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Help With Heat Flow

  1. Nov 15, 2004 #1
    I got 2 questions and I have no idea what they are asking so hopefully someone can help me out here.

    1. Find the temperature equilibrium lines and flow lines for :

    Its just a graph of a circle in the complex plane of radius 1. The 4 points on the axes are labeled and it says 0 degress celsius in the first quadrant and 100 degress celsius in the 2nd quadrant.

    2. Find the temperature equilibrium lines and flow lines for :

    It looks like a thermometer that extends along the y axis from 1 to 3. Right below the x axis it says 0 degress and at the top of the thermometer it says 100 degress.
     
  2. jcsd
  3. Nov 15, 2004 #2

    Astronuc

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    Staff: Mentor

    Heat flows in the direction of the thermal gradient, while the temperature equilibrium lines are isotherms (constant temperature).
     
  4. Nov 15, 2004 #3
    The problem is I dont really understand what is being asked here. Can you give me a little more info on how to do this problem.
     
  5. Nov 16, 2004 #4
  6. Nov 16, 2004 #5
    Anyone got anything. I gotta hand this in by tomorrow afternoon.
     
  7. Nov 16, 2004 #6
    Anyone. I have no idea what he is asking in this problem.
     
  8. Nov 16, 2004 #7
    Ive come to the conclusion that for the first problem I think its two infinintly long parallel plates one at y=1 and one at y=3 so that T(x,y)=50y-50 and that heat flows vertically in the negative y direction along lines x=const. For the second problem I still have no idea. Is it implied that the right side of the circle is at 0 degrees while the left side is at 100 degrees. I think thats what the ticks at i and -i are for as there are not ticks at 1 and -1 but what does this mean. I cant write a formula for the temperature because it varies between different parts of the circle in relation to the radius. Can someone please help me with these questions.
     
  9. Nov 16, 2004 #8

    Astronuc

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    The heat flow lines are perpendicular to isothermal (lines of constant temperature, or temperature equilibrium lines).

    Heat flows from high temperature (100°C) to low (0°C).

    In problem 1, is the circle supposed to be a conductor?

    If the boundaries are at the temperatures specified in the quadrants, then you will have a discontinuity at the point on the circle on the vertical axis.

    With symmetric boundary conditions, a point equi-distant from the two temperatures will have a temperature as the average of the two - think in terms of symmetry - where would the temperature be 50°C?
     
  10. Nov 16, 2004 #9
    Would the temperature be 50 on the vertical axis. Would the temperature equilibrium lines just be vertical lines within the circle.
     
  11. Nov 16, 2004 #10

    Astronuc

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    As far as I can tell the upper left portion of the circle/disk is at 100°C, and the upper right portion is at 0°C, each is an isotherm.

    If the vertical axis is an isotherm of 50°C, then the isotherms in between must transition from a straight line to a circular arc - right?

    In problem 2, it seems to be a linear geometry. So the flow lines must be along the axis and the isotherms are perpendicular (horizontal). Again think symmetry.

    The same applies to electric potentials - think of equi-potentials.

    Have you done much with vector fields and potentials, yet?
     
  12. Nov 17, 2004 #11
    Well then what would the temperatures of the 2 other portions of the circle be. Do you think you can edit my picture showing me where the isotherms would be.
     
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