.

39. House Model: Layout

42. House Model: FE Analysis  Here are the results for the heat flux traveling through each wall of the house model. Heat Flux (W) 0.042 W/m 2 ·ºC for January 0.042 W/m 2 ·ºC for April 0.042 W/m 2 ·ºC for July Back Wall329.03110.04-80.303 Front Wall276.6493.284-68.72 Left Wall489164.81-121.35 Right Wall484.78163.55-120.32 Ceiling852.16292.7-210 Heat Flux Total2431.61824.384-600.693

43. House Model: FEA Simulation Right and Left Walls

44. House Model: FEA Simulation  Front Wall

45. Quantitative Results  Insulation Type (30%)  Duct Thickness (36% compared to 20%)  Stud Sizing (~30%)

47. Future Work  Determine thermal conductivities for each insulation  Find quantitative difference of heat flux for different insulation choices  Compare cost difference between insulations with energy savings or loses

51. References  Heat and Mass Transfer (Cengel; McGraw-Hill)  www.engineeringtoolbox.com www.engineeringtoolbox.com  www.matweb.com www.matweb.com  www.energysavers.com www.energysavers.com  Engineering Analysis with SolidWorks Simulation 2010 (Kurowski; SDC Publications)  http://www.ornl.gov/sci/roofs+walls/insulation/ins_01.html http://www.ornl.gov/sci/roofs+walls/insulation/ins_01.html  http://www.jameshardie.com/ http://www.jameshardie.com/  www.lowes.com www.lowes.com  Habitat for Humanity