,

with boundary conditions , , and , where is time, is distance along the rod, is the length of the rod, and .

The solution is of the form

,

where is the conductivity parameter (a product of the density, thermal conductivity, and specific heat of the rod) and

.

If you increase the number of terms , the solution improves as long as the time is small. As (the final state), the entire rod approaches a temperature of 0 degrees. You can see the effect of the thermal properties by varying the conductivity parameter .