Diamond Heat Spreader Simulator

Steady-State Thermal Analysis Engine

LIVE
Top-Down Thermal Map
10°C40°C70°C100°C130°C160°C
Cross-Section
Layer Temperature Stack
GPU Junction
44.9°C
Die Bottom
42.5°C
TIM Top
41.8°C
TIM Bottom
38.2°C
Diamond Top
37.4°C
Diamond Bottom
36.1°C
Channel Surface
36.1°C
Coolant
22°C
Physics Reference
1. Fourier’s Law of Heat Conduction
q = k · A · ΔT / L

Heat flux (W) through a material. k = thermal conductivity (W/m·K), A = area (m²), ΔT = temperature difference (K), L = thickness (m).

2. Thermal Resistance (Conduction)
R_cond = L / (k · A) [K/W]

Each layer contributes series resistance. R_total = R_die + R_contact + R_tim + R_diamond + R_conv.

3. Newton’s Law of Cooling
q = h · A · (T_s − T_amb)

h = convective heat transfer coefficient. Base: ~25 W/m²K (air), ~5000 W/m²K (liquid). Microchannels enhance h.

4. Convection Resistance
R_conv = 1 / (h_eff · A_eff) [K/W]

h_eff includes microchannel enhancement. A_eff = spreader area × fin area multiplier.

5. Spreading Resistance (Kennedy)
R_spread = φ(ε) / (√π · k · 2a)

Where ε = a/b (die-to-spreader ratio), φ(ε) = (1−ε)(1 + 0.68ε + 0.16ε²). Models heat spreading from a small die to a larger substrate.

6. Contact Thermal Resistance
R_c = R″_c / A

R″_c ≈ 1×10⁻⁶ m²K/W (polished) or 8×10⁻⁶ (rough). Surface roughness directly impacts interface resistance.

7. Microchannel Enhancement
h_eff = h_base · f_cov · f_AR · f_n · f_geo

Multiplicative factors: coverage (1+2.5c), aspect ratio (1+0.3·min(AR,10)), count, geometry (grid 1.8×, sinusoidal 2.0×, fractal 1.6+0.5n).

8. Doping Effect
k_eff = k_base · f_doping(ppm)

Impurities scatter phonons. Boron: −0.01%/ppm. Nitrogen: −0.025%/ppm. Hydrogen: +0.005%/ppm (defect passivation).

9. Junction Temperature
T_j = T_amb + P · R_total [°C]

Fundamental equation. Junction temp = ambient + power × total thermal resistance. Hotspots add localized intensity.

10. Reynolds Number (Microchannels)
Re = ρ · v · D_h / μ

v = Q/(n·A_ch), D_h = 2dw/(d+w). Water: ρ=997 kg/m³, μ=8.9×10⁻⁴ Pa·s. Re<2300 = laminar, Re>2300 = turbulent.

11. Nusselt Number → h
Nu = 0.023·Re⁰·⁸·Pr⁰·⁴ (turb) | Nu = 1.86·Gz¹΄³ (lam)

Dittus-Boelter for turbulent, Shah for laminar developing flow. h = Nu·k_f/D_h where k_f=0.607 W/mK (water). Pr=6.13.

12. Pressure Drop
ΔP = f · (L/D_h) · (ρv²/2)

f = 64/Re (laminar Poiseuille) or 0.316/Re¹΄⁴ (Blasius turbulent). L = channel length ≈ spreader width. Higher flow → better h but more ΔP.

Simplifications

1D thermal resistance network with 2D spreading approximations. Does not solve full 3D heat equation or Navier-Stokes. Qualitatively accurate for comparative analysis—not a replacement for CFD/FEA design validation.