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Simulation

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.

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