Yuxuan Chen
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Yuxuan Chen
中文
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S3 · SIMULATION

Pin-fin cold plate

Thermal resistance and pressure drop from tube-bank correlations

Thermal resistance Rth

0.00773K/W

Base top surface → coolant inlet

Pressure drop Δp
2.14kPa
Mean heat-transfer coefficient h̄
18,152W/(m²·K)
Reynolds number at V_max
2,040
Flow regime
Subcritical mixed

All inputs lie within the correlation rangesValidity ranges

Explore parameters
Pin-fin cold plate at the default values: base plate, staggered cylindrical pins, translucent cover and two manifoldsParametric illustrative model, simplified geometry

Preparing the 3D model

Drag / arrows to orbit · Scroll / +/- to zoom · Home to reset · Click to selectDrag to rotate · Pinch to zoom · Tap a part to select

Streamline sketch · top view

Illustrative, not CFD
Flow · Uniform flow plus a potential-flow doublet at each pin, to read the arrangement only. No wakes, separation, end-wall or side-wall effects.

R_th – Δp trade-off

Recalculated across the full slider range of the selected parameter, others held at their current values. Hollow points have at least one correlation outside its range.

0.0000.0050.0100.0150.0200.20.512510Δp (kPa, log scale)R_th (K/W)

Current: Flow rate 8.0 L/min · Rth 0.00773 K/W · Δp 2.14 kPa

Show data table
Flow rate (L/min)Rth (K/W)Δp (kPa)
20.01860.121
2.750.01580.236
3.50.01410.393
4.250.01070.591
50.009830.828
5.750.009151.10
6.50.008591.42
7.250.008131.76
80.007732.14
8.750.007392.55
9.50.007102.98
10.250.006843.45
110.006603.94
11.750.006394.46
12.50.006205.00
13.250.006035.56
140.005876.15
14.750.005726.76
15.50.005587.40
16.250.005468.05
170.005348.73
17.750.005239.42
18.50.0051210.1
19.250.0050310.9
200.0049311.6

Calculation details

Pins
240
Rows N_L × per row
20 × 12
Wetted area (pins + base)
12,064 + 3,246 mm²
Narrowest-section velocity V_max
0.67 m/s
Nu_D
57.7
C₁ · C₂
0.350 · 1.000
Fin efficiency η_f
0.404
Overall surface efficiency η_o
0.530
NTU · ε
0.27 · 0.234
Convective 1/(η_o hA)
0.00679 K/W
Coolant-rise resistance
0.000945 K/W
Outlet temperature
40.72 °C
ξ · main resistances N_W
0.485 · 20
Bulk properties ρ · c_p · k · μ · Pr
992 · 4180 · 0.629 · 0.648 mPa·s · 4.31
Pumping power
0.285 W
Base temperature @ Q
43.1 °C

Explore parameters

Volumetric flow. Heat load only sets the outlet and wall temperatures (Pr_s correction); its effect on resistance is small.

Coolant
8.0
2L/min20
40
25°C85
400
50W1500

Correlation validity

Every calculation checks whether the inputs lie inside the data range of each correlation; boundary values count as inside.

Zukauskas bank heat transfer

CheckCurrentValid rangeStatus
Re_D,max2,04010 – 2×10⁶Within
Pr4.310.7 – 500Within
10² ≤ Re < 10³ band2,040—Within
Rows N_L20≥ 20Within
S_T/S_L (in-line)1.00—Within

    Gaddis–Gnielinski pressure drop

    CheckCurrentValid rangeStatus
    Re₀2,0401 – 3×10⁵Within
    a = S_T/D2.001.25 – 3Within
    b = S_L/D2.000.6 – 3Within
    c (staggered diagonal ratio)2.24≥ 1.25Within
    Main resistances N_W20≥ 5Within
    Low-Re laminar part2,040≥ 1000Within

      1D pin conduction

      CheckCurrentValid rangeStatus
      Bi = hD/(4k)0.0233≤ 0.1Within

        Coolant property table

        CheckCurrentValid rangeStatus
        Mean bulk temperature40.4 °C5 – 150Within
        Mean wall temperature41.8 °C5 – 150Within
        Base temperature43.1 °C≤ 100Within

          Geometry

          CheckCurrentValid rangeStatus
          H/D4.00≥ 4Within

            Method

            Re uses the narrowest-section velocity V_max. The Zukauskas tube-bank correlation with its row correction gives the mean Nu and h. Pins are uniform fins with adiabatic tips; the uncovered base area uses the same h.

            An effectiveness–NTU relation gives the resistance from the base to the coolant inlet, iterating the mean bulk and wall temperatures. The Gaddis–Gnielinski bundle correlation gives the pressure drop of the array alone.

            Equations

            • Re_D,max = ρ V_max D / μ, V_max = S_T/(S_T − D) · V (or S_T/[2(S_D − D)] · V)
            • Nu_D = C₁ C₂ Re_D,max^m Pr^0.36 (Pr/Pr_s)^1/4, h = Nu_D k / D
            • η_f = tanh(mH)/(mH), m = √(4h / (k_f D)), η_o = 1 − (A_f/A)(1 − η_f)
            • NTU = η_o h A / C, C = ρ V_f c_p (V_f volumetric flow), ε = 1 − e^−NTU, R_th = 1 / (ε C)
            • Δp = ξ N_W ρ u₀² / 2, ξ = ξ_lam + (ξ_turb + f_n)[1 − e^−(Re+k₁)/k₂]

            Properties are interpolated in temperature (μ logarithmically). Water: saturated liquid, IAPWS-95 with the IAPWS viscosity and conductivity formulations. 50% ethylene glycol by mass: fit to Melinder (2010). Both were generated with CoolProp 8.0.0 and are cross-checked against Incropera Table A.6 in the unit tests.

            Assumptions and limits

            • Steady single-phase flow; the base top surface (pin roots) is isothermal. Base conduction and spreading are not included.
            • The cover touches the pin tips with no bypass; cover and side walls are adiabatic. Manifolds distribute uniformly and their losses are excluded.
            • The correlations come from long-tube banks and omit end-wall effects on short pins; Δp has no wall-viscosity correction.
            • Heat load sets only the outlet and wall (Pr_s) temperatures; the base temperature is an average estimate.

            References

            1. Incropera, DeWitt, Bergman, Lavine. Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, 2007 — §7.6 Eq. 7.58, Tables 7.5–7.6; §3.6 pin fins; Table A.6.
            2. Zukauskas, A. Heat transfer from tubes in crossflow. Advances in Heat Transfer 8 (1972) 93–160.
            3. Gaddis, E. S., Gnielinski, V. Pressure drop in cross flow across tube bundles. Int. Chem. Eng. 25 (1985) 1–15; VDI Heat Atlas, 2nd ed., 2010, Ch. L1.
            4. Melinder, Å. Properties of Secondary Working Fluids for Indirect Systems. IIR, 2010; Bell et al., CoolProp, Ind. Eng. Chem. Res. 53 (2014) 2498–2508.