Heat conduction

Heat moves three ways: conduction through solids and still fluids, convection with a moving fluid, and radiation as light (mostly infrared). This lesson is conduction.

Fourier's law says the heat flow through a flat wall is q = k × A × ΔT ÷ L, where k is the material's thermal conductivity in W/(m·K), A the area, ΔT the temperature difference across it and L its thickness. A 0.2 m brick wall (k = 0.8) of 10 m² with 20 K across it passes 0.8 × 10 × 20 ÷ 0.2 = 800 W.

Conductivities range hugely: copper about 400 W/(m·K), steel about 50, glass and brick about 1, water 0.6, mineral wool insulation about 0.04, still air 0.026. Insulation works by trapping air in small pockets so it can't move.

Write the law in the rate = driving force ÷ resistance form: q = ΔT ÷ R, with R = L ÷ (kA), in K/W. Layers one after the other are resistances in series and add: R_total = R₁ + R₂ + … That's how to work out an insulated pipe or a furnace wall made of several materials.

Firebrick 0.2 m thick (k = 1.0) on 1 m² has R = 0.2 K/W. Add 0.05 m of insulation (k = 0.05): R = 1.0 K/W. Total 1.2 K/W. With 600 K between inside and outside, q = 600 ÷ 1.2 = 500 W per m², against 3000 W without the insulation. The thin insulating layer does most of the work.