Heat carried by moving fluid
Hold your hand a few centimetres above a hot tawa. It feels hot at once. Hold it the same distance to the side of the tawa, and it feels much less. Radiation goes out to the side as well as up, so it cannot explain the difference. The extra heat above the tawa is carried by the air itself, which rises from the hot surface. This is convection.
Follow the air step by step. The air touching the tawa is warmed by conduction. Warm air expands, so its density falls below that of the cooler air around it. The chapter on Fluids showed that a body lighter than the fluid around it is pushed up by the upthrust. So the warm air rises, and cooler air flows in from the sides to take its place. That air is warmed in turn and rises too, and a steady circulation begins.
Convection is the transfer of heat by the bulk motion of a fluid: the warmed fluid itself moves and carries its heat with it. It needs a liquid or a gas that can flow, and gravity to make the warm fluid rise.
When nothing but the difference in density drives the fluid, the process is natural convection. A pan of dal on the stove, the rising shimmer above a hot road and the draught up a chimney are all natural convection. When a fan, a pump or the wind drives the fluid, the process is forced convection. Blowing on a spoon of hot dal, a car's radiator fan and the pump of a water cooler are forced convection.
On board the International Space Station everything floats. Why does a candle flame there become a dim blue ball instead of a tall yellow tongue?
The sea breeze at Chennai
On a summer afternoon on Marina Beach in Chennai, a cool wind blows steadily from the sea. At night the air moves the other way, from the land out to sea. Before you use the chips, predict the night-time wind.
The sea-and-land figure starts in the afternoon, when the land is warmer than the sea. At night the land has cooled below the sea. Which way does the air near the ground move at night?
By day the Sun heats the land and the sea equally, but the land warms much faster. Soil and sand have a specific heat of about 800 J/(kg K), against 4200 for water. Sunlight also warms only a thin top layer of land, while the sea mixes its heat through many metres of water. So the air over the land becomes warmer and rises, and cooler air from over the sea flows in along the ground. That is the sea breeze.
At night both lose heat by radiation, and the land cools faster for the same reasons. Now the sea is the warmer surface. The air rises over the sea, and air from the land flows out to replace it: the land breeze. Fishermen on the Coromandel coast used this for centuries. They sailed out before dawn on the land breeze and returned on the sea breeze in the afternoon.
A ceiling fan does not cool the air in a room; its motor even warms it a little. Why does it make you feel cooler?
How fast a surface hands heat to a fluid
The rate at which a surface loses heat by convection grows with its area and with how much hotter it is than the fluid. For most everyday cases the rate is simply proportional to both. The constant of proportionality is the convective heat transfer coefficient \(h\). This lesson uses \(\sigma = 5.67 \times 10^{-8}\,\text{W/(m}^2\,\text{K}^4)\) for one comparison with radiation.
The unit of \(h\) is W/(m² K): watts for each square metre and each kelvin of difference. Its value is not a property of a material. It depends on the fluid and above all on how fast the fluid moves past the surface. Typical values are shown below.
Why does moving the fluid raise \(h\) so much? Next to any surface lies a thin layer of fluid that barely moves, and heat must cross it by conduction. In still air the layer is thick and grows warm, so the temperature drop across it is small. A fan sweeps the warm air away as fast as it forms and thins the layer. The fluid next to the surface stays cool, and heat leaves many times faster.
The side of a pressure cooker has an area of \(0.1\,\text{m}^2\) and is at \(110\,°\text{C}\) in a kitchen at \(30\,°\text{C}\). How fast does it lose heat by convection in still air, with \(h = 10\,\text{W/(m}^2\,\text{K)}\)? How fast when a fan blows across it, with \(h = 50\,\text{W/(m}^2\,\text{K)}\)?
Still air: \(H = hA(T_s - T_f)\) \(= 10 \times 0.1 \times 80\) \(= 80\,\text{W}\).
With the fan: \(H = 50 \times 0.1 \times 80 = 400\,\text{W}\), five times as much.
This is why a table fan pointed at the stove makes the cooker slower to reach pressure. Cooks keep fans away from the stove.
An oil-filled room heater has a surface area of \(1.5\,\text{m}^2\) and is \(25\,\text{K}\) hotter than the air in the room. Take \(h = 10\,\text{W/(m}^2\,\text{K)}\) for natural convection. How much heat does it give to the room each second by convection, in watts?
A bare hot-water pipe of radius \(1.5\,\text{cm}\) runs \(2\,\text{m}\) across a room, \(60\,\text{K}\) hotter than the air. Take \(h = 10\,\text{W/(m}^2\,\text{K)}\). How much heat does it lose by convection each second, in watts?
Three ways at once
A cup of chai at 80 °C on a table in a room at 30 °C loses heat in every way at once. Warm air rises from it by convection, and water evaporates from its surface. Its sides radiate. A little heat is conducted through the base into the table. The chapter on conduction treated the first way on its own; here all of them work together.
Compare the two biggest, per square metre of the cup's surface. In still air, with \(h = 10\,\text{W/(m}^2\,\text{K)}\), convection carries \(10 \times 50 = 500\,\text{W/m}^2\). Treat the cup as black: radiation carries \(\sigma(353^4 - 303^4) = 402\,\text{W/m}^2\). At everyday temperatures the two are of the same size. Blow on the chai, with \(h\) about 50, and convection jumps to \(2500\,\text{W/m}^2\) and wins easily.
At high temperatures radiation dominates, because it grows as \(T^4\). An iron bar at 1000 °C in the same room radiates \(\sigma(1273^4 - 303^4) = 1.48 \times 10^5\,\text{W/m}^2\). Still-air convection gives only \(10 \times 970 = 9700\,\text{W/m}^2\), fifteen times less. So a hot forge cools mainly by radiation, and a cup of chai by radiation and convection together. A spoon in the chai warms mainly by conduction.
Which statements about the three ways of heat transfer are true?
A vacuum flask keeps tea hot for hours. It has two glass walls with a vacuum between them, both walls silvered on the faces that look into the gap, and a cork stopper. Say which ways of heat transfer each part stops, and how.
The vacuum stops conduction and convection between the walls, because both need matter and there is almost none in the gap. The silvering stops radiation: the hot inner wall is a poor emitter, and the outer wall reflects what does arrive. The stopper stops convection and evaporation from the open top, and cork is a poor conductor itself.
Benjamin Thompson, Count Rumford, was puzzled that a thick apple pie stayed hot so long. He then watched a large thermometer of alcohol cooling in which dust happened to float. The dust rose in the middle and sank along the cold glass walls. Rumford realised that liquids carry heat mainly by moving, and that anything which stops them moving slows the loss. A thick pie filling cannot flow, so it holds its heat.
Warm air rises and cool air sinks. So a room heater works best near the floor. The air it warms rises, and cool air flows in beneath to be warmed in turn, so the air of the whole room circulates. A split air conditioner is mounted high on the wall. The cold air it blows out sinks through the room, and warm air rises to it to be cooled.
- Saying that heat rises.Warm fluid rises, because it is less dense. Heat itself flows from hot to cold in any direction.
- Treating \(h\) as a property of a material, like the conductivity.\(h\) depends on the fluid and on how fast it moves. The same plate has a much larger \(h\) in a draught.
- Thinking a fan cools the air.A fan cools a body by forced convection and evaporation. The air temperature does not fall.
- Forgetting radiation at room temperature.For a warm body in still air, radiation carries about as much as convection.