What is Thermal Conductivity? Definition, Units, Formula, Examples, Water, Air, Copper, Aluminium, Steel, Glass


In this article, we will learn what is thermal conductivity, its definition, units, formula or equation, examples for water, air, copper, aluminium, steel, glass, etc.

Let’s explore!

What is Thermal Conductivity? Definition

Let’s try to understand what do you mean by thermal conductivity?

Thermal Conductivity Basics

The capability of the material to conduct heat is referred to as thermal conductivity, and it is denoted as ‘k,’ ‘λ’  or  ‘κ.’ The quantity under discussion is included in thermophysical properties.

  • The opposite of thermal conductivity is thermal resistivity.
  • For heat sinks, materials with high thermal conductivity values are used, while materials with low values are used as thermal insulators. 

Thermal Conductivity Definition

Thermal conductivity is the intrinsic property of a material to conduct or transfer heat or electricity.

  • It is one of the methods of heat transfer, the others being convection and radiation.
  • It is a process that occurs through contact and molecular agitation without involving any movement of the matter itself. 

Heat transfers along a temperature gradient, i-e it always travels from a high-temperature site to a low-temperature site.

  • It can also be defined as the movement from the high molecular energy to the low molecular energy area.
  • Rate equations are used to determine the heat transfer.
  • One of the renowned laws is Fourier’s law of heat conduction.
  • It is explained in detail in section Fourier’s law of the blog. 

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Measurements of Thermal Conductivity

Let’s see how to measure thermal conductivity?

There are several techniques for measuring thermal conductivity. Broadly there are two methods; 

  • Steady-state Technique
  • Transient Technique

Steady-state Technique 

It involves measurement in which material under consideration does not change temperature with time. It is advantageous since it results in straightforward analysis because of constant temperature. 

The primary disadvantage is that it requires an adequately engineered setup for performing the experiments. Searle’s Bar method and Lee’s disc method are categorized under steady-state techniques. 

Transient Technique

It involves recording measurements during the heat-up process. The primary benefit of this technique is quick and easy measurements.  However, the demerit is difficult in mathematically analyzing the data during experiments. The laser flash method and transient line source method are classified as transient techniques. 

Hence, there exist several methods, but the above explained two techniques are widely in use. Each method has its pros and cons. Another critical point to ponder is that it’s easier to study the thermal properties of solids than fluids. 

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Thermal Conductivity Units & Coefficient

Thermal Conductivity Units

Temperature, length, mass, and time are the dimensions to express thermal conductivity. The SI unit of the quantity under discussion is Wm-1K-1 (watt per meter-kelvin). The quantity is also expressed in terms of power/(length*temperature),  defined as the rate of heat conduction through the material of unit thickness for each Kelvin temperature difference.

Coefficient of Thermal Conductivity

“K” is the coefficient of thermal conductivity, which is a material parameter, and it greatly depends on temperature, material’s physical properties, pressure on the material, and water content. The coefficient “K” is measured in watts per meter-kelvin(W/m K).

The substances having a large “k” are good conductors of heat, while those having small value are good thermal insulators 

Thermal Conductivity Equation or Formula

Thermal conductivity is a property, and its value varies from material to material, and every substance has a different capability to conduct heat. The mathematical equation for describing a material’s thermal conductivity is as follows:

K = (QL)/(AΔT)

In the above thermal conductivity formula or equation,

  • K : shows the thermal conductivity in W/m.K
  • Q : demonstrates the amount of heat transferred through the material in Joules/second or Watts
  • L : shows the  distance between the two isothermal planes
  • A : represents the area of the surface in square meters
  • ΔT : demonstrates the difference in temperature in Kelvin

Fourier’s Law Statement & Formula

It is a law of thermal conduction, also called the law of heat conduction. 

  • Statement 

The law states that the heat transfer through a material is directly proportional to the negative temperature gradient and area heat flows. 

  • Mathematical Form 

The mathematical form according to the statement of Fourier’s law is:

                                                        q = -k.T

  • ∇T in the formula is a temperature gradient,
  • q is thermal/heat flux, and
  • k is the thermal conductivity of the material under discussion.

Wiedemann-Franz Law Statement & Formula

The thermal and electrical conductivity of materials is expressed in terms of a law known as Wiedemann-Franz law. The law gives a ratio between the thermal and electrical conductivity of metals. 

  • Statement 

The law describes the relationship of thermal conductivity of metals with electrical conductivity and portrays the idea that good electrical conductors are also good thermal conductors. 

  • Mathematical representation

The law is justified by the mathematical formula given below. 

Kσ=LT

In the above thermal conductivity formula or equation,

  • K : is the electrical component of the thermal conductivity
  • σ : represents the thermal conductivity
  • T : demonstrates the absolute temperature
  • L : shows Lorentz number 

The Lorentz number is given below:

Where k is Boltzmann constant and e is the electronic charge. For 150 years, the law has been considered pretty stable, but recent studies have proven that it has some limitations. 

Factors affecting Thermal Conductivity

Various factors affect thermal conductivity. Some of them are explained in-depth below.

Temperature 

Temperature is a significant factor that affects thermal conductivity in metals and non-metals. Several other conditions are also discussed below in respective headings. 

In metals 

Metals’ heat conductivity is associated with free electrons, and according to the Wiedemann-Franz law (discussed above in the blog), it is proportional to absolute temperature and electrical conductivity.

The Increasing temperature results in a decrease in the electrical conductivity of pure metals, which shows that their thermal conductivity varies with increasing temperature. Similarly, when the temperature reaches 0 K, a sharp decrease is observable. 

The heat conductivity of Alloys of metals increases with increased temperature, but no noticeable change can be seen in electrical conductivity. The heat conductivity value in most pure metals is at a peak at a temperature between 2K-10K.

In non-metals 

The thermal conductivity in non-metals is associated with lattice vibrations. The thermal conductivity of non-metals does not significantly change at high temperatures.

The heat conductivity decreases and their respective heat capacities when the temperature reduces to the point below Debye temperature. 

  • The chemical phase of a substance 

When a material’s phase changes, a drastic change is observed in its heat conductivity; For instance, the thermal conductivity of ice changes from 2.18 Wm-1K-1 to 0.56 Wm-1K-1 when It transforms into the liquid phase. 

  • Electrical Conductivity of material

The Wiedemann law provides a relationship between thermal and electrical conductivity, which is only applicable for metals. In the case of non-metals, the electrical conductivity does not influence heat conductivity. 

  • Material’s structure 

Thermal conductivity is affected by the material’s structure also. Depending on the direction in which heat travels, some materials have different thermal conductivity, known as anisotropic materials. Hence structure arrangement is an essential factor in determining how easy the heat will flow in a specific direction. 

  • Gases, non-metallic solids, and metallic solids

Based on the trends in thermal conductivity, there are three main categories of materials; gases, metallic solids, and non-metallic solids. The difference in heat transfer among all of them can be associated with the different structures. 

Due to the free movement of particles, gas has low thermal conductivity values; hence they are also bad thermal transmitters. In metallic solids, particles or molecules are held in a lattice structure, and therefore, thermal conductivity significantly occurs through vibration. 

The non-metallic solids have a considerable variation, but in a nutshell, thermal conductivity is higher in non-metallic solids. In contrast, considering the variation, those materials having large air pockets will act as good insulators, but those with tight packets of particles will have a high thermal conductivity value. 

Thermal conductivity in metallic solids dramatically differs from the other two categories. Metals have the highest thermal conductivities, which can be attributed to the presence of free electrons. 

  • Thermal Anisotropy

The differences in the coupling of phonons along a specific crystal axis result in different thermal conductivity of materials along different crystal axes. The presence of thermal anisotropy demonstrates that heat flow may not be similar to the temperature gradient direction.

  • Effects of magnetic field 

Maggi-Right-Leduc Effect can explain The change in the thermal conductivity of a conductor placed in a magnetic field. When we apply a magnetic field, The development of an orthogonal temperature gradient is visible. 

  • Isotopic purity of crustal 

The isotopic purity of crystal is also impactful over the thermal conductivity of the material. Let’s consider an example, the thermal conductivity of type IIa diamond (98.9% concentration of carbon-12 isotope) is 10000 Wm-1K-1, and that of 99.9% enriched diamond is 41,000 Wm-1K-1. Hence, the difference can be seen by comparing both values. 

Materials and Thermal Conductivity of Air, Water, Copper, Steel, Glass, Silicon, Brass, Plastic, Epoxy

The blog has discussed the idea in different sections that thermal conductivity varies from material to material, depending on several factors.

Every substance belongs to a different category and hence constitutes a unique thermal conductivity value. The essential materials and their thermal conductivity concerning their structure and other properties are discussed below.

Thermal conductivity varies significantly with temperature and pressure for different materials. However, some essential materials’ thermal conductivity values at specific temperatures are below based on some tests. The table shows the values for each material.

Materials Thermal Conductivity W/m K
Air 0.024 at 0 degrees celsius
Water At 20 degrees celsius
Distilled water 0.598 
Fresh tap water 0.599
Settled tap water 0.591
Sugar solution 5 mass %0.598 
Salt solution 5 mass %0.580
Water vapors0.016
ice2.18
Copper 386 at 20 degrees celsius
Steel At 20 degrees celsius
Stainless steel 25
Steel mild 50
Glass1.05 at 20 degrees celsius
Silicon At 100 degrees celsius
Pure material 145 
Doped material98
Brass (60/40)96 at 20 degrees celsius
PlasticAt 20 degrees celsius 
Acrylic (perspex)0.20
Nylon 60.25 
Polyethylene (low density)0.33
Polyethylene(high density)0.50
EpoxyAt 20 degrees celsius
Epoxy0.17
Epoxy glass fiber0.23
Different Materials and Thermal Conductivity

Thermal Conductivity of Air

Air is a mixture of gases, and it constitutes nitrogen (78.08 volume percent) and oxygen (20.95 v.%). Additionally, air contains 0.94 v.% of inert gases and 0.03 v.% of carbon dioxide.

The air of such composition is dry, and its molecular mass is M = 28.96 g/mole. The thermal conductivity of air at zero degrees Celsius is 0.024 Wm-1K-1. The behavior of the thermal conductivity of air is the same as the viscosity.

In the liquid phase, the heat conductivity decreases with increasing temperature, whereas in the gas phase, it increases. When pressure is low and temperature is high, the thermal conductivity sharply increases due to dissociation. 

Thermal Conductivity of Water

Water constitutes hydrogen and oxygen and exists as liquid, gas, and solid. It is tasteless and odorless at room temperature, and water is an essential component that sustains life.

Water is known as a “Universal solvent,” and it has a stable thermal conductivity at 20 degrees celsius. The different types of water and their thermal conductivity values in W/m K are given in the table above. Most tests are performed at 20 degrees celsius.

Freshwater has a thermal conductivity value of 0.599 Wm-1K-1 at 20 degrees Celsius while the remaining forms of water and thermal conductivities are mentioned in the table above. Water is a good conductor of heat and electric current. 

Thermal Conductivity of Copper

A reddish chemical element and extremely ductile metal belonging to group 11 of the periodic table is copper.

The metal is found in a free metallic state naturally and is a conductor of heat and electricity. At 20 degrees Celsius, Copper has a thermal conductivity of 386 Wm-1K-1.

Thermal Conductivity of Steel

Steel is an alloy made of iron with several other materials added, and stainless steel has an additional 11% chromium.

The high tensile strength and low cost make steel an ideal and essential element in the most common sectors, like

  • building,
  • various industries,
  • infrastructure,
  • tools,
  • tackles,
  • appliances,
  • automobiles,
  • ships,
  • nuclear,
  • machinery, etc.

Steel is versatile and can be combined with different elements, resulting in 3500 different grades of metals. The thermal conductivity value of steel is pretty low when comparing all metals hence known as poor thermal conductors.

They are ideal to be utilized as insulators because they carry heat very slowly. The thermal conductivity of stainless steel and steel mild are 25 Wm-1K-1  and 50 Wm-1K-1, respectively. They are best to be used in high-temperature environments such as the engines of airplanes or cars. 

Thermal Conductivity of Glass

Glass is non-crystalline and amorphous solid transparent and is widely used for several purposes since it’s an amorphous solid.

Therefore, glass has a low thermal conductivity which is 1.05 Wm-1K-1 at 20 degrees Celsius.  Sand and some other minerals are melted, forming glass.

The material is used widely for decorative and technological purposes and in window paneling. 

Thermal Conductivity of Silicon

The word is derived from Latin silex meaning “flint or hard stone.” Silicon is a non-metallic element belonging to carbon and is an essential component in the semiconductor industry, and it makes up about 27.7 % of Earth’s crust.

Being surpassed by oxygen, this element is the second most abundant element in the earth’s crust.

The component is essential while dealing with electro-thermal device modeling or the interpretation of fast transient techniques for measuring thermal impedance because the thermal conductivity of Silicon is required in this field.

Pure silicon and doped material have thermal conductivity values of 145 and 98 Wm-1K-1. It is a good conductor of heat as well as a semiconductor. 

Thermal Conductivity of Brass

Brass is a copper and zinc alloy, and the ratios vary in different kinds of brass.

The alloy is highly appealing and aesthetic in appearance and possesses greater malleability, and it resists corrosion and has a low melting point.

Since the material is not ferromagnetic, it can easily be separated from other metals for recycling.

Brass (60/40) has a thermal conductivity of 96 Wm-1K-1. It is a good conductor of heat, and the acoustic properties of this metal make it ideal and must-use in musical instruments. 

Thermal Conductivity of Plastic

Plastic is a polymer just like synthetic fibers, and it can be molded in any shape and size when softened and can also produce durable items when hardened.

It is a broad term that refers to a massive class of semi-synthetic and synthetic organic polymers. Some of them are Acrylic (perspex), Nylon 6, Polyethylene (low density), Polyethylene(high density), having thermal conductivity values of 0.20, 0.25 , 0.33, 0.50 Wm-1K-1  respectively.

Plastic is derived from the Greek word “plastikos,” meaning “to mold.” Plastics have low thermal conductivity and therefore are suitable for insulation.

Polyethene’s mechanical strength is lower than other plastics, and it is a good insulator of electricity. 

Thermal Conductivity of Epoxy

Epoxy is an essential component family of epoxy resins, and it is used widely commercially and in various industrial products.

They are known as epoxy resins, epoxy, or epoxides and represent a broad group of reactive compounds characterized by the presence of the epoxy ring.

Epoxy is versatile and can be combined with varied curing agents to achieve properties needed for a particular application.

The epoxy resins possess very low thermal conductivity and are primarily used as an insulating material. The thermal conductivity values of epoxy and epoxy glass fiber are 0.17 and 0.23 Wm-1K-1, respectively.

Conclusion

Thermal conductivity is the thermophysical property of substances characterized by the capability of a substance to conduct heat. Different substances have different thermal conductivity values depending on the temperature, pressure, structure, and material class. There are several other factors also that govern the property and its values. 

The SI unit of quantity under consideration is Wm-1K-1 (watt per meter-kelvin). Several techniques are used to calculate the thermal conductivity of the material, but the most common are transient and steady-state techniques.

Several methods are classified under these two broad categories. The most prominent factors affecting thermal conductivity discussed in detail in the blog are temperature, thermal anisotropy, magnetic field, isotopic purity of crystal, electrical conductivity, structure, phase of the material, etc. 

The two prominent laws like Fourier’s law and Wiedmann’s law, are discussed in the blog and their respective formulas. The varying thermal conductivity values will make certain materials the best thermal insulators, while others will be the best thermal conductors.

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