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Heat is transfered from hot region to cold region in solid substances in the form of Conduction process. This can be explained by Fourier's. He is french physicist. His full name is Jean Baptiste Joseph Fourier. He derive equation for the determination of heat transfer in the metal substances. 

The equation explained is q=Q/A=-KdT/dx

is heat flux which is heat per unit area of metal wall

Q is rate of heat tranfer.

negetive sign indicate the heat transfer fron hoter surface to cooler surface.

dt/dx is thermal gradient in the direction of heat flow

the SI units are Watts/meter squire W/M2