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I was looking up the definition of heat conduction, but every website has a different answer. In addition to several different answers, some seemed wrong, or at least oversimplified.

From MachineDesign.com

Conduction transfers heat via direct molecular collision. An area of greater kinetic energy will transfer thermal energy to an area with lower kinetic energy. Higher-speed particles will collide with slower speed particles.

From Phys.org

This transfer occurs at the molecular level—from one body to another—when heat energy is absorbed by a surface and causes the molecules of that surface to move more quickly. In the process, they bump into their neighbors and transfer the energy to them, a process which continues as long as heat is still being added.

However, I have the understanding that atoms and molecules never come into contact with each other. Nothing truly touches.

What am I missing here?

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You are missing the fact that atoms and molecules can exert electromagnetic (mostly electrostatic) forces on each other without having to “touch”. Think about Coulomb’s Law and how two electrons repel each other at a distance due to their electric fields.

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You can think of it as a radiation being happening (similar to electric field)between the atoms at the closest distance. When an atom gains heat the energy of it increase causing them to oscillate.This oscillation will make them come closer to neighbouring atoms where this heat transfer takes place because of the difference in temperature.

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