This is to say that the heat flow and the temperature gradient are vector quantities related by the thermal conductivity tensor.
In the generic anisotropic case, to estimate the temperature field, it is necessary to determine the thermal conductivity tensor of ground.
The thermal conductivity tensor and the anisotropy (defined as [a.
For the stratified geologic regime, this assumption is not valid, and one must introduce the thermal conductivity tensor [[LAMBDA].
parallel]] is larger than the orthogonal component of the thermal conductivity tensor [[lambda].
Although empirical formulas gave just approximate values of hydraulic conductivity and results must be interpreted with caution, they are consistent with the hypothesis of an anisotropic medium with the major conductivity tensor
oriented along the horizontal plane, and the minor direction along the vertical.
z] = radial, angular, and longitudinal components of the water conductivity tensor
The assumption here is that the principal directions of the sample thermal conductivity tensor
are parallel to the corresponding sample surfaces.
Contract Bounds on the Effective Conductivity Tensor of Anisotropic Random Materials
For more general random materials, Sen and Torquato (118, 119) derived a series expansion for the effective conductivity tensor [[Sigma].
By taking certain Pade approximants of Eq 75, Sen and Torquato (118) obtained bounds of arbitrary order on the effective conductivity tensor [[Sigma].
For the sake of convenience the conductivity tensors