🚿 Impinging Jet Array Heat Transfer (Martin)

Compute impinging round nozzle array Nusselt number (Nu_avg), convective heat transfer coefficient (h), stagnation peak flux, and orifice pressure drop using Martin (1977) correlation.

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

Impinging Jet Array Heat Transfer (Martin)

Convection

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👁️ Views 39

⚡ Solves 30

💾 Downloads 399 📦 Fortran Code 10.8 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

🚿 Array of Impinging Nozzle Jets & Stagnation Cooling Layer

Real-time visual simulation of vertical high-speed fluid jets, target impingement spots & radial wall-jet spread

📝 Configuration & Presets

💻 CPU Micro-Jet Array 🔥 Turbine Vane Impingement 🌊 Steel Water Jet Quench 📜 Industrial Paper Dryer

📐 Nozzle Array Geometry

Nozzle Orifice Diameter d [mm]:

Nozzle Pitch S [mm]:

Nozzle-to-Plate Height H [mm]:

Jet Velocity U_j [m/s]:

🌡️ Thermal Boundary Conditions

Target Surface Temp T_s [°C]:

Coolant Jet Temp T_j [°C]:

💧 Fluid Thermophysical Properties

Density ρ [kg/m³]:

Viscosity μ [cP]:

Conductivity k [W/(m·K)]:

Specific Heat c_p [J/(kg·K)]:

Martin (1977) Array Formulation:
• Area Fraction: f = (π/4) / (S/d)²
• Average Nusselt: Nu = 2√f · [ (1 − 2.2√f) / (1 + 0.2(H/d − 6)√f) ] · 2 Re^0.5 (1 + 0.005 Re^0.55)^0.5 Pr^0.42
• Heat Flux: q″ = h_avg · (T_s − T_j) [kW/m²]
• Orifice Drop: ΔP ≈ 0.75 · ρ U_j² [kPa]

📊 Jet Impingement Results

📊 Output Summary
💾 Fortran Source

Average Heat Transfer Coeff (h_avg)

h = 395 W/(m²·K) (Peak = 526)

Average Heat Flux: 19.7 kW/m² | Nu_avg = 30.4

Re_d = 3,840

Stagnation Peak Nusselt (Nu₀) 40.4 Average Nu = 30.4

Nozzle Area Fraction (f) 3.14 % S/d = 5.0

Jet Discharge Pressure Drop 0.80 kPa 0.008 bar

Standoff Aspect Ratio (H/d) 4.00 Prandtl Pr = 0.72

📈 Average Nusselt Number Nu vs Jet Velocity U_j (m/s)

📉 Heat Transfer Coeff h [W/(m²·K)] vs Standoff H/d

=================================================================
 THERMOFLUIDCALC — IMPINGING JET ARRAY REPORT (MARTIN MODEL)
=================================================================
Case Title                 : High-Density Microprocessor Air Jet Impingement Array
Array Geometry             : d = 2.00 mm, S = 10.0 mm (S/d = 5.0), H = 8.0 mm (H/d = 4.0)
Discharge Conditions       : U_jet = 30.00 m/s, Re_d = 3840, Pr = 0.72, Area Fraction f = 3.14%
Thermal Conditions         : Target Ts = 75.0 C, Jet Tj = 25.0 C (DeltaT = 50.0 C)
-----------------------------------------------------------------
AVERAGE NUSSELT (Nu_avg)   : 30.36
STAGNATION PEAK NUSSELT    : 40.45
AVERAGE HTC (h_avg)        : 394.7 W/(m2.K)
PEAK STAGNATION HTC (h_0)  : 525.8 W/(m2.K)
AVERAGE HEAT FLUX (q")     : 19.73 kW/m2
Nozzle Pressure Drop DeltaP: 0.80 kPa (0.0080 bar)
=================================================================

📘 Calculation Methodology & Martin Impingement Standards

Martin (1977) Correlation

The standard correlation accounts for the interaction between neighboring jet fountains and cross-flow spent fluid resistance in periodic nozzle arrays:

                    Nu = 2√f · [ (1 − 2.2√f) / (1 + 0.2(H/d − 6)√f) ] · F(Re) · Pr0.42
                

Stagnation vs Wall-Jet Zone

Peak heat transfer occurs directly beneath the nozzle center ($Nu_0$). In arrays, spent cross-flow deflects outer jets and moderates area-averaged performance.

Key Engineering Assumptions

Square or hexagonal array of sharp-edged circular orifice nozzles.
Validity range: $2000 \le Re_d \le 100,000$, $0.004 \le f \le 0.04$, $2 \le H/d \le 12$.
Constant fluid thermophysical properties at film temperature.

ThermoFluidCalc Engineering Report