🌀 Cavity Enclosure Natural Convection (Catton)

Model natural convection in differentially heated vertical cavity enclosures (double glazing, solar gaps), computing Rayleigh number, average Nusselt, total heat flow Q, and boundary layer thickness.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 39

⚡ Calculs faits 32

💾 Téléchargements 399 📦 Code Fortran 10.8 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🌀 Enclosed Differentially Heated Cavity & Recirculation Roll

Real-time visual simulation of buoyant fluid rising along hot left wall and sinking along cold right wall

📝 Configuration & Presets

🪟 Double Glazing Air Gap ☀️ Solar Thermal Collector ⚡ Transformer Oil Channel ☢️ Nuclear Containment Gap

📐 Cavity Enclosure Geometry

Cavity Height H [m]:

Cavity Spacing Width W [m]:

Cavity Depth L [m]:

🌡️ Wall Temperatures

Hot Wall Temp T_h [°C]:

Cold Wall Temp T_c [°C]:

🧪 Fluid Thermophysical Properties

Density ρ [kg/m³]:

Viscosity μ [cP]:

Conductivity k [W/(m·K)]:

Expansion Coeff β [1/K]:

Catton Enclosure Formulation:
• Rayleigh Number: Ra_W = [ g β (T_h − T_c) W³ ] / (ν α)
• Average Nusselt: Nu = 0.22 · [ Ra_W Pr / (0.2 + Pr) ]^0.28 · (H/W)^−0.25
• Heat Rate: Q̇ = Nu · (k / W) · (H · L) · (T_h − T_c) [W]
• Boundary Layer Thickness: δ ≈ W · Ra_W^−1/4

📊 Cavity Convection Results

📊 Output Summary
💾 Fortran Source

Total Convective Heat Rate (Q̇)

Q̇ = 90.4 W

Average HTC: 3.77 W/(m²·K) | Nu_avg = 2.41

Ra_W = 9.85e+3

Cavity Rayleigh (Ra_W) 9.85e+3 Transition

Enclosure Aspect Ratio (A = H/W) 75.0 Prandtl Pr = 0.72

Wall BL Thickness (δ) 1.61 mm Boundary layer scale

Max Buoyant Velocity 0.911 m/s √(g β ΔT H)

📈 Average Nusselt Nu vs Cavity Spacing W (mm)

📉 Heat Transfer Rate Q̇ (W) vs Temperature Difference ΔT (°C)

=================================================================
 THERMOFLUIDCALC — CAVITY NATURAL CONVECTION (CATTON MODEL) REPORT
=================================================================
Case Title                 : Architectural Double Glazing Insulating Window Cavity
Cavity Dimensions          : Height H = 1.20 m, Spacing W = 0.0160 m, Depth L = 1.00 m (Aspect A = 75.0)
Wall Temperatures          : Hot Th = 20.0 C, Cold Tc = 0.0 C (DeltaT = 20.0 C)
Rayleigh Number (Ra_W)     : 9.848e+3
Prandtl Number (Pr)        : 0.716
-----------------------------------------------------------------
AVERAGE NUSSELT (Nu_avg)   : 2.412
Heat Transfer Coeff (h_avg): 3.77 W/(m2.K)
TOTAL HEAT TRANSFER RATE Q : 90.43 W (0.090 kW)
BL Thickness (delta_bl)    : 1.61 mm
Maximum Buoyant Velocity   : 0.911 m/s
=================================================================

📘 Calculation Methodology & Cavity Convection Standards

Catton & Berkovsky-Polevikov Model

Natural convection in differentially heated tall enclosures transitions through three regimes based on $Ra_W$:

                    • Ra < 10³: Conduction ($Nu = 1$)

                    • 10⁴ ≤ Ra ≤ 10⁷: $Nu = 0.22 (Ra Pr / (0.2+Pr))^{0.28} A^{-0.25}$

Boundary Layer & Core Circulation

Hot fluid rises in a thin layer along the left wall, turns horizontally at the top, and sinks along the cold wall, creating an inner thermally stratified core.

Key Engineering Assumptions

2D rectangular vertical cavity with adiabatic top and bottom.
Boussinesq fluid approximation with temperature-dependent density.
Laminar flow regime up to $Ra_W \approx 10^7$.

ThermoFluidCalc Engineering Report