The conservation of mass is expressed locally by the fact that the flow of mass density ρ ρ satisfies the continuity equation : ∂ ∂ ρ ρ ∂ ∂ t + ∇ ∇ ⋅ ⋅ J ρ ρ = 0 , where J ρ ρ is the mass flux vector. The formulation of energy conservation is generally not in the form of a continuity equation because it includes contributions both from the macroscopic mechanical energy of the fluid flow and of the microscopic internal energy. However, if we assume that the macroscopic velocity of the fluid is negligible, we obtain energy conservation in the following form: ∂ ∂ u ∂ ∂ t + ∇ ∇ ⋅ ⋅ J u = 0 , where u is the internal energy density and J u is the internal energy flux.