#### Transient Conduction with Spatial Effects: Interactive Simulation

This simulation was prepared using MATLAB. This simulation requires MATLAB.

Consider a sphere that cools off over time. This simulation compares the actual transient temperature of the center of the sphere to the temperature predicted by the lumped capacitance approximation. Adjust the slider to change the Biot number.

**Try to answer these questions before determining the answer with the simulation**. We suggest that you write down the reasons for your answers.

- Predict how the actual solution will compare to the lumped capacitance approximation when the Biot number is increased. Predict how they compare when the Biot number is reduced to a value of 0.1 or smaller. What has better agreement, a small Biot number or a large Biot number?
- When the Biot number is large, the shape of the full solution will look different than the lumped capacitance approximation, especially at low times. Describe the difference in shapes and try to explain why in words.