where the constant of proportionality, k > 0 , is the thermal conductivity. This is called Fourier's law of heat conduction. Despite its name, it is not a law but a definition of thermal conductivity in terms of the independent physical quantities q ( r , t ) and T ( r , t ) . As such, its usefulness depends on the ability to determine k for a given material under given conditions. The constant k itself usually depends on T ( r , t ) and thereby implicitly on space and time. An explicit space and time dependence could also occur if the material is inhomogeneous or changing with time.