ThermoFluidCalc Engineering Report

Building Dynamic Thermal Inertia & Response — 2026-08-23 20:54:56
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🧱 Building Thermal Inertia & τ

Simulate building dynamic thermal time constant (tau), 24-hour diurnal solar damping factor, and phase lag (déphasage) using a 3R2C capacitive envelope model.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
📊 Solver Telemetry ● ACTIVE
👁️ Consultations 37
⚡ Calculs faits 31
💾 Téléchargements 391 📦 Code Fortran 4.4 KB
📅 Mise en service Jun 2026
⏱️ Latence < 1 ms
⚡ Outils & Rapports :
💾 Télécharger Fortran 90

🌊 24-Hour Diurnal Solar Heat Wave Damping & Phase Lag (Déphasage)

Real-time visual simulation of outdoor temperature oscillation vs damped indoor response

📝 Configuration & Presets

🏛️ Concrete Office (300 kJ/m²K) 🏡 Brick Villa (165 kJ/m²K) 🌲 Timber House (80 kJ/m²K) 🏫 Passivhaus High-Inertia
🧱 Construction Mass & Geometry
Walls + Roof + Windows + Floor
🌡️ Envelope Insulation & Outdoor Wave
Peak-to-peak outdoor variation (e.g. 14 °C)
Dynamic 3R2C Formulations:
• Total Loss: Htot = U · Aenv + 0.33 · ACH · V [W/K]
• Time Constant: τ = (Cth · 1000) / (3600 · Htot) [hours]
• Damping Factor: μ = 1 / √[ 1 + (ω τ)² ]
• Phase Lag: Δtlag = arctan(ω τ) / ω [hours]

📊 Dynamic Response Results

📊 Output Summary
💾 Fortran Source

Building Thermal Time Constant (τ)
τ = 141.6 Hours
Thermal Phase Lag: Δtlag = 5.9 hours
Damping μ = 0.027
Indoor Temperature Swing ±0.2 °C Outdoor = ±9.0 °C
Total Heat Loss (Htot) 706 W/K Envelope 330W + Vent 376W
Internal Heat Capacity (Cth) 360.0 MJ/K 100000 Wh/K
Solar Peak Attenuation 97.3 % Wave Damped

📈 24-Hour Diurnal Cycle: Outdoor vs Indoor Temperature

📉 Thermal Time Constant (τ) vs Envelope U-Value

=================================================================
 THERMOFLUIDCALC — BUILDING THERMAL INERTIA & DYNAMICS REPORT
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Case Title                 : High-Inertia Passivhaus School (Super-insulated + Exposed Concrete)
Floor Area (Afloor)        : 1200.0 m2 (Volume = 3800.0 m3)
Envelope Area / U-value    : 2200.0 m2 @ 0.150 W/(m2.K)
Total Heat Loss Coeff      : 706.20 W/K (H_tr=330.0, H_ve=376.2)
Effective Heat Capacity    : 360.00 MJ/K (360000 kJ/K)
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THERMAL TIME CONSTANT (tau): 141.60 hours
Diurnal Damping Factor (mu): 0.0270 (97.3 % wave reduction)
Thermal Phase Lag (Dt_lag) : 5.90 hours
Outdoor Diurnal Amplitude  : 18.0 °C (±9.0 °C)
Indoor Damped Temperature  : 0.49 °C (±0.24 °C)
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📘 Calculation Methodology & ISO 13790 Standards

Thermal Inertia & Time Constant

The time constant $\tau = R_{th} C_{th}$ determines how slowly a building loses heat or responds to external climate oscillations:

τ = Cth / Htot [hours]

Damping & Phase Lag (Déphasage)

High thermal mass delays solar heat arrival indoors by up to 8–12 hours, allowing nighttime natural ventilation flushing during off-peak hours.

Key Engineering Assumptions

  • Lumped single-zone 3R2C capacitive thermal network.
  • Diurnal solar cycle approximated by 24-hour sinusoidal wave.
  • Ventilation specific heat transfer $0.33\,\text{Wh/(m}^3\cdot\text{K)}$.