This paper discusses the extremisation of the entropy production in fluidic networks to gain insight into using non-equilibrium thermodynamics for mathematically formulating thermal engineering transfer phenomena. In the study, a variational formulation of the two-phase flow distribution in a fluidic junction is developed. Moreover, based on the flow representation, it is shown that the flow is distributed such that the entropy production rate is either maximised or minimised. Specifically, considering a homogeneous representation of the flow in an adiabatic fluidic network, the flow rates are distributed to maximize the entropy generation rate. Contrarily, when a separate flow representation is adopted, the stationary flow rates are distributed to yield the minimum entropy generation rate. Additionally, various characteristics which affect the flow distribution ratio and phase separation, such as the geometric imbalance, the gravitational static head, the total inlet mass flux, different thermo-physical properties of the fluid, and a generalised number of parallel branches are explored. This supports the possibility of relying on non-equilibrium thermodynamics, instead of introducing case-specific empirical correlations, for obtaining general mathematical formulations of thermal engineering transfer phenomena.
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