Conduction is the only way that heat can pass through opaque solids. If one end is heated, the heat will pass through the to the other end. The reason for this is believed to be the motion of electrons. Molecules moving causes conduction. The faster molecules, which are hotter, vibrate against slower moving cool molecules causing them to heat up. Energy is transferred from the slower molecules to the faster ones. Heat always passes from hotter to cooler objects. This would also explain why heat conductors can be good electrical conductors.
In 1882 ( Fourier ) developed a mathematics formula for this conduction which is called Fourier`s law today. The law says that the heat conducted through a cross section is proportional to the negative of the temperature .The proportionally constant is called the thermal conductivity of the materials.
Metals conduct easily but materials such as glass do not.The thermal conductivity of these materials are extremely small and are called insulators. Some insulators do not conduct heat at all. They are called perfect insulators. The coefficient compares the heat conduction to that of Silver which is used as the standard. These items or objects which are prefect insulators would most probably posses a constant close to zero.
Heat passes through conductors by a process know as gradient transport. It depends on 3 things, the conductivity of the material, the area of the cross section and the spatial gradient of temperature.If the gradient or cross section is large, the heat will flow or be conducted faster. An experiment can be done with bars of metal with different cross sections. The relative conductivity of the differing cross sectional bars is measured along the x axis taking and time into account in a function that is expressed as c(x) .In the experiment heat is conducted through the bar and the cross section of the bar has to be determined. Heat is applied in three ways as a temperature as a heat flux or as a sinusoidal temperature. Heat is measured at the far end of the bar in 2 ways, either through heat loss or as a fixed temperature. Heat is measure according to position. The experiment can be run in2 ways. One way is to measure the heat with heat probes that move and one way where the heat along the entire bar is shown. Bounding conditions and cross sections of the bars are random in a third method of experimentation , the experimentor can choose his own bar cross section and his own bounding condition. This yields tempieture profile.
Heat also passes through materials without large movement of mass from place to place. It speed of movement though the object is perpendicular to the area and is proportional to that areand to the steepness with which the temperature is changing in the direction of flow through the area. This law for heat conduction was first developed in 1804 by Jean Baptist Biota a French physicist .The large values for metals happen because metal are very dace as counts the nimbler of elector of electors that an carry much of the energy of the heat flow