As we have considered that the thermal conductivity of the solid is isotropic in nature, the above relation reduces to,

or,

where  is the thermal diffusivity of the material and its unit m²/s signifies the rate at which heat diffuses in to the medium during change in temperature with time. Thus, the higher value of the thermal diffusivity gives the idea of how fast the heat is conducting into the medium, whereas the low value of the thermal diffusivity shown that the heat is mostly absorbed by the material and comparatively less amount is transferred for the conduction. The called the Laplacian operator, and in Cartesian coordinate it is defined as

Equation 2.19 is known as general heat conduction relation. When there is no heat generation term the eq.2.19 will become,

and the equation is known as Fourier Field Equation.