nx_vessel_thermal.nx

nx_vessel_thermal.nx -- H0 of the VIRTUAL-PROTOTYPE / HARDWARE-IN-THE- LOOP ladder. A lumped-capacitance thermal model of the PHYSICAL fermentation vessel in REAL ENGINEERING UNITS, so the hardware can be sized and tested in software before a dollar is spent -- the way a fighter programme runs the digital twin before bending metal. THE PHYSICS (Newton's law of cooling + a heater): C * dT/dt = P*duty - U*(T - T_ambient) C = heat capacity of the contents [J/K] (= mass * specific heat) P = heater power [W] U = insulation conductance to ambient [W/K] (lower = better insulated) Equilibrium at full duty: T_eq = T_ambient + P/U. If T_eq < setpoint the heater is UNDERSIZED -- the design can NEVER reach target, caught here in software instead of after you buy the part. Integer units (no float): temp/ambient milli-C, P milli-W, U milli-(W/K), C J/K, dt seconds. Derivation: dT_mc = net_mw * dt_s / C_jk. THE EXCEED: R1's controller used abstract Q14 gains; H0 is PHYSICAL -- real watts and J/K and W/K -- so it answers "will a 50 W heater hold 4 L of milk at 43 C in a vessel that loses 1 W/K?" before building anything. genealogy_id: lumped_capacitance_thermal_model + newton_cooling_1701 + digital_twin_mbse