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- 1 decade agoFavorite Answer
The law of heat conduction, also known as Fourier's law, states that the time rate of heat flow Q through a slab (or a portion of a perfectly insulated wire) is proportional to the gradient of temperature difference.

This law forms the basis for the derivation of the heat equation. R-value is the unit for heat resistance, the reciprocal of the conductance. Ohm's law is the electrical analogue of Fourier's law.

- 1 decade ago
I presume that you know what is Fourier's law.

Regarding its limitations we must understand that Fourier's law is applicable only for macroscopic systems where the time scale of the system is much higher than the heat carrier's (phonons or free electrons) average relaxation time.

For micro-scale systems with characteristic length of the order of the mean free path of energy carriers or systems where the time scale is of the order of or lower than the relaxation time, Fourier's Law cannot be used directly for heat conduction.

If you don't understand the terms 'mean free path' or 'relaxation time' don't worry :-) Just understand that at very low spatial and temporal scales Fourier's law is not applicable.