Conservation of Heat Flux and Energy

The integration of the mass conservation into the mechanical energy conservation equation enables us to consider the density ρ as a potential, whose value is recovered in a coherent manner by the divergence of the velocity in the motion balance equation. The conservation of the heat flux Φ can be characterized by a conservation law which, in the first instance, simply gives the Fourier's law. In fluid dynamics, the conservation of mass and the conservation of momentum are two separate laws. Similarly, the conservation of energy and conservation of flux are also characterized by two independent laws. The solution to a problem of heat transfer in a material can typically be acquired by solving the energy balance equation associated with the boundary conditions.