# How To Calculate Thermal Conductivity

## How To Calculate Thermal Conductivity

Thermal conductivity refers to the heat transfer through 1 square meter area in 1 second for a 1m thick material with a temperature difference of 1 degree (K, ℃) on both sides of the material under stable heat transfer conditions, the unit is watts /m.degree (W/m.K, where K can also be replaced by °C). It is a physical quantity that expresses the thermal conductivity of a material, and uses Fourier’s law as the formula for calculating its thermal conductivity.

The thermal conductivity of materials varies with composition, physical structure, state of matter, temperature, pressure, etc. The thermal conductivity of different components varies greatly, resulting in a large difference in thermal conductivity of materials composed of different components. Air is a poor conductor of heat, and the thermal conductivity of single-grain materials is better than that of stacked materials.

In addition, in general the thermal conductivity we defined above is for homogeneous materials. In practice, there are porous, multi-layer, multi-structure, and anisotropic materials. The thermal conductivity obtained by this material is actually a performance of comprehensive thermal conductivity, also known as the average thermal conductivity.

Fourier’s law is a basic law in heat transfer, which can be used to calculate the amount of heat conduction (Fourier’s law of heat conduction).

So, what is the formula for calculating thermal conductivity?

According to Fourier’s law of thermal conductivity, the relevant thermal conductivity calculation formula is expressed as follows:

Φ=-λA(dt/dx)

q=-λ(dt/dx)

Where Φ is the thermal conductivity, the unit is W

λ: thermal conductivity

A: Heat transfer area, the unit is ㎡

t: temperature, in K

x: the coordinate on the heat conduction surface, the unit is m

q: The heat flux density transferred along the x direction (strictly speaking, the heat flux density is a vector, so q should be the component of the heat flux density vector in the x direction) in W/㎡

dt/dx: the rate of temperature change of the object along the x direction

Mathematical expression in general form: q=-λgradt=-λ(dt/dx)n

In the formula: gradt refers to the temperature gradient of a certain point in space; n refers to the normal unit vector on the isotherm passing through the point, which refers to the direction of temperature increase.

The negative sign in the above formula indicates that the direction of heat transfer is opposite to the direction of the temperature gradient

λ is a physical parameter that characterizes the thermal conductivity of the material (the larger the λ, the better the thermal conductivity).

Usually, the thermal conductivity of materials in daily experiments cannot be obtained simply by using the thermal conductivity calculation formula, and the combination of theory and experiment is an important source of thermal conductivity data.

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