Thermal Conductivity

Thermal conductivity refers to the ability of a given material to conduct/transfer heat. It is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’. The reciprocal of this quantity is known as thermal resistivity. Materials with high thermal conductivity are used in heat sinks whereas materials with low values of λ are used as thermal insulators.
Fourier’s law of thermal conduction (also known as the law of heat conduction) states that the rate at which heat is transferred through a material is proportional to the negative of the temperature gradient and is also proportional to the area through which the heat flows. The differential form of this law can be expressed through the following equation:
q = -k.∇T
where ∇T refers to the temperature gradient, q denotes the thermal flux or heat flux, and k refers to the thermal conductivity of the material in question.
An illustration describing the thermal conductivity of a material in terms of the flow of heat through it is provided above. In this example, T is greater than T. Therefore, the thermal conductivity can be obtained via the following equation:
Heat Flux = q = kA \frac{T_1 - T_2}{L} 
==Formula==
Every substance has its own capacity to conduct heat. The thermal conductivity of a material is described by the following formula:
 K = \frac{QL}{A \delta T} 
Where, 
K is the thermal conductivity in W/mK
Q is the amount of heat transferred through the material in Joules/second or Watts
L is the distance between the two isothermal planes
A is the area of the surface in square meters
ΔT is the difference in temperature in Kelvin
==Effect of Temperature on Thermal Conductivity==
Temperature affects the thermal conductivities of metals and non-metals in a different manner.
===Metals===
The heat conductivity of metals is attributed to the presence of free electrons. It is somewhat proportional to the product of the absolute temperature and the electrical conductivity, as per the Wiedemann-Franz law.
With an increase in temperature, the electrical conductivity of a pure metal decreases.
This implies that the thermal conductivity of the pure metal shows little variance with an increase in temperature. However, a sharp decrease is observed when temperatures approach 0K.
Alloys of metals do not show significant changes in electrical conductivity when the temperature is increased, implying that their heat conductivities increase with the increase in temperature.
The peak value of heat conductivity in many pure metals can be found at temperatures ranging from 2K to 10K.
===Non-Metals===
The thermal conductivities of nonmetals are primarily attributed to lattice vibrations.
The mean free path of the phonons does not reduce significantly when the temperatures are high, implying that the thermal conductivity of nonmetals does not show significant change at higher temperatures.
When the temperature is decreased to a point below the Debye temperature, the heat conductivity of a nonmetal decreases along with its heat capacity.
Category:Thermodynamics