We know of an ancient radiation
That haunts dismembered constellations,
A faintly glimmering radio station. 

("Frank Sinatra," by Cake, 1996)

 

HEAT TRANSFER VIA RADIATION

Heat Transfer via Radiation is the Mother of All Heat Transfer methods; without heat from the sun radiated to the earth the discussion of any other type of heat transfer would be a moot point.

Radiation is also the main generating source of heat in an industrial complex from which most of the convection and conduction heat transfer are thence derived. The other originating source of energy is releasing the energy contained in chemical bonds.

PTOA Readers and Students already know that Heat Transfer via Conduction is heat transferred through a physical barrier that separates a hot area from a colder area.

PTOA Readers and Students already know that Heat Transfer via Convection is thermal energy (aka heat) that is contained within and transferred from waves of flowing fluids or from fluids that are flowing through rigid industrial piping.

The important characteristic about Heat Transfer via Radiation is that radiated heat is conveyed in electro magnetic beams that emanate from a point source that appears to be emitting light.  

The electromagnetic beams are invisible and travel in straight lines from all directions from the emitting source.  

Only the surface of an obstacle in the pathway of the rays can absorb the Heat of Radiation.

The graphic below shows radiated beams of electromagnetic energy travelling in straight lines that are emitted from a hot source that is shown as a red triangle.

Only the radiated heat energy that comes in contact with the exposed surface can be absorbed by the surface.

The amount of radiated heat absorbed depends upon what the gold obstacle marked "A" is made out of.

Fortunately for all Earthlings, the Earth happens to be located in the path of the warm energy that is radiated from the Sun.

This Heat Transfer by Radiation from the Sun makes life as we know it on Earth possible.

THE MATHEMATICAL EXPRESSION
FOR HEAT TRANSFER VIA RADIATION

Even though Heat Transfer via Radiation is the Mother of All Heat Transfers, PTOA Readers and Students will live perfectly normal lives without thoroughly understanding the mathematical expression human beings have developed to quantify it.

The below Engineeringtoolbox.com graphic illustrates why Heat Transfer via Radiation is complicated to model.

The illustration shows that not all of the radiated heat is absorbed by the obstacle that gets in the way of radiated energy beams.

In the schematic, the beam of radiation (emitted from a non-visible source) is the dark black arrow pointing in a slanted direction downward. The radiated energy is also labelled "incident radiation" and "irradiation."

Once the "incident radiation" contacts the surface of the obstacle, it separates into three parts.

Some of the "incident radiation" is absorbed and heats up the surface of the obstacle. The amount of "absorbed irradiation" depends upon what the obstacle is made out of.

Some of the "incident radiation" is reflected back into the environment as "reflected  irradiation."

And some of the "incident radiation" could be transmitted through the obstacle. That is the arrow labelled "transmitted irradiation."

The mathematical expression that describes the Rate of Radiated Energy from an emitting source is below.

PTOA Readers and Students must not stress about expertly understanding the expression.

A quick glance reveals that the Rate of Radiated Energy is dependent upon the absolute temperature of the emitter (T⁴, expressed in degrees K ...wow that is a big number!) and the surface area of the emitting source (A).

Hey, when you stop and think about it ... that makes sense!

Logically, the Rate of Radiated Energy (shown as the letter "q" with the dot on top) is going to depend upon:

• how hot the emitting source is in the first place.
• how much of the emitter's surface area is actively radiating energy in the direction of the obstacle.

Whoa, Nelly!

The expression is not quite as complicated as it looks when the emitter is the sun or a campfire.

In that case, the weird looking "ε" (it is the Greek letter for "e") is equal to "1."

And the Greek letter alpha (α) is a constant figured out by two researchers named Stefan and Boltzmann who ... you have probably guessed it by now ... spent their lives modeling Heat Transfer via Radiation and the Rate of Radiated Energy so the rest of us could more easily understand it.

The above mathematical expression can be adjusted to make an expression for "reflected irradiation" (once again depicted in the schematic to the right).

In that case the Delta T between the surface area of the obstacle and the colder temperature of the surroundings becomes the driving force for the rate of reflected irradiation.

 

DELINEATING RADIATION FROM CONVECTION

Very frequently in the process industries, Convection Heat Transfer interfaces closely with Radiation Heat Transfer.

The below schematic could be a (strangely slanting) flame from a burner in a firebox and the wall marked A could be the refractory lining of the firebox.

The emitting point source is the ball of flames; in the area directly around the ball of flames heat energy is being radiated.

However, beams of radiated heat are not shown travelling in straight lines extending to the wall.

Well before reaching the wall, the beams of  radiated energy have heated up the atmosphere in the firebox and diffused into convection waves.

Likewise, the picture below shows a chair that has become ignited in a house fire.

Directly around the fire, the radiated heat energy is emitted from the source.

However, the radiated heat excites the smoke and air particles and ... in this agitated state ... the particles move away from each other and become less dense and therefore start to rise as convection waves.

In summary,

Radiation Heat Transfer is the Mother of All Heat Transfer types because it is at the root of derived heat transfer via conduction and convection.

In the process industries, the burners in the fired heaters and the boilers are the point source emitters of radiated heat energy; this radiated heat energy thence generates heat that is transferred via convection and conduction.

The invisible interface between radiation and convection is precisely where the thermal energy stops being emitted in beams and transforms into convection waves.

 

TAKE HOME MESSAGES: Radiation is the original heating method from which heat transfer via convection and conduction are derived. 

The characteristics that describe Heat Transfer by Radiation are an emitting source that generates invisible beams of electromagnetic energy onto any obstacle that may get in the path of the beams.

The mathematical description for the Rate of Radiation Energy is beyond the scope of PTOA to delve into deeply.

Logically, the amount of energy that can be radiated in a specific time interval is dependent upon the absolute temperature of the emitter and how much of the emitter's surface area is available to send beams of energy to an obstacle.

The interface between Heat Transfer via Radiation and Heat Transfer Via Convection is precisely where the beams of radiated energy diffuse into convection waves.

©2015 PTOA Segment 00066
PTOA Heat Transfer Focus Study Area

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