Thermal Conductivity Calculator
Enter conductivity k, area A, temp difference ΔT and thickness L to compute heat-transfer rate, thermal resistance and heat flux. Copper k=400, A=1, ΔT=100, L=0.01 → 4 MW.
Input Data
Results
At a glance:Fourier's law of heat conduction (Joseph Fourier, 1822, 'The Analytical Theory of Heat'): when a temperature difference is maintained across a material, the heat per unit time is Q/t=k·A·ΔT/L. k is thermal conductivity (W/(m·K), the material's ability to conduct heat), A is area, ΔT is the temperature difference and L is thickness. Microscopically, energy is passed from hotter to colder regions by molecular collisions (gases) or free electrons (metals, via the Wiedemann–Franz law k/σ=L₀T, L₀=2.44e-8) or phonons (insulators). Key relations: (1) thermal resistance R=L/(kA), analogous to electrical R=ρL/A, with ΔT=R·(Q/t) (Ohm's-law analogy); (2) heat flux q=Q/A=kΔT/L (heat per unit area); (3) series layers add R=ΣRᵢ, parallel add conductance 1/R=Σ1/Rᵢ — fully analogous to circuits. Conductivity ranges: metals 50–430 (silver 429, copper 400, aluminum 237, iron 80); alloys 10–100; semiconductors 1–100; ceramics/glass 1–2; water 0.6; polymers 0.1–0.5; gases 0.01–0.1 (air 0.026). Applications: (1) building insulation (glass wool, polyurethane); (2) electronics cooling (heatsinks, heat pipes); (3) heat-exchanger design; (4) A/C and fridge insulation; (5) vacuum flasks.
Formula
Fourier's law: Q/t = k·A·ΔT/L
Thermal resistance: R = L/(kA)
Heat flux: q = k·ΔT/L
Ohm analogy: ΔT = R·(Q/t)
Series: R_total = Σ Rᵢ = Σ Lᵢ/(kᵢA)
$$\frac{Q}{t} = \frac{k A \Delta T}{L}, \quad R = \frac{L}{kA}, \quad q = \frac{k\Delta T}{L}, \quad \Delta T = R \cdot \frac{Q}{t}$$How to Use
- Enter conductivity k (W/(m·K); copper 400).
- Enter area A (m²), temperature difference ΔT (K) and thickness L (m).
- The tool computes heat-transfer rate, thermal resistance and heat flux.
Case Studies
Computer CPU heatsink
CPU 100 W, copper heatsink k=400, A=0.01 m², L=0.01 m, ΔT=50 K → Q=400×0.01×50/0.01=2e4 W, far above need; a fan boosts it further.
Hong Kong's humid summers make PC cooling important; aluminum air coolers are common, water cooling uses copper channels.
Heat pipes exploit phase change (evaporation–condensation) with effective k~10,000 W/m·K, 25× copper — used in laptops and phones.
Building insulation and vacuum flask
Hong Kong summer indoor-outdoor ΔT=10 K. 10 cm glass-wool wall (k=0.04, A=10, L=0.1, ΔT=10) → Q=0.04×10×10/0.1=40 W, saving A/C.
Single glass window (k=1, A=2, L=0.005, ΔT=10) → Q=1×2×10/0.005=4000 W; double-glazed (air gap) drops below 100 W.
Vacuum flask: double silver-coated vacuum wall blocks conduction/convection, silver reflects radiation — keeps drinks hot 24 h.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.