Thermal contact resistance: Definition, Formula (Heat transfer)

What is Thermal contact resistance in heat transfer?

The Thermal contact resistance is the resistance to the conduction heat transfer present between two contacting materials per unit area. Thermal contact resistance arises due to improper contact between two bodies. Due to irregularities present on the surface, Contacting area available for heat conduction is very less.

Due to the surface irregularities, the air or any gas is filled between these gaps which act as insulation for conduction.

Causes of Thermal contact resistance:

microscopic view of contacting surfaces
Microscopic view of contacting surfaces

The surfaces of the mating bodies which look smooth in visual inspection have irregularities on a microscopic level. The above figure shows the microscopic view of contacting surfaces.

As shown in the figure, the surface of the bodies has a crest and valley, therefore the two bodies can contact each other at some points only while in the remaining portion, the air gap is present.

This air gap has comparatively low thermal conductivity, therefore it adds extra resistance to the flow of heat. This resistance per unit area of contacting surface is known as Thermal contact resistance.

Formula of the Thermal contact resistance:

contact resistance

The thermal contact resistance (TCR) for the two contacting surfaces is given by the ratio of temperature difference at the contact of two bodies to the rate of heat flux.

Mathematically, the TCR formula is given by,


Thermal contact resistance units:

SI unit:

In the SI system, the unit of temperature is K, and the unit of heat flow rate is W/m².

`\therefore R_{TC}=\frac{\Delta T}{q}=\frac{K}{\frac{W}{m^{2}}}= \text{K.m²/W}`

∴ The SI unit is K.m2/W

FPS unit:

In an FPS system, the unit of temperature is °F and the unit of heat flow rate is BTU/ft².hr.

`\therefore R_{TC} = \frac{\Delta T}{q}=\frac{°F}{\frac{Btu}{ft^{2}.hr}}= ° F.ft^{2}. \text{hr/Btu}`

∴ FPS unit is °

How to reduce Thermal contact resistance?

Here are some methods that will help to reduce TCR:-

  1. Make the contacting surface highly polished which reduces the air gap between the two bodies.
  2. The application of pressure on contacting bodies helps to improve contact between two bodies.
  3. An increase in the pressure of ambient gas present in gaps helps to reduce contact resistance.
  4. Removing the air gap by application of high thermal conductivity grease between the contacting surfaces reduces the contact resistance.

Related articles:

Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.

2 thoughts on “Thermal contact resistance: Definition, Formula (Heat transfer)”

  1. the Temp of T1 and T2 are unknow ? how do we calculate the thermal resistance between the two layers at the interface between them ?

    • If you have thermal conductivity (K) for material A and B, Thickness (X_(A) & X_(B)), and amount of heat flux (q) then you can find the interface temperature T_(1) and T_(2) by Fourier equation for conduction as,

      q = [T_(i) – T_(1)]/[(L_{Surface A})/(K_{Surface A})]

      q = [T_(2) – T_(o)]/[(L_{Surface B})/(K_{Surface B})]

      Now by using these temperatures T_(1) and T_(2) you can find contact resistance.


Leave a Comment