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Calculate the R-value of the stack of materials

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the R-value of the stack of materials whose total thickness is made up of the
    individual thicknesses:
    material 1; k = 0.123 W/m/K, thickness = 0.103 m
    material 2: k = 0.234 W/m/K, thickness = 0.092 m
    material 3: k = 0.345 W/m/K, thickness = 0.081 m


    Hence calculate the heat flow per unit area through such a stack with has temperatures of
    20 °C and -5 °C on opposite sides of the stack

    2. Relevant equations

    R = ΔT/QA, Where QAis heat flux


    3. The attempt at a solution
    I've no idea how to do this problem! Please help!
     
    Last edited: Jan 13, 2012
  2. jcsd
  3. Jan 13, 2012 #2

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    Welcome to PF, ninaw21! :smile:

    In equilibrium the heat flow through material 1 must be equal to the flow through material 2, which in turn must be equal to the flow in material 3.

    If you introduce 2 variables representing the temperature between materials 1 and 2, respectively materials 2 and 3, you can set up a system of equations that you can solve.

    Do you know how to do that?
     
  4. Jan 13, 2012 #3
    Thank you! I know that they're equal but I dont know the variables to use..
     
  5. Jan 13, 2012 #4

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    Well, what can you come up with?
    Which symbols can you think of?
     
  6. Jan 13, 2012 #5
    q = specific heat x m x Δt,

    where q is heat flow, m is mass in grams, and Δt is the temperature change. ??
     
  7. Jan 13, 2012 #6

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    Hmm, that is the formula that relates absorbed heat to change in temperature.
    I'm afraid that is not the formula to use here.

    Do you have a formula that relates the R-value to the thermal conductivity k?

    Actually, to find the R-value of the stack, you can simply add the R-values of the 3 materials.
     
  8. Jan 13, 2012 #7
    Is this the formula that is used then :

    deltaQ/deltat = kAdeltaT/d, where: deltaQ = heat flow, deltat = time, k = thermal conductivity, deltaT = temp, and d = distance ??
    (Thanks for all the help!)
     
  9. Jan 13, 2012 #8

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    That's closer.

    So you have:
    $$R = {\Delta T \over {dQ \over dt} / A}$$
    and
    $${dQ \over dt} = {k A \Delta T \over d}$$
    where d is distance the heat travels, or in other words, the thickness of the material,
    and where A is the surface of the material.

    Note that the heat flux ##Q_A## that you had in your opening post, is actually the heat flow per unit area and per unit of time.


    Can you deduce what the R-value will be of each material?
     
    Last edited: Jan 13, 2012
  10. Jan 13, 2012 #9

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    I'll make it simpler.
    The relation between R and k is: ##R = {d \over k}##.
     
  11. Jan 13, 2012 #10
    Thank you so much!! :)
     
  12. Jan 13, 2012 #11

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    So... do you have your answer now?
     
  13. Jan 13, 2012 #12
    Yes! :)
     
  14. Jan 13, 2012 #13

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