Thermal conductivity definition, formula, and Thermal conductivities of some common materials

Last updated on April 15th, 2021 at 01:55 pm

In this post, we will find out the definition of thermal conductivity and its formula. We will also see a table containing thermal conductivity values for selected materials. We will also cover the significance of thermal conductivity and the Factors affecting thermal conduction.

Define Thermal Conductivity | What is Thermal Conductivity?

Thermal conductivity describes the ability of a material to conduct heat. It is temperature-dependent and is measured in its SI unit watts per meter kelvin (W m^-1 K^-1)

Thermal Conductivity Formula

The rate of energy transfer by conduction (energy per unit time) through a material can be calculated using:

Q / t = kAΔT / L ….(1)
where Q/t is the heat energy transferred in joules (J) per unit time, t, in seconds (s)

from equation (1) we get the Thermal conductivity formula:
k = (Q L)/( tAΔT) ………… (2)

k is the thermal conductivity of the material (W m^-1 K^-1)
A is the surface area in meters squared perpendicular to the direction of heat flow (m2)
ΔT is the temperature difference across the material in kelvin or degrees Celsius (K or °C)
L is the thickness of the material through which the heat is being transferred in meters (m).

Definition of Thermal conductivity from its expression

From its expression in the previous paragraph, we can define Thermal conductivity.

When A = 1, t = 1, Temperature difference ΔT =1 and L=1, then k = Q

Thermal Conductivity (k) is the quantity of heat transmitted due to a unit temperature difference between 2 ends of a conductor of unit length(or unit thickness), in unit time under steady conditions in a direction normal to a surface of the unit area.

SI unit of k is Watt meter^-1 Kelvin^-1 

Thermal Conductivity Significance

A material with a high k value will conduct heat faster than a material with a lower value of k.

If a steady temperature difference is to be maintained between the ends of say, a rod, then heat energy must be supplied at one end of the rod and the same heat must be taken out at the other end of the rod.

Here comes the importance of the ‘capability of heat transfer’ of the material. Materials of high k are used as heat sinks and materials of low k are used as thermal insulation.

Thermal conductivities of some common materials | Thermal Conductivity Value table for selected materials

Material	Thermal conductivity (Watt meter-1 Kelvin-1 )
silver	420
copper	380
aluminium	240
steel	60
ice	2.2
brick, glass	~1
concrete	~1 (depending on composition)
water	0.6
human tissue	0.2
wood	0.15
polystyrene	0.08
paper	0,06
fiberglass	0.04
air	0.025

Factors affecting thermal conduction

The rate at which heat will be transferred through a system depends on the:

• nature of the material. The larger a material’s thermal conductivity, the more rapidly it will conduct heat energy.

• temperature difference between the two objects. A greater temperature difference will result in a faster rate of energy transfer.

• thickness of the material. Thicker materials require a greater number of collisions between particles or movement of electrons to transfer energy from one side to the other.

• surface area. Increasing the surface area relative to the volume of a system increases the number of particles involved in the transfer process, increasing the rate of conduction. The rate at which heat is transferred is measured in joules per second (J s^-1), or watts (W).

Derivation of Thermal conductivity (K) formula with its dimension