Heat Conduction (Fourier)
Heat conducted through a slab over time.
Formula
Variables
How it works
This relation gives the amount of heat energy that flows by conduction through a flat slab when one face is hotter than the other. It comes from Fourier’s law, which says the heat flow rate is proportional to the temperature gradient: a larger temperature difference, a better conductor, a larger area, or more time all increase the heat transferred, while a thicker slab reduces it. The formula assumes steady one-dimensional conduction through a uniform material, so the temperature profile across the slab is effectively linear.
When to use it
Use this for steady heat transfer through walls, panes, insulation layers, or any flat material where heat moves mainly straight across from a hot side to a cold side. It is especially useful in thermal engineering, building heat-loss estimates, and materials problems involving conductivity.
Worked example, step by step
A 2.0 cm thick glass window has area 1.5 m². The inside surface is at 20°C and the outside surface is at 5°C, and the thermal conductivity of glass is 0.80 W m⁻¹ K⁻¹. Find the heat conducted in 10 minutes. Step 1: Convert to SI units. d = 2.0 cm = 0.020 m t = 10 min = 600 s ΔT = 20 - 5 = 15 K Step 2: Substitute into Q = kAΔT t / d. Q = (0.80)(1.5)(15)(600) / 0.020 Step 3: Calculate the numerator. 0.80 × 1.5 = 1.2 1.2 × 15 = 18 18 × 600 = 10800 Step 4: Divide by thickness. Q = 10800 / 0.020 = 540000 J Final answer: Q = 5.4 × 10^5 J of heat is conducted through the glass in 10 minutes.
Common mistakes to avoid
- Using Celsius temperature values directly instead of the temperature difference
- Forgetting to convert thickness, area, or time into SI units before substituting
- Confusing heat energy Q with heat rate, which would be Q/t = kAΔT/d
Did You Know?
Metal feels colder than wood at the same temperature only because it conducts heat from your hand far faster.
Share this formula
More in Thermodynamics & Heat
View allHeat Energy
BasicHeat needed to change a substance’s temperature.
Latent Heat
IntermediateHeat for a phase change at constant temperature.
Ideal Gas Law
IntermediateRelates pressure, volume, moles and temperature.
Boyle's Law
BasicPressure and volume are inversely related at constant T.
Charles's Law
BasicVolume is proportional to temperature at constant P.
Gay-Lussac's Law
IntermediatePressure is proportional to temperature at constant V.