Square Bar Quench: Corner-Effect Martensite Front (2D)

This 2D cross-section simulator quenches the same kind of red-hot plain-carbon steel bar as its 3D counterpart, but shaped as a square rather than a cylinder — and solves it with an independent method: a real 2D finite-difference grid over the full cross-section, rather than a 1D radial reduction that assumes circular symmetry. Every grid cell conducts heat to its neighbours and, at the bar's surface, convects heat to the quenchant through however many faces it exposes — one for a face-center cell, two for a corner. Each cell's coldest-reached temperature feeds the same Koistinen-Marburger transformation law as the 3D sim to decide how much martensite has formed and how hard that spot becomes. The payoff is a real, distinct metallurgical phenomenon the radial model cannot show: corners are cooled from two directions at once and harden first, while the core — insulated on every side — stays softest longest, reproducing the classic "corner effect" seen when heat-treating square and rectangular stock.