Variational principles in terms of entransy for heat transfer

A variational principle for heat conduction is formulated which results in the steady state heat conduction equation established from the Fourier law. Furthermore based on the thermodynamics in terms of entransy a more general functional is defined for incompressible fluids. We show that extremizing this functional gives rise to the state described by the Navier-Stokes-Fourier equations with vanishing substantive derivatives of the temperature and velocity field. In this sense one may conclude that this variational principle is consistent with the Navier-Stokes-Fourier equations. Therefore the variational principle developed in the present work demonstrates a great advantage over the minimum entropy production principle.