INSULATION STUDIESBy: Matthew Irvine and Cristina Belew

Introduction

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 Information

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

SUMMARY OF RESULTS

2 x 4 Stud, 1 x 1 m2 Section: Overview Equation for heat flux

Q = (T2 – T1)/Rtotal

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

2 x 4 Stud, 1 x 1 m2 Section: R-values R of Convection – 1/h*A

h- convection coefficient (W/m·°C) A- area of convection (m2)

R of a certain material – L/k*A k- thermal conductivity L- thickness of material (m) A- area of material (m2)

Rtotal = Routside,convection + Rdrywall + Rinsulation + Rhariboard + Rair pocket + Rsiding + Rinside,convection

R (W/m·°C)

Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rinsulation Rdrywall Rair pocketR-Total January

R-Total April

R-Total July

0.042 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 2.12 0.0713 0.156 2.636 2.642 2.651

0.03 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 2.96 0.0713 0.156 3.483 3.489 3.497

0.046 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 1.93 0.0713 0.156 2.452 2.458 2.467

2 x 4 Stud, 1 x 1 m2 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) January April July

0.042 W/m2·°C 7.367 2.513 -1.886

0.03 W/m2·°C 5.577 1.904 -1.430

0.046 W/m2·°C 7.9200 2.701 -2.027

Heat Flux (W- simulation) January April July

0.042 W/m2·°C 7.4297 2.5393 -1.8999

0.03 W/m2·°C 5.6123 1.9192 -1.4372

0.046 W/m2·°C 7.9925 2.7312 -2.0429

Error (%) January April July

0.042 W/m2·°C 0.84% 0.63% 0.91%

0.03 W/m2·°C 0.76% 0.79% 1.11%0.046 W/m2·°C 0.73% 0.50% 0.78%

2 x 4 Stud, 1 x 1 m2 Section: FEA (January)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

2 x 4 Stud, 1 x 1 m2 Section: FEA (April)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

2 x 4 Stud, 1 x 1 m2 Section: FEA (July)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

2 x 6 Stud, 1 x 1 m2 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) Ri Rjanuary RApril Rjuly Rhardiboard Rplywood Rinsulation Rdrywall Rair pocket

R-Total January

R-Total April

R-Total July

0.042 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 3.33 0.0713 0.156 3.846 3.852 3.860

0.03 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 4.66 0.0713 0.156 3.483 3.489 3.497

0.046 W/m2·°C 0.100 0.0294 0.0353 0.0441 0.0567 0.106 3.04 0.0713 0.156 2.452 2.458 2.467

2 x 6 Stud, 1 x 1 m2 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) January April July

0.042 W/m2·°C 7.367 2.520 -1.8860.03 W/m2·°C 5.577 1.904 -1.430

0.046 W/m2·°C 7.920 2.701 -2.027

Heat Flux (W- simulation) January April July

0.042 W/m2·°C 7.4297 2.5393 -1.89990.03 W/m2·°C 5.6123 1.9192 -1.4372

0.046 W/m2·°C 7.9925 2.7312 -2.0429

Error (%) January April July

0.042 W/m2·°C 0.61% 0.80% 0.51%

0.03 W/m2·°C 0.47% 0.69% 0.38%0.046 W/m2·°C 0.65% 0.85% 0.55%

2 x 6 Stud, 1 x 1 m2 Section: FEA (January)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

2 x 6 Stud, 1 x 1 m2 Section: FEA (April)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

2 x 6 Stud, 1 x 1 m2 Section: FEA (July)

0.042 W/m2·ºC 0.03 W/m2·ºC 0.046 W/m2·ºC

Conclusions from Theoretical and SolidWorks Studies of 1 x 1 m2 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

Ri RJanuary RApril RJuly Rhardiboard Rplywood Rinsulation Rdrywall Rstuds1/R-Total January

1/R-Total April

1/R-Total July

0.042 W/m2·°C 0.038 0.0113 0.0136 0.0170 0.0649 0.041 0.81 0.0275 1.002 0.9833 0.9966

0.03 W/m2·°C 0.038 0.0133 0.0136 0.0170 0.0649 0.041 1.14 0.0275 0.7545 0.7543 0.7524

0.046 W/m2·°C 0.038 0.0133 0.0136 0.0170 0.0649 0.041 0.74 0.0275 1.077 1.076 1.073

Studs 0.2764 0.0813 0.0975 0.1218 0.4663 0.2925 0.1972 1.7551 0.3259 0.3241 0.3216

𝑅𝑠𝑡𝑢𝑑𝑠 = 1ℎ𝑜𝑢𝑡𝑠𝑖𝑑𝑒 ∗𝐴𝑠𝑡𝑢𝑑𝑠 + 𝐿𝑑𝑟𝑦𝑤𝑎𝑙𝑙𝑘𝑑𝑟𝑦𝑤𝑎𝑙𝑙 ∗𝐴𝑑𝑟𝑦𝑤𝑎𝑙𝑙 ,𝑠𝑡𝑢𝑑𝑠 + 𝐿𝑝𝑙𝑦𝑤𝑜𝑜𝑑𝑘𝑝𝑙𝑦𝑤𝑜𝑜𝑑 ∗𝐴𝑝𝑙𝑦𝑤𝑜𝑜𝑑 ,𝑠𝑡𝑢𝑑𝑠 + 𝐿ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑𝑘ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑 ∗𝐴ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑 ,𝑠𝑡𝑢𝑑𝑠 + 𝐿𝑠𝑡𝑢𝑑𝑠𝑘𝑠𝑡𝑢𝑑𝑠 ∗𝐴𝑠𝑡𝑢𝑑𝑠 + 1ℎ𝑖𝑛𝑠𝑖𝑑𝑒 ∗𝐴𝑠𝑡𝑢𝑑𝑠

𝑅𝑖𝑛𝑠 = 1ℎ𝑜𝑢𝑡𝑠𝑖𝑑𝑒 ∗𝐴𝑖𝑛𝑠 + 𝐿𝑑𝑟𝑦𝑤𝑎𝑙𝑙𝑘𝑑𝑟𝑦𝑤𝑎𝑙𝑙 ∗𝐴𝑑𝑟𝑦𝑤𝑎𝑙𝑙 ,𝑖𝑛𝑠 + 𝐿𝑝𝑙𝑦𝑤𝑜𝑜𝑑𝑘𝑝𝑙𝑦𝑤𝑜𝑜𝑑 ∗𝐴𝑝𝑙𝑦𝑤𝑜𝑜𝑑 ,𝑖𝑛𝑠 + 𝐿ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑𝑘ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑 ∗𝐴ℎ𝑎𝑟𝑑𝑖𝑏𝑜𝑎𝑟𝑑 ,𝑖𝑛𝑠 + 𝐿𝑖𝑛𝑠𝑘𝑠𝑡𝑢𝑑𝑠 ∗𝐴𝑖𝑛𝑠 + 1ℎ𝑖𝑛𝑠𝑖𝑑𝑒 ∗𝐴𝑖𝑛𝑠

3 Sections of Wall with 2 x 4 Studs: Heat Flux Comparisons

Heat Flux (W-simulation) 0.042 W/m2·°C 0.03 W/m2·°C 0.046 W/m2·°C

January 25.79 20.98 27.24

April 8.680 7.161 9.300

July -6.590 -5.370 -6.971

Heat Flux (W-Theoretical) 0.042 W/m2·°C 0.03 W/m2·°C 0.046 W/m2·°C

January 25.85 21.57 27.57

April 8.880 7.414 9.414

July -6.685 -5.585 -7.138

Error (%) 0.042 W/m2·°C 0.03 W/m2·°C 0.046 W/m2·°CJanuary 0.21% 2.73% 1.20%

April 2.25% 3.41% 1.21%

July 1.43% 3.85% 2.34%

𝑄= ሺ𝑇𝑜𝑢𝑡𝑠𝑖𝑑𝑒 − 𝑇𝑖𝑛𝑠𝑖𝑑𝑒ሻ∗( 1𝑅𝑠𝑡𝑢𝑑𝑠 + 1𝑅𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 )

3 Sections of Wall with 2 x 4 Studs: FEA (January)

0.046 W/m2·ºC 0.03 W/m2·ºC 0.042 W/m2·ºC

3 Sections of Wall with 2 x 4 Studs: FEA (April)

0.046 W/m2·ºC 0.03 W/m2·ºC 0.042 W/m2·ºC

3 Sections of Wall with 2 x 4 Studs: FEA (July)

0.046 W/m2·ºC 0.03 W/m2·ºC 0.042 W/m2·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 Rconvection, inside Raluminum Rfiberglass Rreflective barrier Rouside,convection

2 inch 0.1371 0.0007076 3.529 0.00002453 0.1523

4 inch 0.1371 0.0007076 5.714312 1.69064E-05 0.1054695

6 inch 0.1371 0.0007076 7.298 0.00001219 0.08072

𝑹𝒕𝒐𝒕𝒂𝒍 = 𝟏𝒉𝒂𝒊𝒓 𝒇𝒍𝒐𝒘∗𝒂+ 𝐥𝐧൬𝒓𝒂𝒍𝒖𝒎𝒊𝒏𝒖𝒎𝒓𝒂𝒊𝒓 𝒇𝒍𝒐𝒘 ൰𝟐𝝅∗𝒌𝒂𝒍𝒖𝒎𝒊𝒏𝒖𝒎 ∗𝑳+ 𝐥𝐧ቀ𝒓𝒇𝒊𝒃𝒆𝒓𝒈𝒍𝒂𝒔𝒔𝒓𝒂𝒍𝒖𝒎𝒊𝒏𝒖𝒎ቁ𝟐𝝅∗𝒌𝒇𝒊𝒃𝒆𝒓𝒈𝒍𝒂𝒔𝒔 ∗𝑳+ 𝐥𝐧൬𝒓𝒓𝒆𝒇𝒍𝒆𝒄𝒕𝒊𝒗𝒆 𝒃𝒂𝒓𝒓𝒊𝒆𝒓𝒓𝒇𝒊𝒃𝒆𝒓𝒈𝒍𝒂𝒔𝒔 ൰𝟐𝝅∗𝒌𝒓𝒆𝒇𝒍𝒆𝒄𝒕𝒊𝒗𝒆 𝒃𝒂𝒓𝒓𝒆𝒓 ∗𝑳+ 𝟏𝒉𝒂𝒕𝒕𝒊𝒄 𝒂𝒊𝒓 ∗𝒂

Duct Insulation: Heat Flux

Heat Flux- Simulation January April July

2 inch 5.074 1.735 1.3057

4 inch 3.3025 1.1323 0.8393

6 inch 2.584 0.883 0.6652

Heat Flux- Theoretical January April July

2 inch 5.090 1.744 1.304

4 inch 3.260 1.115 0.8492

6 inch 2.6202 0.89835 0.67376

Error (%) January April July

2 inch -0.31% -0.52% 0.13%

4 inch 1.30% 1.55% -1.17%

6 inch -1.38% -1.71% -1.27%

𝑄= 𝑇𝑜𝑢𝑠𝑡𝑖𝑑𝑒 − 𝑇𝑖𝑛𝑠𝑖𝑑𝑒𝑅𝑡𝑜𝑡𝑎𝑙

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 inches 6 inches

Duct Insulation: FEA Simulation (April)

6 inches 4 inches

2 inches

April Analysis:Temperature flow through the center at 22.2 ºC and surrounding temperature at 15.56 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 inches 6 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 Rinside Rjanuary Rapril RJuly Rinsulation RdrywallR- Total January

R- Total April R-Total July

0.042 W/m2·°C 0.108 0.108 0.108 0.163 2.12 0.0713 2.407 2.407 2.518

0.03 W/m2·°C 0.108 0.108 0.108 0.163 2.96 0.0713 3.247 3.247 3.358

0.046 W/m2·°C 0.108 0.108 0.108 0.163 1.93 0.0713 2.217 2.217 2.328

𝑅𝑡𝑜𝑡𝑎𝑙 = 1ℎ𝑖𝑛𝑠𝑖𝑑𝑒 ∗𝐴+ 𝐿𝑑𝑟𝑦𝑤𝑎𝑙𝑙𝑘𝑑𝑟𝑦𝑤𝑎𝑙𝑙 ∗𝐴𝑑𝑟𝑦𝑤𝑎𝑙𝑙 + 𝐿𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑘𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ∗𝐴+ 1ℎ𝑎𝑡𝑡𝑖𝑐 ∗𝐴

Attic Insulation: Heat Flux

Heat Flux- Theoretical January April July

0.042 W/m2·°C 8.068 2.758 -1.986

0.03 W/m2·°C 5.981 2.045 -1.489

0.046 W/m2·°C 8.759 2.995 -2.148

Heat Flux- Simulation January April July

0.042 W/m2·°C 8.0884 2.7731 -1.9886

0.03 W/m2·°C 5.9816 2.0508 -1.4877

0.046 W/m2·°C 8.7592 3.003 -2.1457

Error (%) January April July

0.042 W/m2·°C 0.25% 0.55% 0.13%

0.03 W/m2·°C 0.01% 0.28% -0.09%

0.046 W/m2·°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: Layout

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) 0.042 W/m2·ºC for January

0.042 W/m2·ºC for April

0.042 W/m2·ºC for July

Back Wall 329.03 110.04 -80.303

Front Wall 276.64 93.284 -68.72

Left Wall 489 164.81 -121.35

Right Wall 484.78 163.55 -120.32

Ceiling 852.16 292.7 -210

Heat Flux Total 2431.61 824.384 -600.693

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

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

Result Details

Values (W/m^2*C) hi hjanuary hapril hjuly khardiboard kplywood kcellulose kdrywall kair pocket kfiberglass kmineral wool

10 34 28.35 22.7 0.14 0.12 0.042 0.178 0.026 0.03 0.046Hardiboard Plywood Insulation Drywall Air Pocket

Thickness (2x4) (m) 0.0079375 0.0127 0.0889 0.0127 0.004064 Temperature (Celcius) January April JulyThickness (2x6) (m) 0.0079375 0.0127 0.1397 0.0127 0.004064 Outside 2.778 15.56 27.2

Inside 22.2 22.2 22.2l/ka

Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rcellulose Rdrywall Rair pocket R-Total for January R-Total for April R-Total for JulyR-Values 0.100 0.0294 0.0353 0.0441 0.0567 0.106 2.12 0.0713 0.156 2.636 2.642 2.651

Heat Flux (W) 7.367 2.513 -1.886Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rcellulose Rdrywall Rair pocket R-Total R-Total for April R-Total for July

R-Values 0.100 0.0294 0.0353 0.0441 0.0567 0.106 3.33 0.0713 0.156 3.846 3.852 3.860Heat Flux (W) 5.050 1.724 -1.295

Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rfiberglass Rdrywall Rair pocket R-Total for January R-Total for April R-Total for JulyR-Values 0.100 0.0294 0.0353 0.0441 0.0567 0.106 2.96 0.0713 0.156 3.483 3.489 3.497

Heat Flux (W) 5.577 1.903 -1.430Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rfiberglass Rdrywall Rair pocket R-Total for January R-Total for April R-Total for July

R-Values 0.100 0.0294 0.0353 0.0441 0.0567 0.106 4.66 0.0713 0.156 5.176 5.182 5.191Heat Flux (W) 3.752 1.281 -0.963

Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rmineral wool Rdrywall Rair pocket R-Total for January R-Total for April R-Total for JulyR-Values 0.1 0.0294 0.0353 0.0441 0.0567 0.106 1.93 0.0713 0.156 2.452 2.458 2.467

Heat Flux (W) 7.921 2.701 -2.027R-Values Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rmineral wool Rdrywall Rair pocket R-Total for January R-Total for April R-Total for July

0.1 0.0294 0.0353 0.0441 0.0567 0.106 3.04 0.0713 0.156 3.556 3.562 3.571Heat Flux (W) 5.461 1.864 -1.400

Thickness (attic-m) Insulation Drywall0.0889 0.0127

Ri Rjanuary Rapril Rjuly Rcellulose Rdrywall R- Total January R- Total April R-Total JulyR-Values 0.108 0.108 0.108 0.163 2.12 0.0713 2.407 2.407 2.518R-Values Ri (july) 0.163 Heat Flux (W) 8.068 2.758 -1.986

Ri Rjanuary Rapril Rjuly Rfiberglass Rdrywall R- Total January R- Total April R-Total JulyR-Values 0.108 0.108 0.108 0.163 2.96 0.0713 3.247 3.247 3.358R-Values Ri (july) 0.163 Heat Flux (W) 5.981 2.045 -1.489

Ri Rjanuary Rapril Rjuly Rmineral wool Rdrywall R- Total January R- Total April R-Total JulyR-Values 0.108 0.108 0.108 0.163 1.93 0.0713 2.217 2.217 2.328R-Values Ri (july) 0.163 Heat Flux (W) 8.759 2.995 -2.148

Values (W/m^2*C) hi hjanuary hapril hjuly khardiboard kplywood kcellulose kdrywall kfiberglass kmineral wool R (2x4) R(2x6)10 34 28.35 22.7 0.14 0.12 0.042 0.178 0.03 0.046 0.14 0.98

L Hardiboard Plywood Insulation Drywall Stud Area Hardiboard Plywood Insulation Drywall StudsThickness (2x4) (m) 0.02362 0.0127 0.0889 0.0127 0.0889 Thickness (2x4) (m2) 2.5977 2.5977 2.5977 2.5977

0.3618 0.3618 0.3618 0.3618Thickness (2x6) (m) 0.02362 0.0127 0.1397 0.0127 0.1397 Thickness (2x6) (m2)

Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rcellulose Rdrywall Rstuds R-Total for January R-Total for April R-Total for JulyR-Values (ins) 0.038 0.0113 0.0136 0.0170 0.0649 0.041 0.81 0.0275 1.002 0.9833 0.9966R-Values (studs) 0.2764 0.0813 0.0975 0.1218 0.4663 0.2925 0.1972 1.7551 0.3259 0.3241 0.3216

Heat Flux (W) 25.79 8.68 -6.591Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rcellulose Rdrywall Rstuds R-Total for January R-Total for April R-Total for July

R-Values (ins)R-Values (studs)

Heat Flux (W)Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rfiberglass Rdrywall Rstuds R-Total for January R-Total for April R-Total for July

R-Values (ins) 0.038 0.0133 0.0136 0.0170 0.0649 0.041 1.14 0.0275 0.7545 0.7543 0.7524R-Values (studs) 0.2764 0.0813 0.0975 0.1218 0.4663 0.2925 0.1972 1.7551 0.3259 0.3241 0.3216

Heat Flux (W) 20.98 7.161 -5.370Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rfiberglass Rdrywall Rstuds R-Total for January R-Total for April R-Total for July

R-Values (ins)R-Values (studs)

Heat Flux (W)Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rmineral wool Rdrywall Rstuds R-Total for January R-Total for April R-Total for July

R-Values (ins) 0.038 0.0133 0.0136 0.0170 0.0649 0.041 0.74 0.0275 1.077 1.076 1.073R-Values (studs) 0.2764 0.0813 0.0975 0.1218 0.4663 0.2925 0.1972 1.7551 0.326 0.324 0.322

Heat Flux (W) 27.24 9.300 -6.971Ri Rjanuary Rapril Rjuly Rhardiboard Rplywood Rmineral wool Rdrywall Rstuds R-Total for January R-Total for April R-Total for July

R-Values (ins)R-Values (studs)

Heat Flux (W)

Radius (meter) Air Core Steel Duct Insulation Reflective Barrier hi ho,jan ho,april ho,july ksteel kfiberglass kreflective barrier

0.0508 0.0605 0.111125 0.1143 25 10 10 10 43 0.03 200Length 0.914

Rconv Rsteel Rfiber Rreflective Rconv,o Rtotal Temperature Tinside Tjanuary Tapril Tjuly

0.1371 0.0007076 3.529 0.00002453 0.1523 3.819 22.22 2.778 15.56 27.2

Heat Flux (W) January April July5.090 1.744 -1.304

Radius (meter) Air Core Steel Duct Insulation Reflective Barrier hi ho,jan ho,april ho,july ksteel kfiberglass kreflective barrier

0.0508 0.0605 0.161925 0.1651 25 10 10 10 43 0.03 200Length 0.914

Rconv Rsteel Rfiber Rreflective Rconv,o Rtotal

0.1371 0.0007076 5.714312 1.69064E-05 0.1054695 5.957605963

Heat Flux (W) January April July3.260 1.115 -0.8393

Radius (meter) Air Core Steel Duct Insulation Reflective Barrier hi ho,jan ho,april ho,july ksteel kfiberglass kreflective barrier

0.0508 0.0605 0.212725 0.215725 25 10 10 10 43 0.03 200Length 0.914

Rconv Rsteel Rfiber Rreflective Rconv,o Rtotal

0.1371 0.0007076 7.298 0.00001219 0.08072 7.517

Heat Flux (W) January April July2.584 0.883 -0.6652

Duct Insulation Calculation

2 inch Insulation (Fiberglass)

4 inch Insulation (Fiberglass)

6 inch Insulation (Fiberglass)

2 x 6 Theoretical Calculations Mineral Wool

Attic Insulation Calculation Fiberglass

Attic Insulation Calculation Mineral Wool

2 x 4 Theoretical Calculations Mineral Wool

2 x 4 Theoretical Calculations Cellulose

2 x 6 Theoretical Calculations Cellulose

2 x 4 Theoretical Calculations Fiberglass

2 x 6 Theoretical Calculations Fiberglass

2 x 4 Theoretical Calculations Cellulose

2 x 6 Theoretical Calculations Cellulose

2 x 4 Theoretical Calculations Fiberglass

2 x 4 Theoretical Calculations Mineral Wool

2 x 6 Theoretical Calculations Fiberglass

Attic Insulation Calculation Cellulose

2 x 6 Theoretical Calculations Mineral Wool

ftXft study (4") Outside Temperature Indoor Temperature Inside Convection Outside Convection Cellulose (.042W/°C·m2) Fiberglass (.03W/°C·m2) Mineral Wool (.046 W/°C·m2)

January 37 72 8.333 34 7.4297 5.6123 7.9925April 60 72 8.333 28.35 2.5393 1.9192 2.7312July 81 72 8.333 22.7 -1.8999 -1.4372 -2.0429

Theoretical: 7.367 5.577 7.922.52 1.904 2.701

-1.886 -1.43 -2.027

% Difference: 0.84% 0.63% 0.91%0.76% 0.79% 1.11%0.73% 0.50% 0.78%

ftXft study (6") Outside Temperature Indoor Temperature Inside Convection Outside Convection Cellulose (.042W/°C·m2) Fiberglass (.03W/°C·m2) Mineral Wool (.046 W/°C·m2)January 37 72 8.333 34 5.0809 3.7696 5.4967

April 60 72 8.333 28.35 1.7378 1.2898 1.8798July 81 72 8.333 22.7 -1.3016 -0.96665 -1.4077

Theoretical 5.05 3.752 5.4611.724 1.281 1.864

-1.295 -0.963 -1.4

% difference 0.61% 0.47% 0.65%0.80% 0.69% 0.85%0.51% 0.38% 0.55%

ftXft study (attic) Outside Temperature Indoor Temperature Upper Convection Lower Convection Cellulose (.042W/°C·m2) Fiberglass (.03W/°C·m2) Mineral Wool (.046 W/°C·m2) Theo Theo TheoJanuary 37 72 9.26 9.26 8.0884 5.9816 8.7592 8.068 5.981 8.759

April 60 72 9.26 9.26 2.7731 2.0508 3.003 2.758 2.045 2.995July 81 72 6.13 6.13 -1.9886 -1.4877 -2.1457 -1.986 -1.489 -2.148

% Error 0.25% 0.01% 0.00%0.55% 0.28% 0.27%

Wall Section (2x4) Outside Temperature(F) Indoor Temperature(F) Cellulose (.042W/°C·m2) Fiberglass (.03W/°C·m2) Mineral Wool (.046 W/°C·m2) 0.13% -0.09% -0.11%January 37 72 25.79 20.98 27.24

April 60 72 8.680 7.161 9.300July 81 72 -6.590 -5.370 -6.971

Theoretical: 25.85 21.57 27.578.880 7.414 9.414

-6.685 -5.585 -7.138

% Difference: -0.21% -2.73% -1.20%-2.25% -3.41% -1.21%-1.43% -3.85% -2.34%

Duct Insulation (Fiberglass) 2 in Fiberglass 4 in Fiberglass 6 in FiberglassJanuary 5.074 3.3025 2.584

April 1.735 1.1323 0.883July 1.3057 0.8393 0.6652

Theoretical 5.090 3.260 2.62021.744 1.115 0.898351.304 0.8492 0.67376

% Difference -0.31% 1.30% -1.38%-0.52% 1.55% -1.71%0.13% -1.17% -1.27%

Wall Simulations Cellulose for January Cellulose for April Cellulose for JulyBack Wall 329.03 110.04 -80.303Front Wall 276.64 93.284 -68.72Left Wall 489 164.81 -121.35Right Wall 484.78 163.55 -120.32Ceiling 852.16 292.7 -210Heat Flux Total 2431.61 824.384 -600.693

References Heat and Mass Transfer (Cengel; McGraw-Hill) www.engineeringtoolbox.com www.matweb.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.jameshardie.com/ www.lowes.com Habitat for Humanity