1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Effect of thickness on heat transfer/insulation

  1. Jul 27, 2004 #1
    Hi,

    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?

    Thanks.
     
  2. jcsd
  3. Jul 27, 2004 #2

    Doc Al

    User Avatar

    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
    Thanks.

    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

    russ_watters

    User Avatar

    Staff: Mentor

    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

    User Avatar

    Staff: Mentor

    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?

    Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Effect of thickness on heat transfer/insulation
  1. Heat Transfer (Replies: 5)

Loading...