Conduction is the transfer of thermal energy through a material because of a temperature difference. In engineering, it helps predict how fast heat leaks through walls, pipes, electronics, engine parts, and insulation. Fourier's law is the main equation used to connect heat flow to material properties, wall thickness, area, and temperature difference.
Understanding it lets designers control heating, cooling, energy loss, and safety.
Key Facts
- Fourier's law in one dimension: q = -kA dT/dx
- For a flat wall at steady state: q = kA(T1 - T2)/L
- Heat flux is heat rate per area: q'' = q/A = k(T1 - T2)/L
- Thermal resistance of a plane wall: Rcond = L/(kA)
- Using thermal resistance: q = (T1 - T2)/Rcond
- The negative sign in q = -kA dT/dx means heat flows from higher temperature to lower temperature.
Vocabulary
- Conduction
- Conduction is heat transfer through a material by microscopic collisions and energy exchange between particles.
- Thermal conductivity
- Thermal conductivity, k, measures how easily a material conducts heat.
- Temperature gradient
- The temperature gradient, dT/dx, is the rate at which temperature changes with position.
- Heat flux
- Heat flux is the heat transfer rate per unit area, usually measured in W/m2.
- Steady state
- Steady state means temperatures at each location do not change with time even though heat may still be flowing.
Common Mistakes to Avoid
- Using Celsius differences incorrectly is wrong only when absolute temperatures are needed, but temperature differences in Celsius and kelvin have the same size. For conduction through a wall, ΔT = 20 C is the same as ΔT = 20 K.
- Forgetting the wall area gives the wrong heat rate because Fourier's law for total heat transfer includes A. A larger wall conducts more total heat under the same temperature difference.
- Putting thickness in centimeters instead of meters causes unit errors. Convert L to meters when using k in W/(m K) so the answer comes out in watts.
- Treating the temperature as curved in a simple steady wall is incorrect when k is constant and there is no internal heat generation. In that case, temperature changes linearly from T1 to T2.
Practice Questions
- 1 A brick wall has k = 0.72 W/(m K), area A = 12 m2, thickness L = 0.20 m, T1 = 25 C, and T2 = 5 C. Find the steady heat transfer rate through the wall.
- 2 A 0.05 m thick insulation panel with area 3.0 m2 conducts 18 W when its two faces are at 40 C and 10 C. Find its thermal conductivity k.
- 3 Two slabs have the same area and thickness and the same temperature difference across them. Slab A has k = 2 W/(m K), and slab B has k = 0.2 W/(m K). Explain which slab is better insulation and why.