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Exercise 2

Consider again a temperature distribution in the square .

Now, however, the heat sources extend only along parts of the left and right edges. Specifically, the temperatures are prescribed to be

( for ), ( for ),

Everywhere else on the boundary of the square (at the other points of the left and right edges and at all points of the upper and lower edges) the boundary is assumed to be insulated; at such points heat can flow along the boundary, not across it. Why?

Problem 9:

In the menu click on "40 Contour". Draw a curve at every point of which you believe the temperature is 40°C; do the same for 60°C and 80°C. (These are called isothermal curves; they are contour lines for the temperature function .) By definition, an isothermal curve (or isotherm) is a curve along which the temperature is constant.

Problem 10:

Now click on "Start1" and the machine will display the correct contour lines.

Problem 11:

In the menu click on "Vector". Draw a small arrow indicating (what you believe to be) the direction of heat flow at six different points, two on each of the computer-drawn contour lines. (Choose points where the contour lines appear continuous.)

Problem 12:

Click on "Start2" to have the computer display the actual direction of heat flow at each point.

Problem 13:

You may change the hot- and cold-temperature intervals on each side by altering the entries in "Range1" and "Range2". For example, to prescribe for (instead of ), replace "0.375:0.625" by "0.2:0.4" in "Range1". Choose the ranges as you wish, then carry out the first three steps again.

 
 
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