🎬Point Source Diffusion-From Transient Pulse to Steady Source

The simulation of point heat sources reveals that the Dirac delta function can model fundamentally different behaviors based on whether the source is continuous or momentary. When the source is continuous (steady-state), the system achieves an equilibrium where the temperature is stable ( $\partial T / \delta t = 0$ ), resulting in the classic inversely proportional ( $1 / r$ ) temperature distribution near the source. Conversely, when the source is an instantaneous pulse (unsteady-state), the entire system remains transient ( $\partial T / \partial t \neq 0$ ), causing the heat energy to spread outwards as a thermal wave that eventually dissipates entirely, meaning the temperature at every point must rise, peak, and decay back to the ambient zero level.

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Point Source Diffusion-From Transient Pulse to Steady Source | Animated Resultsviadean on Notion