🪨 Porous Media Convection (Darcy-Forchheimer)

Compute convective heat transfer in saturated porous media: porous Nusselt number, Darcy-Forchheimer non-linear pressure drop, filtration pumping power, and porous Rayleigh Ra_K.

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

Convection

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⚡ Solves 30

💾 Downloads 470 📦 Fortran Code 10.8 KB

📅 Released Jun 2026

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🪨 Saturated Porous Matrix & Interstitial Seepage Flow

Real-time visual simulation of fluid filtration through packed grains, Darcy pressure drop & thermal dispersion

📝 Configuration & Presets

♨️ Geothermal Aquifer 🧪 Catalytic Packed Bed 🧽 Metal Foam Heat Sink 🧱 Wall Fibrous Insulation

📐 Bed Geometry & Porous Structure

Bed Flow Length H [m]:

Bed Cross Width W [m]:

Permeability K [m²]: 1 Darcy ≈ 9.87×10⁻¹³ m²

Porosity φ (0 to 1):

⚡ Flow Velocity & Temperatures

Superficial Darcy Velocity U_D [m/s]:

Bed Depth L [m]:

Hot Boundary Temp T_h [°C]:

Cold Boundary Temp T_c [°C]:

🧪 Solid & Fluid Thermal Properties

Solid Conductivity k_s [W/(m·K)]:

Fluid Conductivity k_f [W/(m·K)]:

Darcy-Forchheimer Convection Formulation:
• Effective Conductivity: k_e = φ k_f + (1 − φ) k_s
• Pressure Drop: ΔP = [ (μ/K) U_D + ρ (C_F/√K) U_D² ] · H
• Porous Nusselt: Nu = √(1 + 0.318 Pe_K) | Pe_K = U_D H / α_e
• Porous Rayleigh: Ra_K = (ρ g β ΔT K H) / (μ α_e)

📊 Porous Convection Results

📊 Output Summary
💾 Fortran Source

Total Heat Transfer Rate (Q̇)

Q̇ = 218.72 kW

Effective HTC: 87.5 W/(m²·K) | Nu = 72.53

k_e = 2.41 W/m·K

Forchheimer Pressure Drop (ΔP) 150.86 kPa Hydraulic resistance

Pumping Power (P_pump) 18.86 kW Mechanical energy required

Porous Rayleigh (Ra_K) 1.43e+2 Peclet Pe_K = 16538.9

Effective Conductivity (k_e) 2.413 W/(m·K) Volumetric mixture

📈 Porous Nusselt Nu vs Darcy Velocity U_D (m/s)

📉 Forchheimer Pressure Drop ΔP vs Velocity U_D (m/s)

=================================================================
 THERMOFLUIDCALC — POROUS MEDIA CONVECTION (DARCY-FORCHHEIMER) REPORT
=================================================================
Case Title                 : Deep Geothermal Sandstone Aquifer Hot Water Seepage
Porous Bed Dimensions      : Height H = 2.00 m, Width W = 5.00 m, Depth L = 5.00 m
Porous Matrix Properties   : Permeability K = 2.500e-11 m2, Porosity phi = 0.25
Effective Conductivity     : ke_eff = 2.413 W/(m.K) (ks = 3.00, kf = 0.65)
Filtration Conditions      : Darcy Velocity UD = 0.0050 m/s, DeltaT = 100.0 C
-----------------------------------------------------------------
POROUS NUSSELT NUMBER (Nu) : 72.528
Effective HTC (h_porous)   : 87.49 W/(m2.K)
TOTAL HEAT TRANSFER RATE Q : 218718.22 W (218.718 kW)
Forchheimer Pressure Drop  : 150859.40 Pa (150.859 kPa)
Filtration Pumping Power   : 18857.426 W
=================================================================

📘 Calculation Methodology & Porous Convection Standards

Darcy-Forchheimer Model

Combines linear viscous drag (Darcy law) and non-linear quadratic form drag (Forchheimer inertial term):

                    ∇P = − (μ/K) UD − ρ (CF/√K) UD²
                

Effective Thermal Conductivity

Represents the parallel/series mixture volume average of solid matrix and interstitial saturated fluid ($k_e = \phi k_f + (1-\phi) k_s$).

Key Engineering Assumptions

Homogeneous, isotropic porous matrix.
Local thermal equilibrium between fluid and solid phases ($T_f = T_s$).
Laminar and transitional filtration velocities ($Re_K = \frac{U_D \sqrt{K}}{\nu} < 10$).

ThermoFluidCalc Engineering Report