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You should have explained that the question cannot be answered without a great deal of knowledge about the conditions that are present, such as the temperature difference involved, the shape, size and surface of the hot object and nature of its surroundings. For example, if the object is a hot electrical cable, buried under ground then convection will not be possible. For the same cable suspended from pylons conduction will not be important.

Let us assume that we are dealing with a simple, metallic or ceramic block, resting on a reasonably good conductor and surrounded by air. Let us also assume that the block is also in a perfectly ordinary room on the planet Earth and not, for example, orbiting the Earth in the International Space Station.

The rate of change of temperature difference due to conduction is directly proportional to temperature difference between the hot object and the cold surroundings.

Equation

(where  is the temperature difference)

By including a constant or proportionality k1 we can turn this into an equation, thus:

Equation

For natural convection we have seen that the rate of change of temperature difference is proportional to the temperature difference raised to the power of 1.25 (the five – fourths law):

Equation

Finally for radiation we have seen that the rate of change of temperature difference is proportional to the difference of the temperatures raised to the fourth power (the Stefan-Boltzmann Law):

Equation

Which of these is dominant depends on the temperature difference θ and the precise conditions, which affects k1, k2 and k3,

Unless the block is sitting on a very good insulator then at sufficiently low temperatures conduction will always be the most important mechanism for heat loss. However at higher temperatures the block will heat the surrounding air sufficiently so that a convection current is set up. At high enough temperatures this will be more efficient at removing heat than conduction. At even higher temperatures the block will be radiating large amounts of infra-red radiation. If the temperature is high enough it will even give out large amounts of visible light (think of the filament of a simple light bulb). At these temperatures radiation will make the largest contribution to heat loss.

 Heat Transfer Graph

The precise temperatures at which each mechanism becomes dominant varies greatly with the conditions, however, at sufficiently high temperatures radiation always wins.

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