Chemical Engineering - Heat Transfer - Discussion

With an increase in temperature, the thermal conductivity of non-metallic amorphous solids generally decreases.

Explanation:
In non-metallic amorphous solids (like glass, polymers), heat is mainly transferred by vibrations of atoms (phonons), not by free electrons as in metals.
As temperature increases, atomic vibrations become more disordered, leading to increased phonon scattering.
This reduces the mean free path of phonons, thus reducing thermal conductivity.

Final Answer:
Decreases with an increase in temperature.

An amorphous solid is any noncrystalline solid in which the atoms and molecules are not organized in a definite lattice pattern. Such solids include glass, plastic, and gel. Solids and liquids are both forms of condensed matter; both are composed of atoms in close proximity to each other.

Non-metals are generally referred as insulators or poor conductors of heat; so their resistance decreases with increase in temperature and hence the conductivity increases as they are inversely proportional.

In non-metals, the primary reason for hear flow is lattice vibration (not free electrons). Hence on increasing temp, vibrations also increase thus increasing K.

According to Fourier's law of heat conduction, the thermal conductivity of a solid is inversely proportional to temperature.

Q=kAT/x.

But in amorphous solid, there are weak bonding, so that no chance of free electron movement, then how it is increasing?

With increase in temperature free electron movement will be promoted in amorphous solids there by k increases.

The most common example of pure conduction is heat flow in opaque solids such as the brick wall of a furnace.

basically non metal heat flow is driven by vibration not free electron as told by @nigam

Then why the thermal conductivity decreases with increase in temperature?