# Physical meaning of thermal conductivity tensor

• Hansol
In summary, thermal conductivity has a form of second-rank tensor where the diagonal components represent normal stress and the off-diagonal components represent shear stress. Similarly, the off-diagonal components of the thermal conductivity tensor also have a special physical meaning, with kxy representing the heat flux in the x direction due to a temperature gradient in the y direction. This applies to kyx as well, although it can be difficult to remember which is which. As an example, imagine how heat would flow in a carbon-fibre composite where the fibres are at an angle to the y axis.

#### Hansol

Good afternoon everyone!

I've learned that thermal conductivity has a form of second-rank tensor. As you know, diagonal components of stress tensor mean normal stress and other components mean shear stress and like that do off-diagonal components of thermal conductivity tensor have some special physical meaning??

I think thermal conduction only considers 'direction' so I think k_xy, k_xz have to have same value with k_y and k_z
Is it right??

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kxy means the heat flux in the x direction due to a temperature gradient in the y direction. (Or is that kyx? I can never remember. But hopefully you get the point.)
Think, for example, how heat would flow in a carbon-fibre composite where the fibres are at an angle to the y axis.

Chestermiller
mjc123 said:
kxy means the heat flux in the x direction due to a temperature gradient in the y direction. (Or is that kyx? I can never remember. But hopefully you get the point.)
Think, for example, how heat would flow in a carbon-fibre composite where the fibres are at an angle to the y axis.
Oh... I understand your clear explanation! Thank you for answering me :)