Conduction is the redistribution of thermal energy that occurs in a solid body due to differences in temperature. It’s one of three modes of heat transfer, along with convection and radiation.
Conductive heat transfer can be described by Fourier’s Law. It states that the rate of heat transfer between two points is proportional to the area of through which the heat transfer occurs, to the difference in temperature between the two points, and to a material constant called thermal conductivity.
Fourier’s law can only be applied if the temperature gradient is known, which requires the distribution of temperature within the body to be known. The temperature distribution in a body can be determined by solving the heat equation – a partial differential equation that describes how heat will flow throughout an object.
These topics – conduction, Fourier’s Law, thermal conductivity and the heat equation – are covered in detail in the animated video below.