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How It Works
Fourier's law of heat conduction states that heat flows from hot to cold at a rate proportional to the temperature difference and the material's conductivity: q = K × ΔT / x. Knowing any three of these variables lets you solve for the fourth.
High-conductivity materials like copper (K ≈ 385 W/(m·K)) transfer heat quickly, while insulators like fiberglass (K ≈ 0.04) resist heat flow. This equation is the foundation of building insulation design, electronics cooling, and industrial heat exchanger sizing.
Example Problem
A 0.15 m thick brick wall (K = 0.72 W/(m·K)) separates a 22 °C interior from −5 °C outside. What is the heat loss per square meter?
- Temperature differential: ΔT = 22 − (−5) = 27 °C
- Apply the formula: q = 0.72 × 27 / 0.15
- Result: q = 129.6 W/m²
Adding 0.10 m of fiberglass insulation (K = 0.04) would dramatically reduce this to about 10 W/m², showing why insulation matters.
Frequently Asked Questions
What is thermal conductivity and what does it measure?
Thermal conductivity (K) measures how well a material conducts heat. It is defined as the amount of heat (in watts) that passes through a 1-meter thickness of material per square meter of area for each degree of temperature difference. Higher values mean the material transfers heat more readily.
What is the thermal conductivity of common building materials?
Concrete has K ≈ 1.0 W/(m·K), brick about 0.72, wood around 0.12–0.17, fiberglass insulation 0.04, and still air 0.026. Engineers use these values to design walls, roofs, and insulation layers that meet energy codes.
How does thickness affect heat transfer through a wall?
Heat transfer rate is inversely proportional to thickness. Doubling the wall thickness cuts the heat flow in half, which is why adding insulation is one of the most effective ways to reduce energy loss in buildings.
What is the difference between thermal conductivity and thermal diffusivity?
Conductivity (K) measures how much heat a material transfers per unit time, while diffusivity (α = K/(ρ·cp)) measures how fast temperature changes propagate through it. A material can conduct a lot of heat but change temperature slowly if it has high density and heat capacity.
Related Calculators
- Thermal Diffusivity Calculator — find how quickly temperature changes propagate through a material.
- Thermal Expansion Calculator — calculate length or volume changes due to temperature.
- Specific Gas Constant Calculator — determine the gas constant for a particular gas.
- Fourier Number Calculator — dimensionless time for transient heat conduction analysis.
- Energy Unit Converter — convert heat energy between joules, BTU, and calories.
References:
Incropera, Frank P. & DeWitt, David P. 2002. Fundamentals of Heat and Mass Transfer. John Wiley & Sons. 5th ed.
Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th ed.