Radiative Heat Transfer: Medium Overview, Part 2 of 2.


This is the third article in the series about Radiative Heat Transfer (RHT). In the previous two articles I have described the basics and then gone over one example. That first example is comparable to how the Earth gets energy from the sun. The example was that of a fire warming up a person’s hands by the fire.

One concept that is important to understand about RHT is that it is one of the basic methods that nature uses to keep objects at the same temperature. Nature does not generally allow objects at different temperatures to stay at different temperatures. The goal of nature is for two objects to be in equilibrium with each other. It takes energy to keep objects at different temperatures.

Now I will continue to use the example of a persons hands and the ground to provide an example of how the surface of the Earth transfers energy to the atmosphere. I will continue to use the objects I have been using for all of the examples. For this case only the hands and the ground will be needed.

The amount of energy that is transferred is determined by the temperature difference of the two objects. The closer they are in temperature, the less energy is transferred. So for the case of the hands and the ground, the total energy is much less than when the fire was involved. That is why a fire can warm up a group of people. The ground is radiating energy, but it isn’t warming anything up. It is taking energy from objects that are warmer than it is.

In this example there is one important difference. With the fire, geometry played an important role. In this case geometry is not going to be important. I will basically ignore geometry in this example by using one single assumption. That is that the hands are close to the ground and the ground will in fact absorb all the energy from the hands. I use that assumption because that is comparable to the geometry in the case of the atmosphere in relation to the ground. The atmosphere does completely surround the surface of the Earth. Geometry does not matter in that situation so I will apply the same conditions to this example.

So for the case of the ground absorbing energy from the hands I will once again use the basic equation for heat transfer which is a specific situation derived from the Stefen-Boltzmann equation.

The Inconvenient Skeptic

Radiative Heat Transfer between Two Objects

This is comparable to using the Stefan-Boltzmann equation separately for each object which would look like this:

Total Heat Transferred = EnergyHands – EnergyGround

Total Heat Transferred = σ (TemperatureHands)4 – σ (TemperatureGround)4

Q = 510 W/m2– 271 W/m2

Q = 239 W/m2

That is the total maximum energy transfer possible between the hands and the ground. Even though the hands are “receiving” 271 W/m2 of energy from the ground, the hands are in fact losing energy to the ground.

Now it is important to see the difference that a different temperature for the ground makes. Lets consider two other cases where the temperature of the ground is different than the -10 °C that it is in the above case. The new temperatures for the ground are to go up and down 20 °C. Here are the energy levels for the new temperatures:

-30 °C = 198 W/m2

10 °C = 364 W/m2

For these two cases, the energy transferred to the ground would then be:

Q = 510 – 263 = 312 W/m2

Q = 510 – 364 = 146 W/m2

The more radiated heat there is from the cooler body, the less heat transfer there is from the warmer body to the cooler body. The different temperatures of ground do not cause warming in the hands, but different temperatures of ground result in different rates of heat transfer.

It is still not possible to compare this example to the one in part 1.  The reason is the units are still in W/m2.   Multiplying the above values by the size of the hands (0.02 m2) will result in the amount of Watts that are being transferred. Here is the chart for the total energy transfer based on different ground temperature.

The Inconvenient Skeptic

Total energy Transferred from hands to ground at different temperatures.

Notice that it is much less energy than the energy from the fire, even when the ground is very cold.  It is limited by the low energy level that the hands have.  35 °C does not provide a very energetic surface for RHT.  Especially when there is not a big temperature difference between objects.  When the ground is -10 °C, the total energy is about 5 W.  That is about 1/6th the energy the hands get from the fire when 1 m away.  Even when the ground reaches the lowest possible temperature, the energy transfer is 1/3rd what the hands got from the fire.

This also shows the exact effect that transferring energy from a slightly warmer object to an object that is only slightly cooler.  There is very little energy transferred by RHT.  When the temperature difference is 10 °C, the RHT is only 1 W.  Even a 30 °C temperature difference results in only 3.5 W of energy transfer.  The effect of the temperature of the cooler body does make a difference, but it does not CAUSE any warming in the hands.  More energy is always flowing from the hands than to the hands in this situation.  Different temperatures of the ground only change the rate of heat loss.

This is exactly what is happening when energy is transferred from the surface of the Earth into the atmosphere.  There is very little temperature difference and the average temperature of the surface is less than that of the hands.  The very nature of the conditions limits how much energy is transferred from the surface to the atmosphere.

Understanding this and the previous articles provides the foundation needed to understand what happens when additional CO2 is added into the Earth’s atmosphere. The study of energy transfer from the Earth’s surface to the atmosphere is slightly more complicated, but the same principles apply. Energy is transferred from the warmer object (Earth’s surface) to the cooler object (atmosphere). Increasing the concentration of CO2 does cause a change, but that change is limited.

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Posted in Radiative Heat Transfer by inconvenientskeptic on November 14th, 2010 at 1:00 pm.

9 comments

This post has 9 comments

  1. Richard111 Nov 17th 2010

    From this layman’s perspective you are discussing NET radiative heat transfer between non-gaseous objects thus infering wide band land wave radiation is emitted/absorbed by the surface of each object. This seems logical and intuitive to me.
    Looking forward to gases being included.

  2. Glenn Tamblyn Nov 18th 2010

    John

    One caveat with this comment “The effect of the temperature of the cooler body does make a difference, but it does not CAUSE any warming in the hands. More energy is always flowing from the hands than to the hands in this situation. Different temperatures of the ground only change the rate of heat loss.”

    Strictly speaking, the return radiation from the ground is reducing the cooling that the hand would otherwise experience without the presence of the ground. Is reduced cooling, warming?. That’s semantics. Also an important point to note. The hand has an internal heat generation system in the form of the human metabolism. So its thermal behaviour in this situation isn’t the same as an inert material at the same temperature. Such a material would cool until it was in equilibrium with the ground.

    In your first post on RHT another poster asked me whether the presence of the Earth resulted in the Sun being a bit warmer. You wanted to hold over that discussion to a later time. This might be the appropriate point.

    The answer is yes, infinitesimally.

    Imagine the Sun has no planets and you are standing on the surface of the it looking out. Beneath your feet the Sun is radiating huge amounts of energy produced in its interior. Looking out you see nothing but frigidly cold deep space. This does radiate energy as well but incredibly tiny amounts and some of this reaches the Sun. So the surface of the Sun is at a temperature where the amount of energy it is radiating equals the energy from its interior plus the energy it is receiving from space. This space originating energy is so tiny it’s effect wouldn’t be measurable compared to the Suns internal energy, but it is still there.

    Now we add a planet, at a distance of around 144 million km. Lets call it the Earth. And its temperature isn’t the frigid temps of space but +15 Degc.

    So now looking out we see pretty much deep space apart from that little shining dot. The small patch of deep space that we would be able to see if the Earth wasn’t there is now blocked so it’s tiny, tiny amount of energy isn’t reaching the Sun. But instead, energy from the warmer Earth is reaching the Sun. Still tiny but not quite as tiny. The net result is that the energy reaching the Sun from space is now a little higher. Still miniscule but not quite as miniscule as before.

    So the temperature of the Sun will be slightly higher in this situation so that the Sun can radiate its core energy and this increased space energy. Proably still too small to measure but still real. And this increased space energy is actually some of the Sun’s own energy, absorbed by the Earth and radiated back to the Sun

    In effect the Sun has a phenomenon equivalent to our Greenhose Effect. It is a tiny little bit warmer because the presence of planets causes a bit of its energy to be shot back to it. It just isn’t on the same scale as the terrestrial GH Effect.

    Finally John
    “This is exactly what is happening when energy is transferred from the surface of the Earth into the atmosphere. There is very little temperature difference and the average temperature of the surface is less than that of the hands. The very nature of the conditions limits how much energy is transferred from the surface to the atmosphere.”
    I don’t know where you are going with this. Lets wait & see.

  3. inconvenientskeptic Nov 18th 2010

    Glenn,

    When a pizza comes out of the oven it is hot. If just set out on the counter, it will cool down quickly. If it is put in a box, then it will slow down less quickly.

    The difference between changing the rate of energy loss and inducing warming are very different, even if it sounds like semantics.

    I didn’t use the pizza example because convection dominates that type of situation. Although radiative is present. Once the box warms up (which it quickly does), then RHT is between the pizza and the box. Since the box is warm, there is little transfer directly to the box.

    As for the sun.. The answer is that the Earth does not make the sun warmer at all. The sun is radiating heat from it’s surface to the 3K space that surrounds it. That the Earth intersects that energy after it is transferred makes no difference to the sun.

    The planets and sun lose energy directly to space. Space doesn’t stop the energy or warm up, that is why the Earth can capture that energy later. The transfer to 3K has already been completed from the suns perspective.

    The Earth is radiating to space, but at ~250 W/m2. At a distance of 1 million km, it is zero. Ok, Technically 0.012 W/m2 at 1 million km, for energy transfer, that is zero.

    Since you are raising no objections, I take it you agree that my examples and descriptions are accurate, even if you don’t understand the direction I am going. Science is the key. 🙂

  4. Glenn Tamblyn Nov 19th 2010

    John

    I am only able to drop in occassionally due to work commitments etc so my comments will be sporadic. Once you have completed your argument I will put together a more detailed outline of the points I agree and disagree with.

    As to your posts so far on RHT, what you have said is technically correct, although you choice of phrasing in producing a simplified description could easily mislead some people – we have had this conversation before about how simplifications can produce mistaken perceptions.

    Your use of phrases like “So think of the transmitted energy from the colder object as a barrier that limits the amount of energy it can receive.” could easily create a mistaken impression. A reader who understands the concept of 2 different flows and that the result is the NET of the difference between them won’t fall into the trap. However another reader who is not as quantitatively fluent might interpret you as saying that ‘a barrier’ exists. The subject of human cognition and how this influences how people assimilate information is one that I am quite involved in right now. Your readers can easily misunderstand what you mean.

    As for “As for the sun.. The answer is that the Earth does not make the sun warmer at all. The sun is radiating heat from it’s surface to the 3K space that surrounds it. That the Earth intersects that energy after it is transferred makes no difference to the sun.” is simply incorrect. Go back to your thermodynamics lectures John.

    This might see like pedantry but it is an important point.

    The Sun is radiating an amount of energy outwards. This is unaffected by anything else. Equally radiation is arriving from deep space. As you said, at around 3K. While this is tiny compared to to the Sun’s output, it is not zero. In fact it has been studied extensively – this is the Cosmic Background Microwave Radiation that is telling us so much about the early Universe. So the energy budget for the Sun is gargantuan amounts of energy generated internally, and a miniscule amount arriving from outside. And ultimately this total amount of energy is radiated by the Sun.

    When you interpose a planet, you block a tiny amount of the tiny amount – again, more of that geometry. But the planet, being heated by the Sun ( and to a much lesser extent by internal radioactive decay) is warmer than 3K. So the radiation coming from the planet to the Sun has more energy than the small bit of deep space blocked by the planet. So the energy budget of the Sun now includes a slightly larger miniscule component coming from outside. And this energy substantially originated from the Sun.

    Now this is pedantic because the amounts are incredibly trivial but they are still there! The Sun is infinitesimally warmer because the Earth is present. Now lets make it less pedantic

    Instead of the Earth, lets make it a Giant planet 100 times the diameter of Jupiter and orbiting as close as Mercury. Same pronciple, but the effect would now merely be small, rather than miniscule.

    The point of the pedantry is that all radiation flows need to be taken account of. The risk is that if we discount tiny flows for the advantages of simplicity, we can fall into the trap of thinking they need never be considered in situations when they are actually not tiny.

  5. inconvenientskeptic Nov 19th 2010

    Glenn,

    The Earth provides 0.0000004 W/m2 to the sun. At some point the answer is small enough that it is zero. Just because an answer can be determined does not mean it has relevance.

    To compare… That is the same energy that a person would get from a 500C fire if they were 8.8 km away.

    If it makes you feel better to have a non zero number instead of zero. That is personal preference.

  6. Richard C (NZ) Nov 21st 2010

    Glenn, John,

    Just catching up here so this might be covered later.

    The radiation from hand to ground or earth to sun is re-emitted so the wavelength and therefore heating ability has changed (the reason why long-wave ovens never took off).

    Also there will be reflected radiation and scattering.

    See Chapter 64. Effect of Scattering on the Combined Reflection and Thermal Radiation Emission of a Typical Semitransparent TBC Material

    Summary

    A parametric study was undertaken to examine the effects of scattering on the combined reflection and thermal radiation emission of a typical semitransparent thermal barrier coating material. Some ceramic materials are semitransparent in the wavelength ranges where thermal radiation is important. Therefore, absorption, emission, and scattering of thermal radiation by the layer will affect the heat transfer and temperatures profile. The total radiation leaving one side of the layer is the external radiation reflected back by the interface, radiation emitted internally by the layer and transmitted through the interface, radiation scattered by sites inside the layer and transmitted through the interface, and radiation transmitted through the layer from the surroundings on the opposite side. Total internal reflection of scattered and internally emitted radiation affects the radiation leaving the layer and the temperature profile. A one dimensional model of a semitransparent layer heated on one side and cooled on the other by convection and radiation is used. The coating is assumed to be gray (absorption and scattering coefficients are not function of wavelength). The absorption coefficient, scattering coefficient, and convective heat transfer coefficients are varied. The total radiation leaving the layer in each direction is presented as a function of scattering for a range of absorption coefficients. Temperature profiles inside the layer are presented showing the effect of scattering and absorption.

  7. Richard Sharpe Nov 28th 2010

    It would seem that what Glenn is saying is that the Sun is ever so slightly warmer than it would be if the Earth was not present. This seems uncontroversial.

  8. inconvenientskeptic Nov 28th 2010

    Richard,

    The same argument could be made that Pluto causes all the bodies in the solar system to be slightly warmer than they would otherwise.

    I understand what he is saying, but transfer through space is different. The RHT is from the one body to space. The temperature of the 2nd body does not matter for transfer between the sun and the Earth.

    Once a value has reached a certain small magnitude, the real world meaning is gone. The argument becomes comparable to the angels on the head of a pin.

  9. Glenn Tamblyn Nov 29th 2010

    “The same argument could be made that Pluto causes all the bodies in the solar system to be slightly warmer than they would otherwise.” Yes it does. Again infinitesimally but yes. Any two bodies that are within line of sight of each other affect each other no matter how slightly.

    “I understand what he is saying, but transfer through space is different.” Huh? NOT IT ISN’T JOHN.

    The RHT is from the one body to space. The temperature of the 2nd body does not matter for transfer between the sun and the Earth.” Neither does it matter for transfer betwee the Earth and the Sun. The RFHT is from a body to EVERYTHING within its line of sight.

    “Once a value has reached a certain small magnitude, the real world meaning is gone.” Sure, practically of course it is. But we are not discussing real world. We are discussing the Principles of RHT so your readers can work out how to apply them to all sorts of different situations.

    ” The argument becomes comparable to the angels on the head of a pin” Spot On. What matters is that we don’t forget those Angels, because sometimes they hit the Burger Bar big tim and we actually have to take note of them.

    It is a dangerous bit of slight of hand to say that because we can ignore something in one situation because it is so small, we then conveniently forget that we DO have to take it into account in another situation.

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