Constructal theory through thermodynamics of irreversible processes framework

Point to volume flow problem is revisited on a thermodynamics of irreversible processes (TIP) basis. The first step consists in evaluating the local entropy production of the system, and deducing from this expression the phenomenological laws. Then, the total entropy production can be simply evaluated. It is demonstrated that total entropy production can be written in a remarkable form: the product of the so-called entropy impedance with the square of the heat flux. As the heat flux is given, optimisation consists in minimising the entropy impedance. It is also shown that minimising entropy impedance minimises the maximum temperature difference. Applied to the elemental volume, this optimisation process leads to a shape factor close to the one already published. For the first construction, the equivalent system is defined as stated by Prigogine: when subjected to the same constraints, two systems are thermodynamically equivalent if their entropy production is equal. Two optimisation routes are then investigated: a global optimisation where all scales are taken into account and the constructal optimisation where the system is optimised scale by scale. In this second case, results are close to Ghodossi’s work. When global optimisation is performed, it is demonstrated that conductive paths have to be spread uniformly in the active material (i.e. the number of elemental volumes must go to infinite). Comparing the two routes, global optimisation leads to better performance than constructal optimisation. Moreover, global optimisation enlarges the domain of construction benefits. All these results are finally proven by 2D simulations.