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!

Fourier/heat problem involving hyperbolic sine

  1. Mar 14, 2017 #1
    1. The problem statement, all variables and given/known data
    A rectangular box measuring a x b x c has all its walls at temperature T1 except for the one at z=c which is held at temperature T2. When the box comes to equilibrium, the temperature function T(x,y,z) satisfies ∂T/∂t =D∇2T with the time derivative on the left equal to zero. Find the temperature T in the box in the form T(x,y,z) = T1 + τ(x,y,z) where τ is the fourier series τ(x,y,z)=∑∑anmsin(nπx/a)sin(mπy/b)f(z).

    Find f(z) and find anm

    2. Relevant equations
    All others listed in the question

    3. The attempt at a solution
    so I see that it's sin functions in x and y in the fourier series because there are zero's at 0 and a, b for both. However since there's only one 0 for z at z=0, I'm assuming that f(z) has to be sinh. But I don't think I can just take the argument there to be jπz/c.

    If someone can bump me forward I'm sure I can figure the rest of the question out.
  2. jcsd
  3. Mar 14, 2017 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    What partial differential equation must τ(x,y,z) satisfy?
  4. Mar 14, 2017 #3
    T(x,y,z) satisfies ∂T/∂t =D∇2T and T(x,y,z) = T1 + τ(x,y,z)
  5. Mar 14, 2017 #4


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    What differential equation does the "tau" function τ(x,y,z) satisfy under equilibrium conditions?
    Use this to determine the form of f(z).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Fourier heat problem Date
DSB-SC signals Mar 14, 2018
Fourier Heat Conduction Law Mar 20, 2013
Heat Transfer fourier's law Problem Mar 19, 2013
Archived Fourier's law heat conduction Dec 11, 2010
Fourier Law + Heat Transfer Jun 9, 2007