Thermal Conductivity explained with formula and comparison

Thermal conductivity (commonly represented by k) refers to a material’s inherent ability to transport or conduct heat. It is one of three heat transport techniques, the other two being convection and radiation. Heat transport processes can be expressed mathematically using proper rate equations. This heat transfer mode’s rate equation is based on Fourier’s law of heat conduction.

It is also described as the amount of heat that can be carried per unit time per unit area through a plate of unit thickness of a certain material, with the faces of the plate varied by one unit of temperature.

Thermal conductivity is caused through molecule agitation and contact, rather than by bulk movement of the material itself. Heat flows along a temperature gradient, from a high temperature and high molecular energy region to a lower temperature and lower molecular energy region. This process will be repeated until thermal equilibrium is established. The pace at which heat is transmitted is determined by the magnitude of the temperature gradient as well as the material’s specific thermal properties.

Formula of Thermal Conductivity

Thermal conductivity is measured in terms of W/m.K (Watts per meter per degree Kelvin) and is the reciprocal of thermal resistivity, which evaluates an object’s ability to resist heat transmission. The following formulas can be used to obtain the thermal conductivity equation:

k=Q × L/A (T2−T1)

In this equation,

L refers to the length or thickness of the material m,

Q represents heat flow W,

A is the surface area of material m2, and

T2-T1 is temperature gradient K.

Variation in Thermal Conductivity

A material’s thermal conductivity is highly reliant on a variety of factors. These include the temperature gradient, material characteristics, and the length of the heat channel.

The thermal conductivity of the materials around us varies greatly, from those with low conductivities like air (0.024 W/m•K at 0°C) to those with high conductivities like copper (385 W/m•K).

The thermal conductivity of materials determines how we use them; for example, low thermal conductivity materials are excellent for insulating our homes and businesses, whereas high thermal conductivity materials are ideal for applications where heat must be moved quickly and efficiently from one area to another, such as cooking utensils and cooling systems in electronic devices. We can obtain optimal performance by selecting materials with the right heat conductivity for the application.

Relationship between Temperature and Thermal Conductivity

Because molecular mobility is the foundation of thermal conductance, a material’s temperature has a substantial influence on its thermal conductivity. Because molecules travel faster at higher temperatures, heat is transported through the material at a faster pace. This means that the thermal conductivity of the same sample can alter dramatically when the temperature rises or falls.

Understanding how temperature affects thermal conduction is crucial for ensuring that items respond as predicted when subjected to thermal stress. This is especially critical when developing fire and heat protection materials and working with products that create heat, such as electronics.

How does Thermal Conductivity affect the structure?

Thermal conductivity levels vary greatly amongst materials and are heavily influenced by the structure of each substance. These are anisotropic materials, which have varying thermal conductivity values depending on the direction of heat travel. Because of the way the structure is constructed in these circumstances, heat travels more easily in one direction.

Materials can be separated into three categories when discussing thermal conductivity trends: gases, nonmetallic solids, and metallic solids. The discrepancies in heat transfer abilities of these three categories can be linked to variances in their structures and molecular motions.

Because the molecules in gases are not as closely packed as those in solids, their relative thermal conductivities are lower, and heat transfer is heavily dependent on the free movement of molecules and molecular velocity.

  1. Gases are ineffective thermal transmitters. Nonmetallic solids, on the other hand, have molecules that are bound into a lattice network, and so heat conductivity is predominantly caused by vibrations in these lattices. Because of the near closeness of these molecules in comparison to those of gases, nonmetallic solids have the higher thermal conductivities of the two, but there is a wide range within this category.
  2. This variance is due in part to the quantity of air present within the solid; materials with a large number of air pockets are excellent insulators, whereas those with a smaller number of air pockets have a higher thermal conductivity value.
  3. Thermal conductivity in metallic materials differs from the previous instances even again. Metals, with the exception of graphene, have the highest thermal conductivities of any substance and the unique combination of thermal and electrical conductivity.

Both of these properties are communicated by the same molecules, and the Wiedemann-Franz Law explains the link between the two. This law states that at a certain temperature, electrical conductivity is proportional to thermal conductivity; however when the temperature rises, the thermal conductivity of the material increases while electrical conductivity decreases.

How to measure and test Thermal Conductivity?

Thermal conductivity is an important component of the material and its relationships and understanding it allows us to get the maximum performance out of the materials we utilize in all aspects of our life. Thermal conductivity calculation and testing are essential components of this attempt. Thermal conductivity testing methods are divided into two types: steady-state and transient. This distinction is a distinguishing feature of how each approach operates.

  1. Steady-state methods necessitate that the sample and reference parts be in thermal equilibrium before initiating measurements.
  2. Transient approaches, which do not require this rule to be followed, produce results more quickly.

Let’s discuss some applications of thermal conductivity in real life.

This study investigates the thermal conductivity of a mullite ceramic created via foaming and starch consolidation of mullite powder, and how it varies with the porosity of the ceramic. The thermal conductivity was measured using the TPS 2500 S and the Hot Disc transient plane source (TPS) method. The heat conductivity of mullite ceramic increases as its porosity increases.

As composite phase transition materials, nano-graphite (NG)/paraffin composites were created. The inclusion of NG enhanced the composite material’s thermal conductivity. The thermal conductivity of the material containing 10% NG was 0.9362 W/m•K.

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