Thermal Analysis Tool

Conduction

Steady-state heat conduction through flat walls, cylindrical walls, and spherical shells.

Geometry

Q = k · A · (T₁ − T₂) / L R = L / (k · A)

k — Thermal Conductivity W/(m·K)

A — Area m²

L — Thickness m

T₁ — Hot Side °C

T₂ — Cold Side °C

Common Thermal Conductivities (W/m·K)

Copper: 385–400

Aluminium: 200–237

Steel (mild): 45–52

Stainless 316: 13–16

Titanium: 16–22

Cast Iron: 40–55

Glass: 0.8–1.4

PTFE: 0.23–0.25

Nylon 6/6: 0.24–0.28

Epoxy: 0.2–0.5

Air (25°C): 0.026

Water (25°C): 0.607

Convection

Newton's law of cooling with direct h input, or estimate h via common correlations.

Mode

Q = h · A · (T_surface − T_fluid)

h — Conv. Coefficient W/(m²·K)

A — Surface Area m²

T_surface °C

T_fluid °C

Typical h Ranges (W/m²·K)

Free conv., air: 2–25

Forced conv., air: 25–250

Free conv., water: 50–1 000

Forced conv., water: 300–20 000

Boiling water: 3 000–100 000

Condensation steam: 5 000–100 000

Radiation

Radiative heat transfer using the Stefan-Boltzmann law.

Mode

Q = ε · σ · A · (T_s⁴ − T_surr⁴) σ = 5.670 × 10⁻⁸ W/(m²·K⁴)

ε — Emissivity 0 (mirror) → 1 (blackbody)

A — Surface Area m²

T_surface °C

T_surroundings °C

Typical Emissivity Values

Polished Al: 0.04–0.09

Oxidised Al: 0.20–0.35

Polished Cu: 0.02–0.05

Oxidised Cu: 0.60–0.85

Stainless (polish): 0.10–0.20

Stainless (oxidised): 0.50–0.80

Flat black paint: 0.93–0.97

White paint: 0.87–0.95

Anodised Al: 0.77–0.85

Human skin: 0.95–0.98

Thermal Resistance Network

Build a 1D series thermal circuit. Add conduction layers and convection surfaces, set T_hot and T_cold, and find temperatures at every node.

Boundary Temperatures

T_hot (Node 0) °C — left boundary

T_cold (Last Node) °C — right boundary

Resistance Layers

Conduction: enter L/k (thickness ÷ conductivity) and A — e.g. 3 mm aluminium: L/k = 0.003/200 = 1.5×10⁻⁵. Convection: h and A — R = 1/(h·A). Contact: enter R directly (K/W).

# Type Param 1 Param 2

Fin Analysis

Rectangular fin efficiency, heat transfer, and optional heat sink array analysis.

Mode

Rectangular fin, adiabatic tip: m = √(h · P / (k · A_c)) where P = 2(w+t), A_c = w·t η = tanh(m·L) / (m·L) Q_fin = η · h · P · L · (T_base − T_∞) Q_max = h · P · L · (T_base − T_∞)

Fin Length L m (height from base)

Fin Width w m (into page)

Fin Thickness t m

k — Fin Material W/(m·K)

h — Conv. Coeff. W/(m²·K)

T_base °C

T_ambient °C

Transient — Lumped Capacitance

Valid when Bi = h·Lc/k < 0.1. Models a thermally uniform solid heating or cooling in a fluid.

Inputs

θ(t) = (T_i − T_∞)·exp(−t/τ) → T(t) = T_∞ + θ(t) τ = ρ·V·cp / (h·A_s) Bi = h·(V/A_s) / k

ρ — Density kg/m³

cp — Specific Heat J/(kg·K)

k — Conductivity W/(m·K) — for Bi check

V — Volume m³

A_s — Surface Area m²

h — Conv. Coeff. W/(m²·K)

T_initial °C

T_fluid (ambient) °C

Evaluate at time t s

Target Temperature °C — time to reach

Common Material Properties

Materialρ (kg/m³)cp (J/kg·K)k (W/m·K)

Aluminium2700900200 Copper8960385390 Steel (mild)785049050 Stainless 316800050015 Titanium450052022 Water99841820.607