Thermopile Spreading-Resistance Lab (2D)

A real thermoelectric generator is rarely heated by a plate exactly the size of its junction array — more often a smaller heater pad, pipe or chip sits on part of the pile, and the rest of the driving heat has to spread sideways through the pile's own body to reach the junctions further out. This 2D cross-section solves that spreading directly: an unsteady 2D heat-diffusion equation is integrated by explicit finite differences every frame, with the hot contact patch and cold plate as fixed-temperature (Dirichlet) boundaries and the array's sides left thermally insulated. Each of the N series-wired junctions reads its own driving ΔT straight off the solved temperature field at its position, so junctions under the patch approach the full T_h − T_c while ones toward the edges run measurably cooler — and the pile's total EMF, current and delivered power are then built from N genuinely different, self-computed junction temperatures instead of one assumed uniform value. Narrow the hot-contact width and watch the solved EMF fall visibly below the "ideal" no-spreading EMF the 3D version always assumes.