The transient heat conduction analysis, as demonstrated by the Python animation, is the clear visualization of the diffusive nature of heat transfer and the governing role of the Fourier number ( $F_o$ ). The simulation illustrates that when the sphere's surface instantly reaches the new temperature ( $T_0$ ), the interior doesn't respond simultaneously; instead, the change is initially localized at the boundary. The animation shows that the sphere's core remains thermally isolated for a significant time until the Fourier number, which dictates the rate of heat penetration relative to the sphere's size, increases sufficiently. This progression visually confirms that heat conduction is a time-dependent process, where the temperature profiles gradually flatten and decrease, illustrating the system's smooth, time-consuming approach toward a uniform, steady-state thermal equilibrium.
Understanding Heat Transfer: The Sphere in the Oil Bath
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