IndisputableMonolith.Thermodynamics.HeatTransferFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Heat Transfer from Phi-Ladder — Tier F Thermodynamics
   6
   7The three heat transfer modes (conduction, convection, radiation) have
   8characteristic time constants that scale with each other. In RS terms,
   9the heat flux efficiency ratio r follows the phi-ladder across modes.
  10
  11Five canonical heat transfer regimes (pure conduction, mixed convection,
  12forced convection, natural convection, radiative) = configDim D = 5.
  13
  14RS prediction: adjacent regime Nusselt numbers (dimensionless heat transfer)
  15ratio by phi^2 (two rungs per mode transition).
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Thermodynamics.HeatTransferFromJCost
  21open Constants
  22
  23inductive HeatTransferRegime where
  24  | pureConduction | mixedConvection | forcedConvection | naturalConvection | radiative
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem regimeCount : Fintype.card HeatTransferRegime = 5 := by decide
  28
  29noncomputable def nusseltAtRung (k : ℕ) : ℝ := phi ^ (2 * k)
  30
  31theorem nusseltRatio (k : ℕ) :
  32    nusseltAtRung (k + 1) / nusseltAtRung k = phi ^ 2 := by
  33  unfold nusseltAtRung
  34  have hpos : 0 < phi ^ (2 * k) := pow_pos phi_pos _
  35  rw [show 2 * (k + 1) = 2 * k + 2 from by ring, pow_add]
  36  field_simp [hpos.ne']
  37
  38structure HeatTransferCert where
  39  five_regimes : Fintype.card HeatTransferRegime = 5
  40  phi_sq_ratio : ∀ k, nusseltAtRung (k + 1) / nusseltAtRung k = phi ^ 2
  41
  42noncomputable def heatTransferCert : HeatTransferCert where
  43  five_regimes := regimeCount
  44  phi_sq_ratio := nusseltRatio
  45
  46end IndisputableMonolith.Thermodynamics.HeatTransferFromJCost
  47