Heat Transfer: Conduction and Convection
Conduction is the transfer of thermal energy through a material by collisions between particles without bulk movement of the material, and convection is the transfer of thermal energy by the movement of a fluid (a liquid or gas) caused by differences in density. In brief: metals are good conductors because of their free electrons, and gases and air-filled materials are good insulators. In conduction, the rate of heat flow is P = kAΔT ÷ d. In convection, warmer, less dense fluid rises and cooler, denser fluid sinks, creating a circulating current.
A metal spoon in hot soup becomes hot, a radiator warms a whole room, and a double-glazed window reduces heat loss. All of these use conduction or convection. This guide explains both processes, gives the conduction formula, compares conductors and insulators in a table, works through a calculation for a window and corrects common mistakes.
How does conduction work?
When one end of a solid is heated, the particles there vibrate faster and pass energy to neighboring particles by collisions and by bonds. In metals, free (delocalized) electrons move through the lattice and carry energy rapidly, which is why metals feel cold to the touch (they conduct heat away from your hand quickly) and are good conductors. Non-metals conduct through lattice vibrations, and are poorer conductors. Gases are very poor conductors because the particles are far apart. Materials which trap air, such as wool, foam and fiberglass, are good insulators.
The rate of heat transfer through a layer of thickness d and area A, with a temperature difference ΔT across it, is P = kAΔT ÷ d, where k is the thermal conductivity (W/m·K). It is proportional to the area and temperature difference and inversely proportional to the thickness.
How does convection work?
When a fluid is heated, it expands and its density falls. The warmer fluid rises and the cooler, denser fluid sinks to take its place, producing a convection current. This happens in a kettle (heated at the bottom), in a room with a radiator, in the atmosphere (producing winds and sea breezes) and in ocean currents. Convection cannot occur in solids or in a vacuum, and needs gravity for the density differences to drive the flow (in free fall there is no natural convection). Forced convection uses fans or pumps, as in a central heating system or a fan oven.
Conductors and insulators compared
| Material | k (W/m·K) | Comment |
|---|---|---|
| Copper | about 400 | Excellent conductor |
| Aluminum | about 240 | Cooking pans, heat sinks |
| Glass | about 0.8 | Poor conductor |
| Water | about 0.6 | Poor conductor, but convects |
| Wood | about 0.1 to 0.2 | Insulator |
| Still air | about 0.026 | Very good insulator |
Worked example: heat loss through a window
A single-pane window of area 1.5 m2 and thickness 4.0 mm has a temperature of 20 °C on the inside surface and 0 °C on the outside surface. For glass k = 0.8 W/m·K.
- ΔT = 20 K and d = 4.0 × 10−3 m.
- P = kAΔT ÷ d = 0.8 × 1.5 × 20 ÷ 0.0040 = 24 ÷ 0.0040 = 6,000 W.
- Interpretation: this is an idealized figure for the conduction through the glass alone, with the surface temperatures fixed. In real windows the thin layers of air next to the glass reduce the temperature difference across the glass a lot, so the actual heat loss is much lower (a few hundred watts), but it shows why glass is a weak insulator.
- Double glazing traps a layer of air or argon between two panes. A 12 mm layer of still air (k = 0.026) with the same ΔT and area would give P = 0.026 × 1.5 × 20 ÷ 0.012 = 65 W, which is about 90 times less than the glass pane.
How was heat transfer studied?
Joseph Fourier developed the mathematical theory of heat conduction in 1822 in The Analytical Theory of Heat, which gave the equation of heat flow. Count Rumford studied convection in liquids in the 1790s. The Dewar flask (vacuum flask) was invented by James Dewar in 1892 to reduce all types of heat transfer.
Where is heat transfer used?
Cooking pans use conductors for the base and insulators for the handle. Houses use loft insulation and double glazing, and refrigerators have cooling coils at the top of the freezer to establish convection. Computers use heat sinks and fans to carry heat away from processors.
Which mistakes are common?
Mistake 1: Saying that metals feel cold because they are cold
Metals at room temperature conduct heat away from the skin faster than wood, so they feel colder, though both are at the same temperature.
Mistake 2: Thinking that “heat rises”
Hot fluid rises because it is less dense. Heat itself flows from hot to cold in any direction.
Mistake 3: Expecting convection in solids
Convection requires a fluid that can flow.
Mistake 4: Thinking that insulators stop heat transfer completely
They reduce the rate. Over time the heat still flows.