WWAVETANKCOMPUTATIONAL PHYSICS LAB

INSTRUMENT 05 / HEAT PLATE

Heat diffusion
through materials.

A diffusion laboratory for seeing thermal energy spread. Draw hot and cold regions, add insulation, and measure how gradients drive flow toward equilibrium.

TEMPERATURE FIELD T(x,y,t) 100°
160 × 96 CELLS · EXPLICIT FINITE DIFFERENCE0.00 ms/frame
PROBE20.0°temperature at crosshair
MEAN TEMPERATURE22.8°plate average
HOT–COLD SPREAD80.0°distance from equilibrium
STEEPEST GRADIENT56.57largest local change / cell
WHAT IS HAPPENING?

Why does a sharp temperature peak flatten out?

REPRESENTATIVE EQUATION∂T/∂t = α∇²T

Heat flows down the temperature gradient. The hottest point cools fastest because its contrast with nearby cells is largest. The heat equation compares every cell with its neighbors. A hot peak loses energy; a cool hollow gains it; a flat region has no reason to change.

The plate is a finite grid, so each step reads the four neighboring temperatures. Insulation lowers the local conductivity rather than “blocking heat” outright. The step size is deliberately limited so the numerical model settles smoothly instead of inventing oscillations.