Thermal conductivity (K) is a property of materials that describes their ability to conduct heat. It is a tensor quantity. A tensor is a mathematical object that represents a physical quantity with multiple components that transform under coordinate transformations. In the case of thermal conductivity, it is described by a second-rank tensor.
The thermal conductivity tensor takes into account the anisotropic nature of certain materials, meaning that the ability to conduct heat can vary with direction. For isotropic materials, which have the same properties in all directions, the thermal conductivity tensor reduces to a scalar value. In this case, the thermal conductivity is a scalar quantity.
In summary, the thermal conductivity can be either a scalar (for isotropic materials) or a second-rank tensor (for anisotropic materials).