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Effect of thickness on heat transfer/insulation

  1. Jul 27, 2004 #1

    I'm currently doing an experiment to investigate the effect that changing the thickness of insulation has on cooling curves. However, I do need some theory to compare the results to. Does anyone know anywhere that I could find such information, or actually know themselves what effect changing the thickness should have?

  2. jcsd
  3. Jul 27, 2004 #2

    Doc Al

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    Staff: Mentor

    heat conduction

    Perhaps this will get you started. In general, the rate of heat transfer by conduction is inversely proportional to the thickness of the material:
    [tex]\frac{\Delta Q}{\Delta t} = \frac{k A \Delta T}{d}[/tex]
    where ΔQ/Δt is the rate of heat flow, ΔT is the temperature difference, k is the thermal conductivity of the material, A is the area, and d is the thickness.

    (Do a web search on heat conduction to find plenty more information.)
  4. Aug 3, 2004 #3

    Does this mean that if all variables are kept constant except for the thickness of the insulation, and the temperature inside the insulated area is modelled by [tex]T_{n}=T_{O}\times{e}^-^k^n[/tex] (The insulated area is heated up, and then the air is allowed to cool) that k will by directly proportional to the thickness?
  5. Aug 3, 2004 #4
    How would you simoustaneously maintain both ΔQ/Δt and ΔT constant?
  6. Aug 4, 2004 #5


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    In the summer, with air conditioning.

    edit: To make that sound a little less snide, let me explain. Obviously, if you don't have air conditioning, the air in your house will slowly increase its temperature to match the outside temperature: ΔT decrease to zero and ΔQ/Δt will follow. On the most basic level, the purpose of an air conditioner is to maintain a ΔT between inside and outside. Constant ΔT and ΔQ/Δt requires an another term: another ΔQ/Δt. Energy enters your house through the wall and leaves your house through the air conditioner.
    Last edited: Aug 4, 2004
  7. Aug 11, 2004 #6
    Sorry, I think that what I said was not exactly what I meant. By keeping 'all other variables' constant, I meant that I would keep k and A constant, while varying d.

    Sorry for the confusion.
  8. Aug 13, 2004 #7
    Another question regarding the modelling of this situation:

    If two different materials were used, (ie. 1 layer of material A, and 1 layer of material B, pressed together) as the barrier, how would the equation [tex]\frac{\Delta Q}{\Delta t} = \frac{k A \Delta T}{d}[/tex] need to be modified to compensate for that?
  9. Aug 13, 2004 #8

    Doc Al

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    composite layers

    For two slabs of material:
    [tex]\frac{\Delta Q}{\Delta t} = \frac{A \Delta T}{d_A/k_A + d_B/k_B}[/tex]
  10. Aug 13, 2004 #9
    Thanks, that helps a lot. Is there an internet site or book that contains information on dual layer conduction? I've been looking but I haven't been able to find one.
    Last edited: Aug 13, 2004
  11. Aug 14, 2004 #10
    Reference the Fundamentals of Heat and Mass Transfer by Incropera and Dewitt.
  12. Aug 14, 2004 #11
    It gets confusing sometimes....When composite slabs are involved.If 2 or 3 slabs are involved then it wont be a problem.But I had encountered some really tough problems on this.So I think the best thing to do is to find somekid of anology btw Electric circuts and the Slab-Systems.....

    So by putting R=d/kA,where R is Thermal resistance.
    Then everything is like that of Eletric circuits....Ohms law holds good for thermal conduction also.
  13. Aug 17, 2004 #12
    Ok, I understand how to do that now, but I basically now have two formulas. From my experimentation I have:
    [tex]T_{t}=T_{Difference}\times{e}^-^k^t[/tex], where [tex]TT_{Difference}[/tex] is the initial difference in temperature, and [tex]T_{t}[/tex] is the difference after t seconds.
    and from the theory I have:
    [tex]\frac{\Delta Q}{\Delta t} = \frac{A \Delta T}{d_A/k_A + d_B/k_B}[/tex]

    I am trying to find a mathematical relationship between the value of k in formula one, and the value of DQ/Dt in the second equation. Is it possible to do this using something like:
    dQ/dt=dQ/dT*DT/dt, or am i on the wrong track?

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