By: Matthew Irvine and Cristina Belew

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

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

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

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

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)

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

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 – ºC April – ºC July ºC  Desired inside temperature ºC Drywall Insulation Plywood Air Pocket Hardiboard

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Heat Flux (W- simulation) JanuaryAprilJuly W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Error (%)JanuaryAprilJuly W/m 2 ·°C0.84%0.63%0.91% 0.03 W/m 2 ·°C0.76%0.79%1.11% W/m 2 ·°C0.73%0.50%0.78%

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

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

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

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Heat Flux (W- simulation) JanuaryAprilJuly W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Error (%)JanuaryAprilJuly W/m 2 ·°C0.61%0.80%0.51% 0.03 W/m 2 ·°C0.47%0.69%0.38% W/m 2 ·°C0.65%0.85%0.55%

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

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

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

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.

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

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Studs

3 Sections of Wall with 2 x 4 Studs: Heat Flux Comparisons Heat Flux (W-simulation) W/m 2 ·°C0.03 W/m 2 ·°C0.046 W/m 2 ·°C January April July Heat Flux (W-Theoretical) W/m 2 ·°C0.03 W/m 2 ·°C0.046 W/m 2 ·°C January April July 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%

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

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

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

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

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 inch E inch

Duct Insulation: Heat Flux Heat Flux- SimulationJanuaryAprilJuly 2 inch inch inch Heat Flux- TheoreticalJanuaryAprilJuly 2 inch inch inch 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%

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

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 ºC

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

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

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 W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C

Attic Insulation: Heat Flux Heat Flux- TheoreticalJanuaryAprilJuly W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Heat Flux- SimulationJanuaryAprilJuly W/m 2 ·°C W/m 2 ·°C W/m 2 ·°C Error (%)JanuaryAprilJuly W/m 2 ·°C 0.25%0.55%0.13% 0.03 W/m 2 ·°C 0.01%0.28%-0.09% W/m 2 ·°C 0.00%0.27%-0.11%

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.

House Model: Layout

House Model: FE Analysis  Here are the results for the heat flux traveling through each wall of the house model. Heat Flux (W) W/m 2 ·ºC for January W/m 2 ·ºC for April W/m 2 ·ºC for July Back Wall Front Wall Left Wall Right Wall Ceiling Heat Flux Total

House Model: FEA Simulation Right and Left Walls

House Model: FEA Simulation  Front Wall

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

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

References  Heat and Mass Transfer (Cengel; McGraw-Hill)     Engineering Analysis with SolidWorks Simulation 2010 (Kurowski; SDC Publications)     Habitat for Humanity