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Problem on the transfer of heat into different materials

  1. Jul 27, 2009 #1
    Hi all,

    1. The problem statement

    A copper specimen, initially at 293K, is immersed in a bath of liquid salt at 773K. The bath is agitated and the heat transfer at the surface of the metal is effectively perfect. A temperature of 723K is measured at 5mm below the surface of the metal item after 3 seconds. Estimate the depth below the surface at which a temperature of 723K would be reached in 3 seconds if the specimen were made of titanium alloy.

    Copper

    Thermal Conductivity = 380 W m-1 K-1
    Specific Heat Capacity = 390 J kg-1 K-1
    Density - 8900 kg m-3

    Titanium

    Thermal Conductivity = 6 W m-1 K-1
    Specific Heat Capacity = 500 J kg-1 K-1
    Density - 4500 kg m-3


    2. Relevant equations

    This equation wasn't given in the question but seems to be relevant.

    8ff29039f45e4bd1e41276b599137007.png

    where fb5544db7cc3913abfb5d87fc35a6207.png is the rate of heat flow, k is the thermal conductivity, A is the total cross sectional area of conducting surface, ΔT is temperature difference, and x is the thickness of conducting surface separating the 2 temperatures.

    3. The attempt at a solution

    I'm very confused as to how to approach this problem. I first attempted to rearrange the equation for Area, but I would also need to have ΔQ which would require a mass to calculate. Could I just use and arbitrary volume for both components and use the density to calculate a mass?

    Thanks
     
  2. jcsd
  3. Jul 27, 2009 #2

    Mapes

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi lemonbrook, welcome to PF. A common way of estimating the required time for a temperature change to propagate a distance [itex]L[/itex] is [itex]L^2/D[/itex], where [itex]D[/itex] is the material's http://en.wikipedia.org/wiki/Thermal_diffusivity" [Broken].
     
    Last edited by a moderator: May 4, 2017
  4. Jul 27, 2009 #3
    That it!

    Thanks very much!
     
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