A science question

I don't see what you are getting at.If heat is "trapped", then whatever is being heated gets hotter. This increases the gradient, until the flow is balanced again. The temperature gradients are driven to whatever is needed for energy to escape the system at the same rate it is produced. Any excess or underflow will inevitably alter change the temperature gradient; it is a feedback loop.In the atmosphere, the situation is more complex due to radiation, and also transport of water vapour; but it is still a balance of input and output.Within the Earth it is simpler. The temperature gradient below the Earth's surface MEANS that heat is flowing out. I'm not sure if you understand that bit yet. Insulation around a source of energy (like the core, with radioactive decay producing energy) does not actually "slow" the release of energy. It just forces a higher gradient to drive the heat flow required to release the energy.Indeed, the temperature gradient was used by Lord Kelvin in the late nineteenth century to "prove" that the Earth was only twenty to a hunred thousand years old. In fact the Earth is several billion years old, because it is not "cooling". It is releasing heat being generated by decay. We can calculate how mush by knowing the temperature gradient and also the insulating properties of the rock.Cheers -- Sylas

While acknowleding the various complexities you mention about how heat is transported; we do know from the large temperature gradient that Earth is radiating more energy than it receives. There is a flow of energy from the core to the surface, as shown by the gradient, and energy is not accumulating at the surface, as shown by the more or less fixed temperature over a scale of years. There could be two possible sources of the heat flowing up to the surface from the core. One possibility is that the Earth is cooling from an initially molten state. Another is that there is some continuous source of energy within the Earth which is maintaining its high temperature.If there was no source of energy, the Earth would have long since cooled to solid cold rock. It would take hundreds of thousands of years; but the Earth is over 4 billion years old. This was a problem for geology in the nineteenth century; geology made the Earth seem old, physics and thermodynamics suggested it was much younger.But there is a source of energy. The heat of the core is maintained by radioactive decay, and this energy transports to the surface as heat flow; by both conduction and convection. The temperature gradient is a consequence of this steady flow of heat, and the gradient is an infallible indicator of a flow of heat energy from the core to the surface.Cheers -- Sylas

To the best of my limited knowledge, the same principles as apply for the Earth also apply for the Sun. There is a large temperature gradient through the portions of the Sun that are opaque to radiation. This means that the Sun's surface is receiving energy from the inner levels, and that from there it radiates out.The temperature profiles for the atmosphere are different, in both the Sun and the Earth, because they are in a region where there is considerable radiative transfer. We know that the radiation transfer is outwards given the gradients within Sun and Earth.Cheers -- SylasPS. Added in edit. This post should not be taken as disagreement... sfs is right that temperature profiles in the atmospheres of Sun and Earth sometimes go in reverse. For example, the very outmost parts of Earth's atmosphere have temperature rising with altitude; and the same effect is seen in the stratosphere. The causes of this are beyond my scope to explain; but the fact that there is a of energy flowing through the amosphere without stopping (radiation) is significant. There are also other effects; such as the latent heat in water vapour being carried into the atmosphere. It is also significant that the actual internal energies involved are very low, since the atmosphere has a very limited capacity to absorb heat. The heat flow by conduction is negligible by comparison with the radiation passing through.Most of the atmosphere gets heated from the surface of the Earth, but the outer layers have a larger input direct from solar radiation. This (I think) basically accounts for the gradients.For the Sun, the major cause of heating for the chronosphere seems to be magnetic fields. The high temperatures of the corona have long been a serious puzzle for physicists. They knew from thermodynamics that something was heating the corona; but they could not identify what it was. Thermal transfer is ruled out because of the gradient. The puzzle recently took a major step towards solution. See Solar Mystery Nears Solution With Data From SOHO Spacecraft.This message has been edited by Sylas, 03-14-2005 04:37 PM