Lumped Capacitance Model vs Full Model
This MATLAB simulation models the time-dependent center temperature of a spherical marble with the lumped capacitance model (solid blue line) and the full solution (solid black line), as shown in the top plot. The percent difference between the two solutions is shown in the bottom plot. Vary the Biot number Bi with the slider bar and observe how the percent difference between the two solutions changes. Note that the lumped capacitance model is valid if Bi < 0.1. Physical parameters and the number of terms used in the full solution can be edited in the m-file.
This simulation requires MATLAB.