/thermal-engineering

name: pie-thermal-engineering
version: 1.0.0
description: "Thermal engineering for infrastructure: heat transfer (conduction, convection, radiation), cooling load analysis for data centers, heat exchanger sizing via LMTD and e-NTU, PUE/TUE/WUE efficiency metrics, and airflow management patterns. Activates for thermal analysis, data center cooling design, heat exchanger sizing, efficiency calculations, and airflow management."
user-invocable: true
allowed-tools: Read Grep Glob Bash
metadata:
  extensions:
    gsd-skill-creator:
      version: 1
      createdAt: "2026-02-26"
      triggers:
        intents:
          - "heat transfer"
          - "thermal"
          - "conduction"
          - "convection"
          - "radiation"
          - "cooling load"
          - "heat exchanger"
          - "LMTD"
          - "NTU"
          - "PUE"
          - "TUE"
          - "WUE"
          - "airflow"
          - "hot aisle"
          - "cold aisle"
          - "data center cooling"
          - "BTU"
        contexts:
          - "data center thermal analysis"
          - "infrastructure cooling design"
          - "thermal system optimization"
applies_to:
  - skills/physical-infrastructure/**
  - "*.calc"

Thermal Engineering Skill

At a Glance

Calculate heat transfer rates, size heat exchangers, and analyze data center thermal performance from component-level junction temperatures to facility-wide efficiency metrics.

**Activation:** InfrastructureRequest type='thermal', any heat exchanger sizing request, PUE/WUE calculation, airflow management design, or cooling load analysis.

**Key capabilities:**

• Three-mode heat transfer: conduction (Fourier), convection (Newton), radiation (Stefan-Boltzmann)
• Thermal resistance networks (series/parallel, analogous to electrical circuits)
• Data center cooling load breakdown (IT, UPS, lighting, fans, envelope)
• Heat exchanger sizing via LMTD and epsilon-NTU methods
• PUE/TUE/WUE/CUE efficiency metric calculations with target benchmarks
• Airflow management: hot/cold aisle containment, raised floor, economizer modes

**Integration:** Works in tandem with pie-fluid-systems: the fluid skill sizes cooling loop pipes and pumps; this skill quantifies the heat and determines exchanger performance.

> ENGINEERING DISCLAIMER: All calculations must be verified by a licensed Professional Engineer before use in construction or installation. HVAC and mechanical codes (ASHRAE 90.1, IMC) impose requirements not captured here. User assumes all responsibility for verification.

**Quick routing:** Heat transfer modes -- see Heat Transfer Fundamentals. Resistance networks -- see Thermal Resistance Networks. Data center loads -- see Data Center Cooling Load. Exchanger sizing -- see Heat Exchanger Sizing. PUE/WUE metrics -- see Efficiency Metrics. Airflow layout -- see Airflow Management.

---

Heat Transfer Fundamentals

Conduction -- Fourier's Law

Heat flow through a solid material by molecular vibration:

q = -k x A x (dT/dx)

| Variable | Definition | Units | |----------|-----------|-------| | q | Heat flow rate | W | | k | Thermal conductivity | W/(m K) | | A | Cross-sectional area perpendicular to heat flow | m^2 | | dT/dx | Temperature gradient | K/m |

The negative sign indicates heat flows from hot to cold (opposite to the temperature gradient).

**Thermal resistance (conduction):** R_cond = L / (k x A), analogous to electrical resistance R = rho L / A.

**Thermal conductivity reference values:**

| Material | k (W/(m K)) | Application | |----------|------------|-------------| | Copper | 385 | Heat sinks, cold plates | | Aluminum | 205 | Enclosures, fins, cold plates | | Carbon steel | 50 | Structural, pressure piping | | Stainless steel 304 | 16 | Corrosion-resistant piping | | Concrete | 1.4 | Building structure | | Gypsum board | 0.16 | Wall construction | | Mineral wool | 0.04 | Pipe insulation | | Polyurethane foam | 0.025 | Refrigeration insulation | | Thermal paste (TIM) | 1-8 | CPU/GPU mounting |

Convection -- Newton's Law of Cooling

Heat transfer between a surface and a moving fluid:

q = h x A x (T_surface - T_fluid)

| Variable | Definition | Units | |----------|-----------|-------| | q | Heat flow rate | W | | h | Convective heat transfer coefficient | W/(m^2 K) | | A | Surface area exposed to fluid | m^2 |

**Thermal resistance (convection):** R_conv = 1 / (h x A)

**Convective coefficient reference values:**

| Flow Type | Medium | h (W/(m^2 K)) | |-----------|--------|---------------| | Natural convection | Air | 5-25 | | Forced convection | Air | 25-250 | | Forced convection | Water (low velocity) | 500-2,000 | | Forced convection | Water (high velocity) | 2,000-10,000 | | Boiling | Water | 3,000-60,000 | | Condensing | Steam | 5,000-100,000 |

For convection correlations (Nusselt number, Reynolds, Prandtl relationships) -- @references/heat-transfer.md

Radiation -- Stefan-Boltzmann Law

Heat transfer by electromagnetic emission between surfaces:

q = epsilon x sigma x A x (T1^4 - T2^4)

| Variable | Definition | Units | |----------|-----------|-------| | epsilon | Surface emissivity (0 = perfect reflector, 1 = blackbody) | dimensionless | | sigma | Stefan-Boltzmann constant = 5.67e-8 | W/(m^2 K^4) | | T1, T2 | Surface temperatures | K (Kelvin only) |

**CRITICAL:** Temperatures MUST be in Kelvin for radiation calculations. K = C + 273.15.

**Emissivity reference values:**

| Surface | epsilon | Notes | |---------|--------|-------| | Blackbody (ideal) | 1.0 | Theoretical maximum | | Painted steel | 0.9 | Most painted surfaces | | Oxidized copper | 0.7 | Aged copper surfaces | | Glass | 0.9 | Window and enclosure glass | | Polished aluminum | 0.04 | Reflective radiation shield | | Anodized aluminum | 0.8 | Common enclosure finish |

**When radiation matters:** High temperatures (>200C), large temperature differentials, or vacuum/low-pressure environments. Usually negligible for data center oper