Physical meaning of thermal conductivity tensor

[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??

 

[mjc123]

k_xy means the heat flux in the x direction due to a temperature gradient in the y direction. (Or is that k_yx? 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.

 

[Hansol]

k_xy means the heat flux in the x direction due to a temperature gradient in the y direction. (Or is that k_yx? 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 :)