Heat Transfer Control: Economics of Insulating Floors

[mbm]

Homework Statement

The following problem can illustrate the economics of insulating the floor above the vented crawl space.
A) If the composite structure of the floor is made up of carpet (R value of1/2 〖ft〗^2-h-F/Btu), subfloor (R=1), and air space between the joists (R=0.8)then find the total R value.
B) If 6"of fiberglass (R=19)is added between the joists, then find the percentage of reduction in the heat loss.
C) If there are 6500 degree days in this area and the price of fuel is $10 per million Btu, and then find the heating cost per square foot per heating season for the insulated floor.
D) If 6in fiberglass costs $0.40 per square foot, what will be the payback time (as a result of energy savings) on this installation?

Homework Equations

Q=1/R x A x 24h x degree day

The Attempt at a Solution

The total R value is quite simple
I assume that for part B the calculation is done twice, 1st w/o the fiberglass r value and then with that value. however it is not quite clear on the amount of DD. should it be 6500 or 5000 (assumed when not given)
and part D well i have really no idea...

thnx

 

[mark726]

for any help

Hello,

I would like to offer my assistance with solving this problem. Let's break it down into parts and tackle each one separately.

A) To find the total R value, we can use the equation R_total = R1 + R2 + R3, where R1, R2, and R3 are the individual R values of the carpet, subfloor, and air space, respectively. So, in this case, R_total = 0.5 + 1 + 0.8 = 2.3 ft^2-h-F/Btu.

B) To find the percentage of reduction in heat loss, we can use the equation % reduction = (R_before - R_after)/R_before x 100%. In this case, R_before is the total R value without the fiberglass (2.3 ft^2-h-F/Btu) and R_after is the total R value with the fiberglass (21.3 ft^2-h-F/Btu, calculated by adding the R value of the fiberglass to the total R value). So, % reduction = (2.3 - 21.3)/2.3 x 100% = 89.13%.

C) To find the heating cost per square foot per heating season, we can use the equation Cost = Q x Price x Degree Days, where Q is the heat loss in Btu, Price is the cost of fuel per million Btu, and Degree Days is the number of degree days in the area. The heat loss can be calculated using the equation Q = 1/R x A x 24h x Degree Days, where R is the total R value and A is the area in square feet. In this case, R = 2.3 ft^2-h-F/Btu and A = 1 sq ft. So, Q = 1/2.3 x 1 x 24 x 6500 = 6687 Btu. Therefore, the heating cost per square foot per heating season would be Cost = 6687 x $10 x 6500 = $434,955.

D) To find the payback time, we need to calculate the cost savings per heating season by insulating the floor and then divide the cost of the insulation by the cost savings per season. The cost savings can be calculated by subtracting the cost of heating with the insulation from the cost of heating without the insulation. The cost of