This Fourier equation can be derived by substituting Fourier’s linear approximation of the heat flux vector, q, as a function of temperature gradient, q = − − k ∇ ∇ θ θ , into the first law of thermodynamics ρ ρ c ∂ ∂ θ θ ∂ ∂ t + ∇ ∇ ⋅ ⋅ q = 0 , where the del operator, ∇, is defined in 3D as ∇ ∇ = i ∂ ∂ ∂ ∂ x + j ∂ ∂ ∂ ∂ y + k ∂ ∂ ∂ ∂ z .