Convection and Radiation: Heat Transfer, Breezes and Flasks

How Heat Gets from One Place to Another

The Sun warms the Earth across 150 million kilometres of empty space. Cool breezes blow in from the sea on a hot afternoon. A pot of water heats up all the way through even though only its bottom touches the flame. A vacuum flask keeps tea hot for hours. These everyday facts are explained by the three ways heat travels: conduction, convection and radiation. This tutorial focuses on convection and radiation, as tested in WAEC, NECO and JAMB physics and in PHY 101: natural and forced convection, land and sea breezes, domestic hot-water systems, the nature of thermal radiation, good and bad absorbers and emitters, the vacuum flask, the greenhouse effect, and the Stefan–Boltzmann and Wien laws. Conduction is covered in detail in the tutorial on thermal conductivity.

The Three Methods of Heat Transfer

Conduction: heat passes through a material from particle to particle, without the material itself moving. It is most important in solids, especially metals.
Convection: heat is carried by the movement of the fluid itself (a liquid or a gas). It cannot happen in solids.
Radiation: heat travels as electromagnetic waves, mainly infrared. It needs no medium at all, so it can cross a vacuum.

Convection

When part of a fluid is heated, it expands, so its density decreases. The warmer, less dense fluid rises, and cooler, denser fluid sinks to take its place. This continuous circulation is a convection current, and it carries heat throughout the fluid.

Demonstrating convection

Drop a crystal of potassium permanganate into a beaker of water near one edge, and heat the water gently just below the crystal. A purple stream rises above the flame, moves across the top, sinks down the far side and returns along the bottom, tracing the convection current.

Natural and forced convection

Natural (free) convection is driven by density differences alone, as in a heated pot or rising warm air.
Forced convection uses a fan or pump to move the fluid, as in a car's radiator, a fan heater, a laptop's cooling fan or a blown-air oven. It transfers heat much faster.

Land and sea breezes

Land has a much lower specific heat capacity than water, so it heats up and cools down faster.

Sea breeze (daytime): the land becomes hotter than the sea. Air above the land is warmed, rises and is replaced by cooler air flowing in from the sea. This is why coastal cities such as Lagos enjoy cool afternoon breezes.
Land breeze (night): the land cools faster and becomes colder than the sea. Air above the warmer sea rises, and cooler air flows out from the land towards the sea. Fishermen have traditionally used the land breeze to sail out before dawn.

Other applications of convection

Domestic hot-water systems: the boiler is at the bottom. Hot water rises up the flow pipe to the top of the storage tank, and cold water sinks back down the return pipe. Hot water is drawn off from the top of the tank.
Refrigerators: the freezing compartment is at the top. Air cooled there becomes denser and sinks, setting up a current that cools the whole cabinet.
Ventilation: warm, stale air rises and leaves through high openings, while fresh air enters lower down. Air vents above windows and doors use this effect.
Heaters and air conditioners: heaters work best near the floor, and air conditioners near the ceiling, so that convection spreads their effect around the room.
Weather: rising warm air forms clouds and thunderstorms, and large convection currents drive global winds.

Radiation

Thermal radiation is energy emitted by every object above absolute zero in the form of electromagnetic waves, mostly infrared at everyday temperatures. It travels at the speed of light, needs no medium, and is absorbed by surfaces it falls on, which then warm up. Hotter objects emit far more radiation, and very hot objects (above about 500 °C) also emit visible light, glowing first red and then white.

Good and bad absorbers and emitters

Dull black surfaces are the best absorbers and the best emitters of radiation.
Shiny, white or silvered surfaces are the poorest absorbers and emitters. They reflect most of the radiation that falls on them.
A good absorber is always a good emitter at the same temperature.

This can be shown with a Leslie cube, a metal cube whose four faces are dull black, shiny black, dull white and polished silver. Filled with hot water, all four faces are at the same temperature, but a radiation detector (a thermopile or infrared thermometer) shows that the dull black face emits the most and the polished face the least.

Applications of radiation

White or light-coloured clothes and buildings stay cooler in strong sunshine, and aluminium roofing sheets reflect much of the sunlight that falls on them.
Solar water heaters have black pipes and panels to absorb as much sunlight as possible.
Cooling fins on engines and radiators are often painted black, to emit heat well.
Emergency foil blankets are shiny, to reduce heat lost from the body by radiation.
Thermal imaging cameras detect the infrared radiation that people and animals emit, even in total darkness.

The Vacuum Flask

A vacuum (Thermos) flask keeps hot drinks hot, and cold drinks cold, by reducing all three methods of heat transfer:

The vacuum between the double glass walls stops conduction and convection, because there are no particles to carry heat.
The silvered inner surfaces of the walls reduce radiation, by reflecting infrared back towards the contents.
The stopper, made of cork or plastic (poor conductors), reduces conduction and stops convection and evaporation from the top.
The glass walls are thin, and the walls touch only at the neck, which limits conduction.
Insulating supports (often felt or plastic) hold the fragile glass vessel in its protective case.

The Greenhouse Effect

Short-wavelength radiation from the very hot Sun passes easily through glass. Inside a greenhouse, it is absorbed by the soil and plants, which warm up and re-emit radiation. Because they are much cooler than the Sun, they emit longer-wavelength infrared, which glass does not let through. The energy is trapped, and the greenhouse warms up. A car parked in the sun heats up for the same reason.

Earth's atmosphere behaves similarly. Gases such as carbon dioxide, methane and water vapour let sunlight through but absorb the infrared emitted by the warm ground. Without this natural greenhouse effect, Earth would be about 33 °C colder. Burning fossil fuels and gas flaring add extra greenhouse gases, strengthening the effect and causing global warming.

Radiation Laws (PHY 101)

The Stefan–Boltzmann law

The power radiated by a surface depends very strongly on its absolute temperature:

P = σAeT⁴

Here σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ is the Stefan–Boltzmann constant, A is the surface area, T is the temperature in kelvin, and e is the emissivity, from 1 for a perfect black body down to almost 0 for a perfect reflector. Because of the fourth power, doubling the absolute temperature multiplies the radiated power by 2⁴ = 16.

Worked example 1

A black sphere of surface area 0.010 m² is at 1000 K. Find the power it radiates.

P = 5.67 × 10⁻⁸ × 0.010 × 1 × 1000⁴ = 567 W.

Net radiation

An object also absorbs radiation from its surroundings at temperature T₀, so its net loss is P = σAe(T⁴ − T₀⁴).

Worked example 2

A person has a skin area of 1.8 m², emissivity 0.97 and skin temperature 33 °C, in a room at 20 °C. Estimate the net power lost by radiation.

T = 306 K and T₀ = 293 K, so P = 5.67 × 10⁻⁸ × 1.8 × 0.97 × (306⁴ − 293⁴) ≈ 138 W.

That is comparable to the body's resting heat output, which is why radiation is a major way we lose heat, and why clothing makes such a difference.

Wien's displacement law

The wavelength at which an object radiates most strongly is inversely proportional to its absolute temperature:

λ(max) × T = 2.9 × 10⁻³ m K

Worked example 3

The Sun's surface is at about 5800 K. The human body is at about 310 K. Find the peak wavelength of each.

Sun: λ(max) = 2.9 × 10⁻³ ÷ 5800 = 5.0 × 10⁻⁷ m = 500 nm, in the middle of the visible spectrum.

Body: λ(max) = 2.9 × 10⁻³ ÷ 310 ≈ 9.4 × 10⁻⁶ m, about 9.4 μm, in the far infrared. This is the radiation that thermal cameras and infrared thermometers detect, and it explains the greenhouse effect: the Sun's radiation and the Earth's radiation have very different wavelengths.

Common Mistakes with Convection and Radiation

Saying "heat rises". Hot fluid rises because it is less dense. Heat itself can travel in any direction.
Describing convection in solids. Convection needs a fluid that can flow.
Getting the breezes the wrong way round. The sea breeze blows from the sea by day, and the land breeze from the land at night.
Thinking radiation needs air. It travels best through a vacuum.
Using °C in the Stefan–Boltzmann or Wien laws. Temperatures must be in kelvin.

Convection and Radiation: Practice Questions

Explain why the freezing compartment of a refrigerator is placed at the top.
Why does a sea breeze blow during the day?
Give two features of a vacuum flask and the method of heat transfer each one reduces.
Why are solar water-heater panels painted black?
A black body at 500 K radiates 200 W. What power does it radiate at 1000 K?
Find the peak wavelength emitted by a star with a surface temperature of 10,000 K.

Answers: 1. Air cooled at the top becomes denser and sinks, setting up convection currents that cool the whole cabinet. 2. The land heats up faster than the sea. Warm air over the land rises, and cooler air flows in from the sea to replace it. 3. Any two of: the vacuum (conduction and convection), the silvered walls (radiation), the stopper (conduction, convection and evaporation). 4. Dull black surfaces are the best absorbers of radiation. 5. The temperature doubles, so the power rises by 2⁴ = 16 times, to 3200 W. 6. 2.9 × 10⁻³ ÷ 10,000 = 2.9 × 10⁻⁷ m, or 290 nm (ultraviolet), so the star looks blue-white.

Conclusion

Convection carries heat by the movement of fluids: warmed fluid becomes less dense and rises, setting up convection currents that explain land and sea breezes, hot-water systems, refrigerators and ventilation. Radiation carries heat as infrared electromagnetic waves, even through a vacuum. Dull black surfaces absorb and emit best, while shiny surfaces reflect. The vacuum flask beats all three heat-transfer methods, the greenhouse effect traps long-wavelength infrared, and at university level, the Stefan–Boltzmann law P = σAeT⁴ and Wien's law λ(max)T = 2.9 × 10⁻³ m K make radiation quantitative.