[hamdani yusuf (OP)]

If the separation s exceeds twice the diameter d, we are in "far field" where the rate of exchange  by radiation tends towards a 1/s² law.

If 0 < s < d we approach a "near field" radiative exchange that is almost independent of s.

If s = 0 the exchange is conductive   

It's all pretty standard stuff in radiation physics and thermal engineering.

It looks like rough estimation to me.
What's the tolerance for s = 0? Even when two objects are in contact, there will still be some gap between them in microscopic level.

How much is the discontinuity around the transition between radiative and conductive heat transfer?

https://en.wikipedia.org/wiki/Thermal_contact_conductance

[Bored chemist]

Is there any experimental evidence for that?

Put your finger near- and then on- a block of ice.

[alancalverd]

What's the tolerance for s = 0?

For the present context, it's the point at which their molecules can exchange vibrational kinetic energy without an intermediate photon. Hence the change from T⁴ to T law.

[hamdani yusuf (OP)]

What's the tolerance for s = 0?

For the present context, it's the point at which their molecules can exchange vibrational kinetic energy without an intermediate photon. Hence the change from T⁴ to T law.

Even in a crystal lattice, exchange of kinetic energy between one atom to the other occurs as electromagnetic interaction. Nuclear interaction is rare in a standard ambient environment.

[Bored chemist]

What's the tolerance for s = 0?

For the present context, it's the point at which their molecules can exchange vibrational kinetic energy without an intermediate photon. Hence the change from T⁴ to T law.

Even in a crystal lattice, exchange of kinetic energy between one atom to the other occurs as electromagnetic interaction. Nuclear interaction is rare in a standard ambient environment.

Are you talking about the exchange of VIRTUAL photons as the mechanism for electromagnetic forces?
That's not going to help here.

[alancalverd]

Even in a crystal lattice, exchange of kinetic energy between one atom to the other occurs as electromagnetic interaction.

No, electrostatic.

[hamdani yusuf (OP)]

Even in a crystal lattice, exchange of kinetic energy between one atom to the other occurs as electromagnetic interaction.

No, electrostatic.

Those electrons are moving, at least in microscopic scale, hence not static.
AFAIK, even a single electron has magnetic properties. What prevents them to interact electromagnetically?

[alancalverd]

Pairing, very weak magnetic field, and the fact that electrostatic and magnetostatic interactions, even if combined, are not electromagnetic. You might model the interaction with a virtual photon of bizarre origin but you get the right answer with a ball-and-spring model, so why make it complicated? 

[hamdani yusuf (OP)]

Is there any experimental evidence for that?

Put your finger near- and then on- a block of ice.

When the finger barely touches the ice, the contact area is infinitesimally close to 0. But if we push forward, the contact area will become larger.

T2A gets closer to T2B when the gap between A and B is shrinking. How would the discontinuity of energy transfer appear in the graph?

[hamdani yusuf (OP)]

so why make it complicated

To make it more accurate for wider range of circumstances.

[Bored chemist]

If the separation s exceeds twice the diameter d, we are in "far field" where the rate of exchange  by radiation tends towards a 1/s² law.

If 0 < s < d we approach a "near field" radiative exchange that is almost independent of s.

If s = 0 the exchange is conductive   

It's all pretty standard stuff in radiation physics and thermal engineering.

It looks like rough estimation to me.
What's the tolerance for s = 0? Even when two objects are in contact, there will still be some gap between them in microscopic level.

How much is the discontinuity around the transition between radiative and conductive heat transfer?

https://en.wikipedia.org/wiki/Thermal_contact_conductance

As far as I can tell, that picture is wrong.

[alancalverd]

so why make it complicated

To make it more accurate for wider range of circumstances.

Adding nonsense doesn't improve accuracy. This is physics, not politics, philosophy or religion.

[hamdani yusuf (OP)]

As far as I can tell, that picture is wrong.

How can we make it right? Which parts should we change, remove, or add?

[hamdani yusuf (OP)]

Adding nonsense doesn't improve accuracy. This is physics, not politics, philosophy or religion.

What's the nonsense that I should remove without impairing accuracy?

[alancalverd]

The notion of electromagnetic interactions determining heat transfer by conduction.

[hamdani yusuf (OP)]

The notion of electromagnetic interactions determining heat transfer by conduction.

What are the fundamental interactions/forces involved in heat transfer by conduction?
If it's not an electromagnetic interaction, you can choose the others: weak force, strong force, gravitation.

[hamdani yusuf (OP)]

As far as I can tell, that picture is wrong.

How can we make it right? Which parts should we change, remove, or add?

Here's the picture, just in case you have trouble finding it.

[Bored chemist]

The problem is the definition.
Things are in contact or they are not.
The picture shows what you get if there's a gap between the two objects.

[Bored chemist]

The notion of electromagnetic interactions determining heat transfer by conduction.

What are the fundamental interactions/forces involved in heat transfer by conduction?
If it's not an electromagnetic interaction, you can choose the others: weak force, strong force, gravitation.

Are you talking about the exchange of VIRTUAL photons as the mechanism for electromagnetic forces?
That's not going to help here.

[hamdani yusuf (OP)]

The notion of electromagnetic interactions determining heat transfer by conduction.

What are the fundamental interactions/forces involved in heat transfer by conduction?
If it's not an electromagnetic interaction, you can choose the others: weak force, strong force, gravitation.

Are you talking about the exchange of VIRTUAL photons as the mechanism for electromagnetic forces?
That's not going to help here.

What would help?