Heat Conduction Explorer

Your tasks

1. Keep the text’s example on a 2 × 2 mesh. Read T at the bottom-right corner and at the middle of the bottom edge.
   Check answer

   0.6214 °C and 0.4821 °C, equation (2.55). The plate is hottest at the corner farthest from both cold edges, between the two insulated edges.

2. Run the mesh study. From which mesh does the maximum temperature change by less than 1% from the previous one? Which value would you report?
   Check answer

   8 × 8 changes by −0.95% from 4 × 4; 16 × 16 by −0.23%. Report 16 × 16, 0.5898 °C, which matches the software value 0.5897 °C in text Table 2.1. The 2 × 2 hand mesh is 5% high.

3. Set the right edge to 0 °C as well. Where is the hottest point now, and why there?
   Check answer

   At the middle of the bottom edge, (0.5, 0), about 0.228 °C on a fine mesh. It is the point farthest from the three cold edges, and the insulated bottom edge behaves as a line of symmetry, so heat cannot leave through it.

4. Make all four edges insulated. What does the Explorer report, and what does it mean physically?
   Check answer

   No temperature is fixed anywhere, so [K] is singular: adding a constant to every T̂ changes nothing. Physically there is no steady state at all, because the source keeps adding 600 W per metre of thickness and nothing can leave.