LGA1700-Water-Block-1D-Thermal-Model

1D thermal resistance network for CPU cold plate optimization, calibrated against CFD simulations. Enables rapid parametric design studies to identify thermal bottlenecks and evaluate design modifications without re-running expensive 3D CFD (see my other repo: LGA1700-Water-Block-CFD-Simulation)

A two-zone thermal resistance network model for CPU cold plate analysis, calibrated against high-fidelity CFD simulations. This tool enables rapid parametric design optimization without the computational cost of re-running 3D CFD.

Temperature distribution from CFD

Overview

This project demonstrates a typical thermal engineering workflow:

1. 3D CFD provides high-fidelity physics and calibration data
2. 1D resistance network enables instant parametric studies and bottleneck identification
3. Design optimization through rapid "what-if" scenarios

The model accurately predicts CPU temperature, outlet temperature, and heat distribution for a jet-impingement cold plate with porous fin arrays.

Key Features

• CFD-Calibrated: Validated against LGA1700-Water-Block-CFD-Simulation
• Fast Parametric Studies: Instant evaluation of design changes
• Thermal Bottleneck Identification: Quantifies resistance contributions
• Design Optimization Scenarios: Pre-configured "what-if" studies

Model Architecture

Two-Zone Thermal Resistance Model:

        [ CPU ]
           │
    ( R_contact )
           │
        [ Plate ]
           │
      ┌────┴────┐
      │         │
 R_path,1   R_path,2
      │         │
 [ Fluid 1 ] [ Fluid 2 ]
    (Tb1)       (Tb2 = Tout)

Fluid heating: Tin → Tb1 → Tb2
Heat split: Q1 → Fluid 1, Q2 → Fluid 2

Physics Captured:

• Contact resistance (CPU ↔ cold plate interface)
• Conduction through copper plate
• Convective heat transfer to coolant (water)
• Cumulative fluid heating through zones

Results

Baseline Performance (CFD-Validated)

• CPU Temperature: 73.2°C (346.3 K)
• Outlet Temperature: 32.8°C (305.98 K)
• Heat Load: 250 W
• Mass Flow Rate: 0.01 kg/s

Thermal Resistance Breakdown

Component	Resistance (K/W)	% of Total
Contact Resistance (CPU ↔ Plate)	0.1414	76.3% ← Primary bottleneck
Thermal Paths (Plate ↔ Fluid)	0.0438	23.7%
- Parallel combination	0.0208	-
-- Porous zone path	0.0217	-
-- Outlet zone path	0.4982	-
Total System Resistance	0.1852	100%

Key Finding

Contact resistance dominates thermal performance. Improving the CPU-to-cold plate interface has 10× greater impact than adding fins or increasing flow rate.

Parametric Sensitivity

Contact Resistance (TIM Quality)

R_contact	CPU Temp	ΔT from baseline
0.01 K/W (excellent TIM)	40.3°C	-32.9°C
0.05 K/W (good TIM)	50.3°C	-22.9°C
0.14 K/W (baseline)	73.2°C	0°C
0.30 K/W (poor TIM)	112.8°C	+39.7°C

Mass Flow Rate

Flow Rate	CPU Temp	ΔT
0.005 kg/s (half)	78.9°C	+5.8°C
0.01 kg/s (baseline)	73.2°C	0°C
0.02 kg/s (double)	70.3°C	-2.9°C

Fin Area

Area Multiplier	CPU Temp	ΔT
0.5× (half fins)	77.8°C	+4.6°C
1.0× (baseline)	73.2°C	0°C
5.0× (5× fins)	69.2°C	-4.0°C
10.0× (10× fins)	68.7°C	-4.5°C

Design Optimization Scenarios

Scenario	Modifications	CPU Temp	Reduction
Baseline	-	73.2°C	-
Improved TIM	R_contact = 0.05 K/W	50.3°C	-22.9°C
Higher Flow	2× mass flow	70.3°C	-2.9°C
More Fins	5× fin area	69.2°C	-4.0°C
COMBINED	All improvements	44.1°C	-29.1°C

Installation

# Clone repository
git clone https://github.com/ultravis66/LGA1700-Water-Block-1D-Thermal-Model.git
cd LGA1700-Water-Block-1D-Thermal-Model

# Install dependencies
pip install -r requirements.txt

# Run analysis
python coldplate_thermal_analysis.py

Requirements:

• Python 3.7+
• NumPy
• SciPy

Usage

Basic Usage

Run the complete parametric study:

python coldplate_thermal_analysis.py

Custom Analysis

from coldplate_thermal_analysis import ThermalParams, coldplate_2zone_model

# Define your parameters
params = ThermalParams(
    Q_total=250.0,       # Heat load [W]
    mdot=0.01,           # Mass flow rate [kg/s]
    Tin=300.0,           # Inlet temperature [K]
    R_contact=0.05,      # Contact resistance [K/W] - improved TIM
    # ... other parameters
)

# Run model
result = coldplate_2zone_model(params)
print(f"CPU Temperature: {result.Tcpu:.2f} K")

Calibration Methodology

The effective heat transfer coefficients were calibrated to match CFD results:

1. CFD Simulation

   • 3D conjugate heat transfer
   • Porous media model for fin array
   • Validation: CPU temp = 346.3 K

2. 1D Model Calibration:

   • Minimize residuals: (T_cpu^1D - T_cpu^CFD)² + (Q_porous^1D - Q_porous^CFD)²
   • Calibrated h_porous = 1.18×10⁶ W/m²-K (effective)
   • Calibrated h_outlet = 6.99×10³ W/m²-K

3. Validation:

   • CPU temperature error: 0.0 K
   • Outlet temperature error: 0.1 K
   • Energy balance: 250.0 W (exact)

Note: The calibrated h-values are effective parameters that lump complex porous medium physics (volumetric heat transfer, turbulent mixing, fin effects) into simplified convective coefficients.

Engineering Insights

Why Contact Resistance Dominates

With 76.3% of total thermal resistance, the CPU-to-cold plate interface is the primary bottleneck. This occurs because:

• Limited metal-to-metal contact (surface roughness)
• Thermal interface material (TIM) has lower conductivity than copper
• Interface area is fixed by CPU dimensions

Diminishing Returns on Fins/Flow

The porous zone already has excellent heat transfer (R = 0.0217 K/W). Further improvements yield minimal benefit because:

• Heat must first cross the contact resistance bottleneck
• Additional fins can't access heat trapped at the interface
• Classic series resistance limitation: R_total ≈ R_largest

Practical Design Recommendations

1. Priority 1: Optimize TIM selection and application
2. Priority 2: Maximize contact pressure (within CPU limits)
3. Priority 3: Consider flow rate increase (modest benefit, low cost)

Model Validation

The 1D model was validated against additional CFD simulations with varying contact resistance to confirm predictive capability beyond the calibration point.

Validation Results

Case	R_contact (K/W)	CPU Temp - CFD (°C)	CPU Temp - 1D (°C)	Error (°C)
Improved TIM	0.059	50.7	50.3	0.4
Baseline	0.148	73.2	73.2	0.0

Case	mdot (kg/s)	CPU Temp - CFD (°C)	CPU Temp - 1D (°C)	Error (°C)	ΔT_coolant CFD (°C)	ΔT_coolant 1D (°C)
High Flow	0.04	69.53	68.85	0.68	1.47	1.49

Key Findings:

• Model accurately predicts temperature across a 2.5× range in contact resistance
• Maximum error: 0.4°C (0.5% of temperature rise)
• Validates use of calibrated effective h-values for parametric design studies

This demonstrates the model is predictive, not merely curve-fit to a single operating point. The 1D approach is suitable for rapid design trade studies when exploring TIM selection, fin geometry, or flow rate modifications.

Related Projects

• LGA1700-Water-Block-CFD-Simulation - High-fidelity 3D CFD validation

Technical Background

This model demonstrates a common thermal engineering workflow where:

• CFD provides truth data but is computationally expensive (hours per run)
• 1D models enable rapid iteration (milliseconds per run)
• Calibration bridges the gap between fidelity and speed

Calibration Methodology

The effective heat transfer coefficients were calibrated using CFD results:

Running the Calibration

python calibrate_h_values.py

This script:

1. Takes CFD target values (Tcpu, heat split)
2. Solves inverse problem to find h-values that match
3. Uses scipy.optimize.fsolve to minimize residuals
4. Outputs calibrated coefficients for use in main analysis

Calibration Results

• h_porous = 1.18×10⁶ W/m²-K (effective)
• h_outlet = 6.99×10³ W/m²-K

Note: These are effective parameters that lump complex porous medium physics into simplified convective coefficients.

Author

if you use this work, please cite:

@misc{coldplate1d2025,
  author = {Stolk, Mitchell},
  title = {LGA1700 Water Block 1D Thermal Model},
  {2025},
  publisher = {GitHub},
  url = {https://github.com/ultravis66/LGA1700-Water-Block-1D-Thermal-Model}
}