Solving Heat Loss Rate through R-19 Layer and Brick Wall

  • Thread starter yossup
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In summary: Yes the units can go either British or SI. And British is probably the easier way to go, meaning only his value for brick need to be converted.In summary, the wall loses 10 degrees F of heat over a 10 degree difference, which is .84 W/m2 or 4.54 Btu/hr.
  • #1
yossup
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Homework Statement



Suppose the insulating qualities of the wall of a house come mainly from a 4.0-in. layer of brick and an R-19 layer of insulation, as shown in the figure. What is the total rate of heat loss through such a wall, if its total area is 190ft^2 and the temperature difference across it is 10F?


Homework Equations



dQ/dt = -kA dT/dx

The Attempt at a Solution



uh...so i don't know the thermal conductivity of "r-19" (w/e that is) and it says the temperature difference across both the brick and the r-19 layer is 10F which baffles me on how to solve this problem. :(
 
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  • #2
yossup said:

Homework Statement



Suppose the insulating qualities of the wall of a house come mainly from a 4.0-in. layer of brick and an R-19 layer of insulation, as shown in the figure. What is the total rate of heat loss through such a wall, if its total area is 190ft^2 and the temperature difference across it is 10F?


Homework Equations



dQ/dt = -kA dT/dx

The Attempt at a Solution



uh...so i don't know the thermal conductivity of "r-19" (w/e that is) and it says the temperature difference across both the brick and the r-19 layer is 10F which baffles me on how to solve this problem. :(

This might help:
http://en.wikipedia.org/wiki/R-value_(insulation [Broken])

But it looks like you need the R-value of the brick as well.
 
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  • #3
I have the R-value for the brick wall but I can't find the r-value for r-19 through that wikipedia link...:(
 
  • #4
yossup said:
I have the R-value for the brick wall but I can't find the r-value for r-19 through that wikipedia link...:(

Don't the R values add?

Aren't its units (K·m²/W)?

If the R-19 is US units, then the conversion factor to SI units is 1 ft²·°F·h/Btu ≈ 0.1761 K·m²/W isn't it?
 
  • #5
um...huh? all i have is that the thermal conductivity of brick is .84J/ s * m * C

what exactly is r-19 anyway? arrgh so confusing~
 
  • #6
yossup said:
um...huh? all i have is that the thermal conductivity of brick is .84J/ s * m * C

what exactly is r-19 anyway? arrgh so confusing~

J/s are Watts so that becomes immediately .84 W/(m2*C)
For temperature note Degrees C are Degrees K - 273. But we can treat them the same since ΔC will = ΔK. (That is we are going to be looking at changes in temperature, and the differences will be the same.)

The value they give is apparently U which is 1/R.

And U is in SI units.

So now the trick is to determine R-19 in SI units for the insulation and match up the U value of the brick to get the total insulating property.
 
  • #7
LowlyPion said:
J/s are Watts so that becomes immediately .84 W/(m2*C)
For temperature note Degrees C are Degrees K - 273. But we can treat them the same since ΔC will = ΔK. (That is we are going to be looking at changes in temperature, and the differences will be the same.)

The value they give is apparently U which is 1/R.

And U is in SI units.

So now the trick is to determine R-19 in SI units for the insulation and match up the U value of the brick to get the total insulating property.

To convert US R-19 to proper units you use 19*(0.1761 K·m²/W) = 3.35 K·m²/W

And using the R value of the brick = 1/.84 = 1.19 K·m²/W

Now you can add the two 1.19 + 3.35 = 4.54 K·m²/W
What is the total rate of heat loss through such a wall, if its total area is 190ft^2 and the temperature difference across it is 10F?

Now all that's left is to figure the rate of total heat loss across the area given in the problem with the heat difference between inside and outside of 10 degrees F - Note Fahrenheit not C. And area is in Sq - Ft not Sq - m.

Any idea what units they want the answer in? Watts right?
 
Last edited:
  • #8
The units for thermal conductivity should be W/m-K and in English units Btu-in/hr-ft^2-F. If you want to work in ft then Btu/hr-ft^2-F. The unit for heat loss will be in W/m^2 or Btu/hr-ft^2.
 
  • #9
CFDFEAGURU said:
The units for thermal conductivity should be W/m-K and in English units Btu-in/hr-ft^2-F. If you want to work in ft then Btu/hr-ft^2-F. The unit for heat loss will be in W/m^2 or Btu/hr-ft^2.

Yes the units can go either British or SI. And British is probably the easier way to go, meaning only his value for brick need to be converted.

I should have taken the final question into account at the beginning and saved the extra conversions.

But that said they are looking for the Total Watts over the 190 Sq-feet given.

So long as everything is converted to a consistent set of units it should arrive at the same answer.
 
  • #10
Ohh, I didn't see that a total area was given. Yes then you are correct.
 

1. What is heat loss rate?

Heat loss rate refers to the amount of heat that is lost from a specific area or surface over a specific period of time. It is typically measured in units of watts or BTUs (British Thermal Units) per hour.

2. How is heat loss rate calculated?

The heat loss rate can be calculated by multiplying the temperature difference between the inside and outside of a structure by the thermal resistance (R-value) of the materials that make up the walls, floors, and roof. This calculation takes into account factors such as insulation, air leakage, and conduction through the building materials.

3. What is R-19 layer?

R-19 layer refers to a type of insulation material that has an R-value of 19 per inch of thickness. It is commonly used in walls and attics to reduce heat loss and improve energy efficiency in buildings.

4. How does the brick wall affect heat loss rate?

The brick wall can have a significant impact on the heat loss rate of a building. Brick is a relatively poor insulator, meaning it has a low R-value. This can lead to higher heat loss compared to other building materials with higher R-values, such as fiberglass insulation.

5. How can I reduce heat loss through a brick wall?

To reduce heat loss through a brick wall, you can add additional layers of insulation, such as an R-19 layer, or use a more insulating material, such as spray foam insulation. You can also improve the overall energy efficiency of the building by sealing air leaks and ensuring proper ventilation.

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