Heat conduction in multi-temperature mixtures of fluids: the role of the average temperature

The theory of mixture of fluids in which each constituent has its own temperature is more realistic than the models in which all the components have a common temperature and it is necessary in several physical situations, such as plasma physics. Nevertheless, from the theoretical point of view, the main problem regards the measurement of the temperature of each constituent. In this Letter we consider the simple case of the one-dimensional steady heat conduction between two walls and we adopt the concept of average temperature recently proposed by Ruggeri and co-workers such that the whole internal energy of the mixture depends only on the average temperature. Assuming that the two walls have given temperatures, we can first verify that the temperature behavior is different from the linear one predicted in the mixture theories with a single temperature. Moreover, we can also prove that, for a mixture of n constituents, the measure of the average temperature at 2(n−1) points allows to know the temperature behavior of each constituent everywhere.