{
  "title": "Following the heat: deterministic teaching studies",
  "status": "Calculated values, no measurements or fitted confidence intervals",
  "counts": {
    "flow": 202,
    "barrier_sweep": 150,
    "payload_time": 543
  },
  "constants": {
    "gamma_fixed": 1.4,
    "vibrational_theta_K": 3055.5555555555557,
    "area_m2": 0.1,
    "external_convection_W_per_m2K": 10.0,
    "layer2_thickness_m": 0.002,
    "layer2_conductivity_W_per_mK": 0.2,
    "payload_heat_capacity_J_per_K": 2000.0,
    "environment_C": 80.0,
    "initial_payload_C": 20.0
  },
  "formulas": {
    "fixed": "Tt=T*(1+(gamma-1)*M^2/2)",
    "resistance": "R=1/(h*A)+L1/(k1*A)+L2/(k2*A)",
    "payload": "Tp=Tb+(T0-Tb)*exp(-t/(R*C))",
    "heat_rate": "q=(Tb-Tp)/R",
    "energy": "E=C*(Tp-T0)"
  },
  "checks": {
    "max_mach_squared_residual": 1.0658141036401503e-14,
    "zero_time_and_one_time_constant": "passed"
  },
  "limitations": [
    "Gas stagnation temperature is not wall temperature or heat flux.",
    "Vibrational model excludes dissociation, ionization, chemical reactions and nonequilibrium. Higher-temperature results are simplified-model comparisons, not validated real-air predictions.",
    "Layers have negligible heat capacity and quasi-steady one-dimensional conduction.",
    "Payload is uniform, inert, constant heat capacity, no phase change; parameters are illustrative.",
    "No spatial cooling, freezing, biological preservation, human exposure, structural qualification or food safety demonstrated."
  ],
  "sources": [
    "https://www.grc.nasa.gov/WWW/BGH/stagtmp.html",
    "https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node118.html",
    "https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node124.html"
  ]
}