**Significance **

Energy efficiency has become a major global interest due to numerous environmental issues including global warming concerns. For example, heating ventilation and air conditioning facilities consume a good chunk of the total global energy output. To this end, the development of better design and analysis strategies for flow distribution through the network is highly desirable in enhancing the system performances.

The efficiency of heating ventilation and air conditioning systems are generally determined based on the entropy concept. However, in an attempt to expand its applications and solve fundamental fluid and heat-related problems, an entropic potential number related to the entropy generation and loss availability have been proposed. Additionally, the relationship between the head loss coefficient, a concept of fluid mechanics, to the entropy generation, has attracted significant attention from researchers.

To this note, Universitat Politècnica de València-based researchers: Víctor-Manuel Soto-Francés, José-Manuel Pinazo-Ojer, Emilio-José Sarabia-Escrivá, and Pedro-Juan Martínez-Beltrán looked at the feasibility of using the minimum entropy production principle to compute the steady-state flow distribution in an existing network. This principle is the same as the minimal dissipation of energy that is mostly used in isothermal and incompressible flows. The work is currently published in the journal, *Energy.*

Prior to their work, Niven, a renowned scientist developed two methods: minimum entropy production and maximum entropy production to study steady states of systems. He proposed the existence of a power-law for energy dissipation with an exponent which has to be the same for the whole network. Even though the initial results were discarded by Niven as a general method, the authors in this paper demonstrated why it should not be discarded, by analyzing the role of the chosen exponent and its influence on the underlying physical phenomena.

The existence of a hidden fixed-point value problem associated with the steady-state flow distribution throughout the network was discussed. Specifically, the nature of the fixed point was investigated. On the other hand, the authors’ research was inspired fundamentally by the difficulties in designing return duct-networks due to the flow interaction in branched junctions that resulted in negative head loss coefficients.

This method is specifically developed for tree-shaped duct-networks that are commonly encountered in heating ventilation and air conditioning systems. The authors showed that by keeping the loss coefficient constant and using the same power law for the whole network system, the system’s application is not jeopardized in any way, as demonstrated by the interplay between the flow rate and the loss coefficients. Consequently, a fixed-point function problem formulation was obtained through the combination of minimization step with physical dependence of the flow rate. Whereas the problem solution could lead eventually to stationary points at a maximum, it depends on the components dissipation function shape but its practical implications require further analysis.

According to the Spanish research team, the new method has advantages, though not exclusively, in situations involving return networks with strong flow interactions at branched junctions even though the latter has not been fully analyzed. Preliminary studies are promising and show quite interesting results. Although the study focused on analyzing the steady-state distribution of an already existing tree-shaped heating ventilation and air conditioning duct-network, it can be used to design other types of networks. The authors have extended recently, their results to arbitrary shaped flow networks, although still without branching effects. It can be found in their HEFAT2019 congress paper. This forms the basis of future studies which aim to finally include the branching flow interactions.

**References**

Soto-Francés, V., Pinazo-Ojer, J., Sarabia-Escrivá, E., & Martínez-Beltrán, P. (2019). **On using the minimum energy dissipation to estimate the steady-state of a flow network and discussion about the resulting power-law: application to tree-shaped networks in HVAC systems. **Energy, 172, 181-195.

Víctor-Manuel Soto-Francés, José-manuel Pinazo-Ojer, Emilio-José Sarabia-Escrivá, Peddro-Juan Martínez-Beltrán (2019). **About using the minimum energy dissipation to find the steady-state flow distribution in networks. **Heat Transfer, Fluid Mechanics and Thermodynamics, 14th international conference. HEFAT, Wicklow Ireland.