1. Not finding help here? Sign up for a free 30min 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!

Heat Transfer Problem

  1. Apr 1, 2014 #1
    1. The problem statement, all variables and given/known data
    Two bodies of masses [itex]m[/itex][itex]_{1}[/itex] and [itex]m[/itex][itex]_{2}[/itex] and specific heat capacities [itex]s[/itex][itex]_{1}[/itex] and [itex]s[/itex][itex]_{2}[/itex] , are connected by a rod of length [itex]l[/itex] and cross-sectional area [itex]A[/itex], thermal conductivity [itex]K[/itex] and negligible heat capacity. The whole system is thermally insulated. At time [itex]t=0[/itex], the temperature of the first body is [itex]T[/itex][itex]_{1}[/itex] and the temperature of the second body is [itex]T[/itex][itex]_{2}[/itex] ([itex]T[/itex][itex]_{2}[/itex] [itex]>[/itex] [itex]T[/itex][itex]_{1}[/itex] ). Find the temperature difference between the bodies at time [itex]t[/itex].


    2. Relevant equations
    [itex] dQ/dt = KAdT/dx[/itex]

    [itex] dQ = msdθ [/itex]


    3. The attempt at a solution
    I was able to set up [itex]2[/itex] equations relating the amount of heat transferred through the rod in a time [itex]dt[/itex] to the rise and fall of temperatures of the masses [itex]m[/itex][itex]_{2}[/itex] and [itex]m[/itex][itex]_{1}[/itex] respectively. I don't know how to proceed after this ?
     
  2. jcsd
  3. Apr 1, 2014 #2

    maajdl

    User Avatar
    Gold Member

    Since the heat capacity of the rod is neglected, the temperature profile in the rod is linear:

    dT/dx = (T2-T1)/l

    You need to write your second equation twice: once for m1 and once for m2.
    Then you can simply solve the equations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Heat Transfer Problem
  1. Heat transfer problem (Replies: 10)

  2. Heat Transfer Problem (Replies: 4)

Loading...