Help With Heat Flow Questions: Find Temperature Equilibrium & Flow Lines

[KeithF40]

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.

 

[Astronuc]

Heat flows in the direction of the thermal gradient, while the temperature equilibrium lines are isotherms (constant temperature).

 

[KeithF40]

The problem is I don't really understand what is being asked here. Can you give me a little more info on how to do this problem.

 

[KeithF40]

Im looking through the book to find out what in the world is going on here and its not helping at all.

This is a picture of the first problem :
http://members.aol.com/HomesDelicious/pic1.jpg
This is a picture of the second problem :
http://members.aol.com/HomesDelicious/pic2.jpg

Thanks for any help you can give me.

 

[KeithF40]

Anyone got anything. I got to hand this in by tomorrow afternoon.

 

[KeithF40]

Anyone. I have no idea what he is asking in this problem.

 

[KeithF40]

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 that's what the ticks at i and -i are for as there are not ticks at 1 and -1 but what does this mean. I can't 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.

 

[Astronuc]

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?

 

[KeithF40]

Would the temperature be 50 on the vertical axis. Would the temperature equilibrium lines just be vertical lines within the circle.

 

[Astronuc]

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?

 

[KeithF40]

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.