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Heat Transfer: Conduction, Convection, Radiation

Thermodynamics

Heat moves in three ways: conduction through a material, convection by moving fluid, and radiation as electromagnetic waves. Most real situations involve more than one of them.

Q/t = k A delta T / d
Rate of conduction through a slab of conductivity k, area A, thickness d, temperature difference delta T.
P = epsilon sigma A T^4
Radiated power, with emissivity epsilon, Stefan-Boltzmann constant sigma = 5.67 x 10^-8 W/m^2 K^4, and absolute temperature T.

Conduction

Conduction is the transfer of heat through a material by collisions between neighbouring particles, without the material itself moving. In metals, free electrons carry energy quickly from the hot end to the cold end, which is why a metal spoon in hot soup soon feels hot at the handle. Insulators such as wood, plastic and air conduct poorly, because their particles are not free to move energy along. The rate of conduction increases with the temperature difference and the area, and decreases with thickness. A thick woollen jumper works by trapping still air, which is a poor conductor.

Convection

Convection is the transfer of heat by the bulk movement of a fluid, a liquid or a gas. When a fluid is heated it expands, becomes less dense and rises, while cooler fluid sinks to take its place, setting up a circulation called a convection current. This is how a radiator warms a room, how a kettle heats all its water, and how sea breezes form. Convection only happens in fluids, because solids cannot flow. Forced convection, such as a fan blowing air over a hot component, speeds the process up by moving the fluid mechanically rather than waiting for natural buoyancy.

Radiation

Radiation is the transfer of energy by electromagnetic waves, mainly infrared, and it needs no medium at all, so it can cross a vacuum. Every object emits thermal radiation, with hotter objects emitting more and at shorter wavelengths. Dark, matt surfaces absorb radiation well and also emit it well, while shiny, light surfaces reflect it. The Sun warms Earth by radiation, a campfire warms you mainly by radiation, and a thermos flask cuts heat loss by using a vacuum to stop conduction and convection and shiny walls to reduce radiation. All three mechanisms act together in most everyday heating and cooling.

📝 Worked example: conduction through a wall

Heat conducts through a wall of area A = 2.0 m^2 and thickness d = 0.10 m. Thermal conductivity k = 0.80 W/m K, temperature difference delta T = 20 K. Use rate of heat flow Q/t = k A delta T / d. Substitute: Q/t = 0.80 x 2.0 x 20 / 0.10. Numerator: 0.80 x 2.0 x 20 = 32. 32 / 0.10 = 320 W. So heat flows through the wall at 320 W. Doubling the thickness would halve the rate to 160 W.

Common mistakes

Practice questions

  1. If the temperature difference across a wall doubles, what happens to the rate of heat flow?
    Show answer

    The rate doubles, because Q/t is proportional to delta T.

  2. How does heat from the Sun reach Earth?
    Show answer

    Radiation, because it needs no medium and the Sun's heat crosses the vacuum of space.

  3. Why does a radiator warm a whole room, not just the air next to it?
    Show answer

    Hot water rises and cool water sinks, setting up a circulation that carries heat around the room.

Frequently asked questions

Can all three types of heat transfer be stopped at once?

Yes, that is what a thermos does: a vacuum stops conduction and convection, and shiny walls reduce radiation.

Why is there no convection in a solid?

Convection needs a fluid that can move; in a solid the particles cannot flow, so conduction is the main route.