question about heat flow?

Question

Consider a 2.35 m by 10.0 m housing wall, with a section shown in the diagram.
A builder has the choice of using 1.5 in. by 3.5 in. studs (at $2.30 each; R=4),
or 1.5 in. by 5.5 in. studs (at $4.45 each; R=7). The studs are spaced with a center-to-center distance of 40 cm.
The thinner wall can accommodate R=12 insulation (at $3.30 per m2), whereas the thicker wall can accommodate R=38 insulation (at $6.25 per m2).
Assume that the house is to be built in an area where the average difference between the inside and the outside temperature is 12.0 °C. If the cost of heating is $0.10 per kWh, how long will it take for the homeowner to recoup the extra costs associated with building the better insulated wall? (Enter the number of days.)

Answer 1

The rate of heat transfer across an area through an R factor is

=A(tH-Tc)/R

Since there is no diagram, I will assume there are 25 studs.

The metric dimension of a stud edge is
.0381 m

since there are 25 of them, the wood area is
.9525 * 2.35
2.238 m^2

The balance of the area is insulation

=20.35-2.238
=18 m^2

The transfer of heat will be

12*(2.238/Rwood+18/Rinsulation)

for 2x4 studs (1.5 x 3.5)

=12*(2.238/4+18/12)
=24.714 W

for 2x6 studs (1.5 x 5.5)

=12*(2.238/7+18/38)

=9.5 W

(Note: I know from experience that the actual R factor in a 2x6 nominal wall is R18, not R 38. The conduction through this wall should be 16 W


The cost of the 2x4 wall is
=25*2.3+18*3.3
=$117

The cost of the 2x6 wall is
=25*4.45+18*6.25
=$224

the difference therefore is $107
at .10 per kw hour
$117 is
1,117 kw hours

Every day the difference in kw hours

(24-9.5)*24/1000

.348 kw hours per day
3,209.8 days

8.8 years

(the reality is 15 years if R18 is used as the R factor)

j

Answer 2

about two years it was calculated, by owens-corning. the maker of insulation; factual answer. it'll take longer just to do the math. I am really amazed at how people have to complicate a simple answer.Duuuuhhhhh.....