Radiative Heat Transfer: Medium Overview, Part 1 of 2.

In the last article I provided the basic starting point to explain the topic of Radiative Heat Transfer (RHT). Energy transfer is always from a warm object to a cooler object. Even though all objects that have a temperature radiate heat, objects that are the same temperature cannot warm each other and cooler objects do not warm warmer objects.

From that starting point it is time to discuss the actual transfer of heat from one object to another.

The Inconvenient Skeptic

Temperature and energy levels of the three objects

The main objects that are going to be warmed up in this are the hands and two rocks that are the same size as the hands.   The basic equation for energy transfer between two objects is:

The Inconvenient Skeptic

Radiative Heat Transfer between Two Objects

This basically describes the difference in the two energy levels and determines how much energy is transferred. So the fire is radiating 20244 W/m2 and your hands are radiating 510 W/m2. This would be the case if your hands completely surrounded the fire, but since they don’t, it gets a little more complicated and some geometry is required.  Notice that the units for energy are in Watts per meter squared. The total amount of energy that the fire emits is constant at 20244 W/m2, but the farther away from the fire, the more spread out the energy is.

I am not going to cover the geometry unless enough people want me to cover it, but I will provide a simple analogy. Lets say I want to wash my hands with a liter (or gallon) of water. That is enough water to easily accomplish that. Now lets try to use that same amount of water to wash a large building. The water would be too spread out to cover the building much less wash it.

So instead of just subtracting the energy difference between the two objects, I have to account for the geometry. The assumption that is used is that the hands are 0.02 m2.

Once I take that into account, here is the energy that is transferred from the fire to your hands by distance from the fire.

The Inconvenient Skeptic

Energy (W) that is transferred from a fire at 500 °C to hands at 35 °C based on the distance from the fire.

This is why if your hands get too close, you get burned and if you are too far away, you can’t feel the fire. At 1 m from the fire your hands are receiving about 30 W from the fire. For reference, if your hands are outside on a cold, clear night, then they are losing 9 W to the cold sky.  Here is a link that lets you see different situations.  That site is setup for one body enclosing another.

Notice that if you are 3-4 m (10-13ft) from the fire, you are barely getting any energy from the fire. If your hands get 0.5 m from the fire, your hands are receiving 126 W from the fire. That is too much and your hands will burn.

Now if there are two rocks the exact same size as your hands, they get slightly more energy from the fire than your hands would. That is because they are slightly colder than your hands in comparison to the fire. At 1 meter away the rocks would get 0.4 W more than your hands. That is about 1% more energy. So in the same situation two objects the same size and distance would receive slightly different levels of energy based on their temperature. The warmer the object, the less energy. This is because it is radiating more energy at higher temperatures.

So think of the transmitted energy from the colder object as a barrier that limits the amount of energy it can receive. When two objects are the same temperature, there is no net energy transferred. They are in equilibrium with each other. Hands have a slightly higher barrier than the rocks do, so they receive slightly less energy.

If the rocks are moved very close to the fire, they will absorb lots of energy and warm up. As the rocks get closer to the temperature of the fire, they start receiving less energy. The barrier gets higher and higher as the temperature of the rocks increase. If that didn’t happen, the rocks would get hotter than the fire. That cannot happen.

This situation is most comparable to the energy the Earth gets from the sun. In that case a hot body is giving heat to a cool body at a distance. If the Earth was closer to the sun, it would be too hot and if it was farther away it would be too cold. There is good range for the Earth to be. Much like there is a range that your hands can be without being too hot or cold.

In the next part I will describe the energy transfer from your hand to the ground.  That is comparable to the energy transfer from the surface of the Earth to the Greenhouse Gases in the atmosphere.


Posted in Radiative Heat Transfer by inconvenientskeptic on November 9th, 2010 at 2:14 am.


This post has 6 comments

  1. Jeffrey Eric Grant Nov 10th 2010

    Thank you for the basic article on RHT. It is good to start at the beginning, a point where all concerned have common ground from which to procede. I applaud your effort; I was in a large bookstore this week and was amazed to find that they had NO books dedicated to the science of global warming. Essentially, I was looking for a text book written at the high school level that would explain all of the known relationships that impact this subject. Of course, we don’t know what we don’t know….I am also looking to understand the areas where the science is weak….

  2. Richard111 Nov 10th 2010

    Jeffrey, I have the same complaint. Even my local library is short on science books of any type. Half a shelf of books on global warming (climate change actually) full of pretty pictures and graphs all without any reference to any science. Everything I’ve learnt is from blogs like this.. many thanks to John! and I have learned a lot.

    I’m waiting for John to get to the nitty gritty of heat transfer to and from gases. 🙂

  3. inconvenientskeptic Nov 10th 2010

    My book (still working on getting it published) is exactly the type of book you are asking for. When I started my own research I realized that most conversation is geared to those that know a lot, or very little at all.

    It covers the climate and the debate in a pretty straightforward method. Much like I try to keep my site readable to those that are not deep into the debate.

    Your comments are appreciated. 🙂

  4. Jeffrey Eric Grant Nov 10th 2010

    John, I might be a little late to the party, but if you would like a ‘proofreading’ not for grammar or spelling – but for logic, interpretation and old fashioned intuition – I am your man. Like they say (backwards) “if you have the beer, I have the time”.

    In any event, I like this blog. Keep it up.

  5. Prem Upadhyay Nov 11th 2010

    Congratulations. Great effort. Please keep it up. I would appreciate if you could refer or explain the source of getting the number on the energy transfer from the object like fire, hand etc.

  6. Bill Illis Nov 11th 2010

    A good place to start to see how realistic the radiative transfer theoritical framework is, is to examine how energy levels at the surface, at 1.5 metres high, change throughout the day and throughout the year.

    (Actually, at each 1 second interval should be the metric because solar irradiance is actually measured in Watts/metre^2 / per second – not per day or per hour but the measurement is per second).

    The 1.5 metre energy/temperature levels are completely different than global warming’s theoritical radiative transfer model. There is no need to invoke mysterious back-radiation etc.

    Energy is always flowing out / transferring out to space and it is flowing out at almost exactly the same rate per second that solar energy is coming in. This occurs at all timescales.

    Daytime Max:

    Solar In = 960.0000 Watts/m2/second
    Energy Moving Up and Out = 959.9983 Watts/m2/second


    Energy In = ~ 0 (but is actually a very very small positive number)
    Energy Moving Up and Out = 0.001 Watts/m2/second

    Season (warming up from winter):

    Solar Energy In exceeds Energy Moving Up and Out ==> 0.000006 Watts/m2/second

    and when the season is cooling down from summer, Energy Out exceeds Energy In by the same (unbelievably small) 0.000006

    For a Whole Year (or the last 15 years):

    Solar Energy In = Energy Moving Up and Out (exactly)

    [Now the next step is to examine how the 1.5 metre high atmosphere contains 390 watts/m2 of energy on average but that is only 1.5 seconds worth of the average solar energy coming in during a 24 hour period so it is not an unsual amount of accumulation. Energy and molecules move at speeds we cannot imagine and the proposition that doubled CO2 creates 3.7 watts/m2 of additional radiative forcing at the tropopause is quite ridiculous when all of this is happening at the speed of light and energy is flowing out from the surface at exactly the same rate as energy is coming in – per second that is).

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