Presented by:Mike MeadersAshok Tamang

Objective: To find if we can save energy used in heating and money by using energy efficient windowsProcess: Assumptions Analysis Calculations Result

Our Assumptions

Assumptions: Window dimension:

1 m * 1m Inside air:

Ti = 72 0F = 22.2 0C = 295K Tsi = 15 0C

For air @ Tf: K = 0.0259 W/m.k v = 15.44 * 10^-6 alpha = 21.8 * 10^-6 Pr = 0.708

Other Assumptions: Outside Air:

Winter: Salt Lake City To average = 0 0C = 273K (www.weatherchannel.com) Tso = 7 0C

For air @ Tf: K = 24.1 * 10^-3

W/m.k v = 13.49 * 10^-6 alpha = 18.9 * 10^-6 Pr = 0.714 Tsi = 15 0C

Figurative Analysis

R total = 1/ [(2/R1) + (2/R2-6) + (1/R7-9)]

Ra Lo1 = 1704.8Nu Lo1 (avg) = 3.7898h o1 (avg) = 7.611

 Ra Li1 = 1229.2Nu Li1 (avg) = 3.559h i1 (avg) = 7.682

R1 = 5.5154 + 0.4061/K frame

Ra Lo,2-6 = 26.638 Nu Lo,2-6 (avg) = 1.921 h o,2-6 (avg) = 15.43 Ra Li,2-6 = 19.206 Nu Li ,2-6(avg) = 1.838 h I,2-6 (avg) = 15.87 R2-6 = 10.925 + (0.8547/k frame) + (0.6838/K

pane) + (0.5128/K spacer)

Ra Lo,7-9 = 0.9004 * 10^9 Nu Lo ,7-9(avg) = 119.04 h o,7-9 (avg) = 2.958 Ra Li ,7-9= 705.83 * 10^6 Nu Li,7-9 (avg) = 110.32 h i ,7-9(avg) = 2.946 R 7-9 = 0.7197 + (0.0085/K pane) +

(0.0064/K glass)

Calculations

Derivation of Formula to calculate the heat transfer through the entire window structure

q = [T i(infinity) – T o(infinity) ]/R total

R total = 1/ [(2/R1) + (2/R2-6) + (1/R7-

9)]

K0.0064

K0.0085 0.7197

22.2

K0.5128

K0.6838

K0.8547 10.925

44.4

K0.4061 5.5154

4.44

gaspanespacerPaneframeframe

q

K

0.0064 K

0.0085 0.7197

22.2

K0.5128

K0.6838

K0.8547 10.925

44.4

K0.4061 5.5154

4.44

gaspanespacerPaneframeframe

q

K0.0064

K0.0085 0.7197

22.2

K0.5128

K0.6838

K0.8547 10.925

44.4

K0.4061 5.5154

4.44

gaspanespacerPaneframeframe

q

K

0.0064 K

0.0085 0.7197

22.2

K0.5128

K0.6838

K0.8547 10.925

44.4

K0.4061 5.5154

4.44

gaspanespacerPaneframeframe

q

Results

Using the derived equation for heat loss, we simply need to plug in the thermal conductivity of various materials to compare their effectiveness. There is surprisingly little innovation currently being done to the actual glass pane in producing windows that insulate better. However there is much being done concerning solar radiation admittance. But this is beyond the scope of this project. Thus in these calculations, we will leave the pane material constant at soda lime glass (k= 1.4 W/mK). We will then vary other common materials for the three key points of energy efficient window construction.

Results

Cheapest Window causes average heat loss: q = 34.55 W

Window with all the best features causes average heat loss: q = 22.19 W

The average difference = 12.36 W

ResultsWith some assumptions, we can calculate the average heating costs involved with each type of

window.Assumptions: Subject House has 25 m² of windows throughout the house in 1m x 1m segments

with frames in betweenHeat loss is only through windowsNatural Gas costs in Salt Lake City = $1.007/therm

 Energy Balance: Ein = Eout Qin = 25*q*(24 hrs.)Cost = rate*QinCost = rate*25*q*(86400 s) For Cheapest Windows:Cost = ($1.007/therm) *25*(34.55 W)*(86400 s)*( therm/105,480,400 joules) Average Cost = .71¢/ winter day For Best Insulating Windows:Cost = ($1.007/therm) *25*(22.19 W)*(86400 s)*( therm/105,480,400 joules) Average Cost = .25¢/ winter dayThus, on average, and with very rough estimates, energy efficient windows could save a

homeowner .46¢ per day in mid-winter. This could add up to roughly $37 saved per winter in heating costs. With only these rough figures, it does not seem likely that energy efficient windows could “pay for themselves” as is often advertised by contractors. Even when considering the possible $1500 tax credit for energy window replacement, and additional savings in summer for cooling. Purchasing and installation costs most likely surpass these savings.