## A Discussion of the Equations of Transfer

I was having an email discussion with an old professor of mine (from undergad) about the fraud of the radiative greenhouse effect who has himself implied doubt about the greenhouse effect.  Actually the proff is Dr. Essex who wrote the book “Taken by Storm“.  He suggested that I look at the “equations of transfer” in regard to the problem, which of course I have already done extensively and am quite familiar with.  I will post the reply here since it may help some people:

“Are you still using Haberman’s “Applied Partial Differential Equations with Fourier Series and Boundary Value Problems”?  We used that when I took your class in 2000.

For the flow of heat in matter we end with the diffusion equation as a function of space and time.  If there is a heat source, then Q (heat) gets tacked on to the equation and Q can also be a function of space and time.  The scenario with the radiative greenhouse effect is that you have matter, the ground surface, where there is basically no internal heat generation, but you do have Q at the surface boundary, i.e. at the very first element of the surface, due to sunlight.

Q of course is heat.  Making this simpler than the Sun “going around” the surface location, we can just use constant values to inspect the qualitative and some quantitative features of the solution to this type of problem.  To do that we must use and understand what Q is since whatever is governing Q is basically setting the boundary conditions of the problem, and the behaviour of these solutions are typically largely determined by the boundary conditions.

Q, being heat, is not simply the energy from sunlight, but is given from radiant transfer by a difference of flux values, which are of course proportional to temperature.  For example in a plane-parallel model with emissivities and absorptivities all unity, then Q = Flux_hot – Flux_cool = sigma(T_hot^4 – T_cool^4), and the positive Q means that the heat is flowing to the cooler object, which would cause the cooler object to increase in temperature until Q = 0.  It is simpler to use local flux when dealing with sunlight so that you don’t need to think about how the surface flux of the Sun is diluted by distance, but of course that is there.

So radiant Q is a flow given by a difference of local fluxes between two source objects.  The argument of the radiative greenhouse effect from climate alarm is that Q from the atmosphere to the surface is increased by increasing greenhouse gases, therefore causing the surface to increase in temperature.  Quite plainly, this argument reverses heat flow directionality since the relation between the cooler atmosphere and warmer surface (this is their general state relative to each other) is that heat, using the definition of heat, flows from the warmer surface to the cooler atmosphere.  They call their heat-reversal mechanism “back-radiation”, the argument being that any additional presence of radiant energy in the atmosphere will cause temperature increase on the surface; this conflates energy for heat, because energy is not always heat and can only manifest or act as heat when flowing from warm to cool, causing the cool to increase in temperature.

Q between the Earth’s surface and Earth’s atmosphere is positive, meaning that heat is flowing from the warmer surface to the cooler atmosphere.  Their other argument attempting to explain the mechanism of “back-radiation” is that making Q less positive will increase the temperature of the warmer surface.  This is a complete fabrication and pseudoscience of thermodynamics, and here is where their argument reduces to Zeno’s Paradox.  Q is supposed to become less positive, in fact it is supposed to go to zero, but if in doing so this increased the temperature of the warmer object, then this would also increase the temperature of the cooler object, and then you effectively have Zeno’s Paradox or a variation on it (you never reach the end because the finish line of Q = 0 is itself running away from you).  What they are doing is treating Q as a conserved, constant quantity, which of course heat isn’t, and typically denote heat as given by the energy from sunlight, which is of course not Q (heat) in the first place given that Q is a difference of source fluxes, not a source flux in and of itself.”

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### 18 Responses to A Discussion of the Equations of Transfer

1. songhees says:

@pplonia #climate
‘HumanCaused Global Warming, the Biggest Deception in History’.
On Amazon.ca http://www.drtimball.com

2. Rosco says:

Supposedly Planck solved the “ultra violet catastrophe” with his equation for radiant emissions. Further evidence that his equation is correct, or at least the best available thus far, is that mathematical transformations of his equation by differentiation and integration produce the empirically derived Wien’s and Stefan-Boltzmann equations.

It can be shown by plotting Planck curves for T1 and T2 that the manner in which climate scientists perform their algebraic manipulations is just plain wrong – it does not produce the “right” answer ever.

It can be further demonstrated by plotting Planck curves that the expression Q(net) = sigma(T1^4 – T2^4) is correct every time which is something climate scientists defy with their incorrect use of the SB law. They often use the SB equation with Q(net) as a constant to “force” T1 to increase to maintain the emission when background temperatures increase even though they, T2, are colder than the object, T1.

I cannot explain the results of summing temperature values using Planck curves but I do know the result is not a Planck curve and hence NOT equal to sigmaT^4.

In fact the resulting temperature curves plotted by extracting the temperature from Planck’s equation versus increasing wavelength is exactly a straight line at the value of each individual temperature- as it should be !

But the curves based on algebraic sums of flux versus wavelength are curves which increase or decrease in temperature value versus increasing wavelength. Algebraic sums of flux increase while differences decrease.

Plot a series of similar curves correctly using Q(net) = sigma(T1^4 – T2^4) and all resulting curves are straight horizontal lines at the appropriate values – ONLY the sum value is slightly different – it commences at the temperature of the second highest value of the series and runs a few K over the highest value and represents ~1% error and I suspect this is due to floating point errors inherent in computer spreadsheets at very low values – for example the denominator of Planck’s equation has values of 10^-40 at wavelength of 0.5 microns.

Even emissivity is irrelevant in such an analysis if it is a constant. However, using multiples or sums of Planck curves do not result in the result being a Planck curve except when the “Net” form is used. This leads me to suspect using a fraction multiple of the SB equation may not be strictly correct – the resulting curves do not “work”. Perhaps this assumption about emissivity is mistaken – it is possible.

I consider an analysis of this nature confirms exactly what Joe says about Q and directly disproves what climate scientists allege – unless they know of some other relationship between the laws of radiant emissions physics.

Why anyone would expect an equation involving the inverse exponential of the inverse of temperature to be amenable to the laws of simple algebra is beyond me in the first place !

3. Claudius Denk says:

The horse is dead, Joe. You can stop whacking it.

4. These idiots haven’t stopped trying to ride it! lol

5. John Harrison says:

Joseph. I still can’t help thinking that you have grasped the wrong end of the stick the back radiation does not cause the Earth surface temperature to increase, As I read it this has rarely if ever been the claim made by alarmists. It seems that the claim is that back radiation may slow down the rate of cooling and will result in the Earth surface not cooling as far and as fast as it would without it. This claim does have a degree of logic. If we try the thought experiment of two adjacent black bodies at different temperatures if the colder surface will always radiating some IR towards the hotter. The hotter surface, being a black body will always be absorbing all the incident radiation. Therefore, the net rate of heat loss from the higher temperature surface will be reduced by the presence of the cooler object. If the cooler surface is held at a constant temperature the hotter object will only cool to some equilibrium temperature which will be greater than that in the absence of the second body. Is this analysis not correct?

6. @John Harrison,

It is imperative to stick to the fundamental definitions. Sure, what you say sounds logical, but it is not actually how the RGHE is defined. One of the whole problems with this “debate” (this fraud) is that when the fundamental things are criticized, then the explanation changes to some more colloquial version which, no longer being based on logical physical fundamentals in thermodynamics, changes the goal posts and the reference frames and even the ability to carry on a rational analysis.

The RGHE is defined by the diagrams and the mathematical derivation that create it. Full stop. Why then change what the actual fundamentals are to some other explanation? Doing that makes no sense, and is a hallmark of sophistry.

Now, “the claim is that back radiation may slow down the rate of cooling” is actually meaningless. Slowing down the rate of cooling does not equate to a temperature increase for the thing not cooling as fast. Did you know that the rate of cooling in thermal equilibrium is actually as slow as it is possible to be? At zero. If in thermal equilibrium there is no cooling whatsoever, because the rate of cooling is zero, then does that mean that the thing not doing any cooling at all, even though energy is still coming into it from some source, would indefinitely rise in temperature?

In a thermodynamics textbook which I quote in the video link, we read:

“Much of thermodynamics deals with three closely related concepts: temperature, energy, and heat. Much of students’ difficulty with thermodynamics comes from confusing these three concepts with each other.”

And that is what is happening with this idea of slowed cooling: heat is being confused for energy.

And so although what you say does indeed “sound logical”, it is only “logical” in a colloquial way using anachronistic terminology which confuses and mixes up fundamental physical definitions in thermodynamics, and so is therefore actually only the appearance of logic, a simulacrum of logic, or in other words sophistry and pseudoscience. And the double whammy here is that this phraseology is only employed after ditching the fundamental derivation of the RGHE and what it is claiming after what it is claiming is criticized.

Thermodynamics does not function in the way that you describe in your example, because that example does not abide by what the actual thermodynamic definitions of the relevant quantities are, nor their physics nor their mathematics. I grant that they are sentences which can be written and which sound “logical”. But that is all.

7. Allen Eltor says:

John Harrison says: ”Various therm=0=billy bullshi* about magical backerdisms and heeterfyin dragons’ breath in the sky”
2017/05/21 at 5:03 PM
=================

John:

there’s no such thing as insulation between a fire and rock
that makes less and less firelight reach that rock
making more and more firelight leak out of it.

Rock.
Fire.
Vacuum.

Rock still not hot enough with 100% available firelight arriving,
and with a SINGLE SOLE mode of cooling – same as that of warming – radiant.

When the rock’s still not warm enough
add frigid turbulent bath of compressible fluids: nitrogen, oxygen.
When rock still isn’t warm enough,

suspend MORE and MORE
refractive, insulating media in the bath
such that
LESS and LESS FIRELIGHT
reaches the LIGHT warmed ROCK.

Rock’s still not warm enough.
What to do? What to do, what to do… Oh – I know –

immerse firelight warmed rock,
into a FRIGID BATH
of TURBULENT
THERMALLY CONDUCTIVE
compressed FLUIDS.

These fluids create – by virtue of their very existence – a couple of entirely new modes of –

what? Cooling?
Or Warming?

Say now or you’re the fraud I’m calling you to your face.

The COLD, LIGHT BLOCKING BATH,
creates at the very MINIMUM
an additional 2 MODES of COOLING

it creates CONDUCTION losses – molecules hit the rock, take on heat: electromagnetic energy leaks between the entangling electrons on both masses in classical averaging distribution,
energy is directly handed off till everything’s as equal in temperature as the molecules in their motion, can achieve during the duration of contact –
creating
conduction
COOLING.

That’s what happens when the nitrogen/oxygen bath, merely EXISTS:
as a FRIGID BATH of
THERMALLY CONDUCTIVE,
LIGHT BLOCKING compressible FLUIDS.

The light blocking bath creates the mode of conduction,
and it also creates loss of surface energy
through it never arriving
at the rock:

Oxygen’s daylight
blue-sky condition
as seen by observers on Earth

and seen from space as the translucent oxygen blue haze surrounding the planet.
So – there’s THAT mode of – COOLING
created simply by the mere

existence

of the
FRIGID BATH
of TURBULENT,
THERMALLY CONDUCTIVE,
LIGHT-BLOCKING, compressible fluids.

When the rock STILL isn’t WARM ENOUGH due to being WASHED with COLD COMPRESSIBLE light blocking fluids –

LET’S SUSPEND
REFRACTIVE, LIGHT BLOCKING
INSULATING GAS
in the BATH surrounding the light warmed ROCK
such that MORE and MORE FIRELIGHT is REFRACTED to SPACE.

1)First suspend enough that 1% firelight never gets to the rock.
Like when therewere – enough green house gases suspended in the general atmosphere to cause ONE PERCENT total firelight to
NOT REACH the ROCK.

What is that when ENERGY ARRIVING goes DOWN 1%?

When 1% total firelight DOESN’T reach ROCK
rock TEMPERATURE – firelight LEAVING the ROCK – declines by –
HOW many PERCENT?
1%

HOW MUCH HOTTER do YOU CLAIM the PLANET GOT
when firelight REACHING it DECLINED by ONE PERCENT?

How many MAGICAL BACKERDISMS does it take
to make MORE LIGHT leak out of a ROCK,
magic insulation makes LESS leak INTO?

On to enough green house gases suspended in the bath
to reduce surface energy density by 10%.

10% LESS FIRELIGHT leaking INTO the ROCK, makes – HOW much MORE firelight
leak OUT, Purfesser John A. Harrison of the Washington Sckool of magical backerdisms?
Tell me now how much MORE light
LEAKS out of a ROCK
having
10% LESS
leak into it.
DESCRIBE your MATHEMATICAL STEPS in ACHIEVING this GAIN or YOU’RE the FRAUD BARKING FAKE I’m telling everyone you are here, TODAY.

HOW much MORE ENERGY LEAKS OUT of a ROCK,
that has 10% LESS energy ever REACH it?

Purfesser? HOW MUCH? SHOW me YOUR MATHEMATICALLY ITERATED STEPS or YOU’RE a FAKE too stupid to calculate how much more light comes OUT of a rock
having 10% LESS
reach it.

On to enough green house gases suspended in the bath to reduce surface energy density by say… Oh… I dunno let’s get crazy and say 20% –

20%
total firelight
refracted to SPACE
NEVER to REACH the ROCK- just like – TODAY –

*Today, GREEN HOUSE GASES
cause 20%
total available
firelight energy
to NEVER REACH the ROCK in QUESTION.

HOW MUCH MORE John
did the TEMPERATURE RISE/FALL
between the point when SURFACE ENERGY DENSITY
was reduced by 10%
all the way to 20%?

When a TOTAL – a TOTAL of 20% LESS FIRELIGHT LEAKS into a ROCK
in
MAGIC GAiSSiNeSS WuRLD,

HOW much MORE FIRELIGHT
LEAKS OUT?

Give me the numbers ANY WAY you SEE FIT John.

When INSULATION
suspended between a FIRE and ROCK
causes 20% less FIRELIGHT to EVER REACH the ROCK
HOW much MORE FIRELIGHT
leaks OUT?

Of the rock.

John A. Harrison.

The rock 20% LESS firelight REACHED.

How much MORE leaked OUT because
refractive, insulating magical gas,
than went in?
=========
You came in here insinuating others don’t have a good grasp on your magical story about the magic gas that makes more light leave a rock it makes less get to.

Explain it all so everyone here doesn’t laugh their morning coffee through their noses onto their keyboards.

Explain it so that you don’t look like you’re so stupid you can’t properly predict what happens when more or less firelight falls on a thermal sensor.

And explain it GIVING EXAMPLES of OTHER TIMES in HISTORY
when
INSULATION suspended between a rock and fire,
as the insulation made less and less get TO it.

If you can’t do that
YOU’RE the ignoratti-class drone
who can’t be led to PROPERLY FIGURE OUT what happens when less light hits a rock.

8. Allen Eltor says:

Ooops I left some improperly edited material in that thread; I’m watching TV with my wife.

Figure it out PurFessor – sort through it all and

EXPLAIN to ME
INSULATION between a FIRE and ROCK
making MORE FIRELIGHT LEAVE the rock
it’s making LESS firelight ever REACH.

I want to see that very much. I have told various magic gassers and PurFeSSuRS of Backerdistical Refractification for YEARS – EXPLAIN yourself

so that everyone can SEE CLEARLY
that
INSULATION
making LESS LIGHT reach a ROCK
makes MORE light LEAVE it.

9. Allen Eltor says:

Of course everyone here knows he’s gonna come back,

claim he’s too doggone tired to explain it all again – then slink off – another humiliated loser who tried to tell scientists from every field of endeavor on earth,
that
if you put more and more insulation
between a rock,
and the fire that’s heating it

if the insulation’s magic enough
more and more firelight will come out of the rock
as the insulation makes less and less, get to it.

BoY HoWDiE thay SHOAR got some MAGICAL REFRACTIFYING goin own down to the GUVURMINT SIGNTS PLACE!
The
SAME FELLERS,
who discovered about that DEVIL WEED pot, bein’ like HEROIN,
and
the SAME FELLERS
who discovered about thim DEVIL FRIGURURNTS burnin up all the OZONE over Aunt Artica,
JiST HAPPENS to BE,
the
SAME FELLERS, what DISCOVERED about the MAGICAL GAiSiNESS
that makes MORE LIGHT LEAK back out of a ROCK,
it makes LESS LIGHT,
ever GiT TO!!

Wh00000WEE boY thAT THAiR truly IS,
some

MAGICAL,
M.A.G.I.C.A.L.
B A C K E R D I S T I C A L

R E F L E C T I F Y I N !

Ain’t it PuRFeSSuR JoHN!

Yew got the ”RIGHT END of the STICK” to SHOW us ALL how thim

BACKERDISTICAL
REFLECTiFiCAYSHuNs is a…

HEATURFYIN and HOTTERIZiN the SKY so thair ain’t NOE WAY

we kin ”DuH-NYe THUH SIGNTs?

I think YOU’RE a BOUGHT and SOLD FAKE a FRAUD BARKING SCAMMER who knows the SIGNS of YOUR MONETARY GRAVY TRAIN being DIMINISHED

if the PEOPLE of the STATE who PAY YOU FIND OUT

what an IGNORATTIE, KooK-0-DyNAMiCS barking QUACK-TARD YOU ARE,

SWEARING you FIRMLY BELIEVE

that

INSULATION

between a ROCK and FIRE
makes MORE LIGHT leak out of the rock
it’s making LESS light leak INTO.

10. Allen Eltor says:

THAT’S what GOVERNMENT EMPLOYEES don’t want getting OUT –

THAT’S what all these IGNORATTI CLASS

THERMODYNAMIC GARBAGE

barking

FRAUDS,

don’t want the ENTIRE PUBLIC of SEVERAL NATIONS to KNOW:

THEY are SWEARING THEY ALL THINK IT’S POSSIBLE that IT’S REAL,

that you can put INSULATION

between a ROCK

and FIRE

WARMING it

and as

LESS and LESS

FIRELIGHT reaches the

FIRE WARMED ROCK,

MORE and MORE FIRELIGHT,

will come OUT.

so LESS LIGHT gets to ROCK – ?
MORE AND more LIGHT
will COME out of ROCK!

THIS is the story PEOPLE TAKING MONEY for WAGES
are TELLING ANYONE who will PUT UP with their FRAUDULENT SCAMMING

as if IT’S THEIR R.I.G.H.T. – to COMMIT WILLFUL,

GROSSLY BLATANT

FRAUD.

11. George says:

Joe,

12. Of course.

13. George says:

Joe, a comment you made above in quoting a thermodynamics text book probably hits the whole AGW garbage right on the head. It was very illuminating for me:

“Much of thermodynamics deals with three closely related concepts: temperature, energy, and heat. Much of students’ difficulty with thermodynamics comes from confusing these three concepts with each other.”

That, I think, hits why people and many scientists themselves are confused about AGW. They are confusing radiation with heat. If more people saw that they might realize the error in the basic “science” of AGW.

Thank you, Joe, for all that you do on this blog. God bless you!

14. George says:

Joe,

You understand the science far better than I. Please go to this site and tell “Concerned” and “Eric Adler” how they are wrong in interpreting your work:

http://dailycaller.com/2017/06/24/study-antarctic-sea-ice-loss-driven-by-natural-variability-not-global-warming/

Joe,
A simple thought experiment:

A sphere in internally heated such that the surface emits 238W/m^2, and this will remain unchanged for the experiment.

There is a shell surrounding the sphere in relatively close proximity. Close enough such that inverse square law will have a negligible impact on energy transfer between surface and shell (really just makes the equating simpler to solve but would have no impact qualitatively on the results).

Outside of the shell is 0K vacuum.

The transmissivity of the shell can be changed from 0 (absorbing all, transmitting none) to 1 (absorbing none, transmitting all).

What are the qualitative differences in:

1. Surface temp
2. Shell temp
3.Total flux emitted if measured from just outside of the shell

as the transmissivity is changed from 1 (transparent) to 0(opaque)?

Can you represent it in a generic equation for the scenario?

16. [snip – I think I need to look at this solution a bit more]