In the cartoon, the heat transfer along the bar was a
time-dependent process. From here on, we shall consider only
time-independent (or steady state) processes.
Suppose it is winter, and your classroom is heated by a
radiator on one side, while on the opposite side there is a
loss of heat - through windows, for example.
In "Heat Conduction Simulation" below, we simplify the
situation. Consider rectangular "classroom," and suppose that
this "room" is a unit square. The left edge
is maintained at temperature "Temp1," and the right edge
at temperature "Temp2." Along those parts of the boundary
where the temperature is not specified, the wall is assumed to
be insulated.
The default values for Temp1 and Temp2 are 100°C and
20°C, respectively. Temp1 can be changed by clicking in
its box, typing in any desired value between 0° and
100°, and pressing the Return key. Temp2 works the same
way. The color of the strip will change to reflect the
temperature - see the color chart at the bottom.
The endpoints of the left strip have y-coordinates "Ymin1" and
"Ymax1," and the right strip "Ymin2" and "Ymax2." To change
the length of a strip, either type values into the appropriate
boxes, or "drag and drop" by clicking and holding the mouse
button at one of the ends, dragging it to a new spot, and
releasing the mouse button. The values "Xmin1," "Xmax1,"
"Xmin2," and "Xmax2" determine the widths of the color strips.
Problem
1:
Set the values in the boxes, then click on the "Graph"
button. After a short wait, you should see a color display
depicting the temperature distribution within the square
"room" produced by the specified values. We suggest you
keep the strips thin, but try varying the boundary
temperatures and the lengths of the strips to see how the
distribution depends on these factors.
Problem
2:
For a given temperature distribution (color display), at
each of several points, draw a vector to indicate what you
think is the direction of heat flow. To draw vectors,
change the draw mode by clicking on the "Draw" button (by
default, it reads "Draw: Off"). Click until it reads
"Draw: Vector". Then click and hold the mouse button
anywhere in the graph, drag to draw your vector, and
release the mouse button.Then click on "Graph" to see the
correct vectors of heat flow at each point.
Copyright 1998-2001
Rensselaer Polytechnic Institute. All Rights Reserved.