This tool illustrates the Fourier Series approximation of heat dissipation in an insulated wire with ends at fixed temperatures.

Select the initial heat distribution by clicking one of the Initial Condition radio buttons. Grab the sliders or drag the yellow endpoint temperature indicators to select endpoint temperatures.

The steady state solution and any combination of the first four Fourier terms can be displayed, and the heat distribution is shown in white.

Use the slider handle below the graphing window to select a value of \(t\). Animate the system using the [>>] key. During the animation the key changes to [||], and selecting it will stop the animation. At the end of the animation the key changes to [<<], which resets \(t\) to zero.

When the animation is not running, rolling the cursor over the graphing window produces crosshairs and a readout of the values of \(x\) and \(u\). Depressing the mousekey suppresses the crosshairs.

© 2001 H. Hohn and H. Miller