📢Instant surface temperature lagged core heat

When heat transfer is highly efficient, the surface of a sphere immersed in an external bath of temperature $T_0$ will instantaneously adapt to that temperature, satisfying the boundary condition $T(r=R, \theta, \varphi, t)=T_0$. This boundary condition is necessary for solving the heat equation. However, even though the surface instantly reaches this new temperature, the interior of the sphere does not respond simultaneously. The simulation of this scenario demonstrates the governing role of the Fourier number, illustrating that heat conduction is a time-dependent and diffusive process where the change is initially localized at the boundary. Consequently, the sphere's core remains thermally isolated for a significant time until the Fourier number increases sufficiently to allow heat penetration, resulting in the system’s smooth, time-consuming approach toward a uniform steady-state thermal equilibrium.

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Instant surface temperature lagged core heat | Audiosviadean on Notion