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Received: 23 June 2018 Accepted: 16 October 2018 Fluid dynamic systems are usually optimised through the equation of conservation of energy according to the first law of thermodynamics. In the aeronautic sector, many authors are claiming the insufficiency of this approach and are developing studies and models with the aim of coupling the analyses according to the first and the second law of thermodynamics. Second law analysis of internal fluid dynamics has not been studied with the same attention. Just heat exchangers and heat dissipation by electronic circuits are mostly considered. This paper focuses on the analysis of general internal fluid flow problem and recognizes initially it according to the first law of thermodynamics. The energy equation for a control volume is given in integral form along with a discussion on the concepts of total energy, heat and work. The dissipative terms, which need to be minimised to increase the system efficiency, are deeply analysed leading to a new dimensionless formulation of the equation of conservation of energy. It is based on Bejan number, according to the formulation by Bhattacharjee and Grosshandler. This formulation has been directly connected to second law analysis concerning both entropy generation and exergy dissipation making a step toward a future unification of the two alternative formulations of Bejan number which have been historically developed. The ambition of this research is far from providing a definitive solution. Otherwise, it aims to both raise problems and stimulate a discussion. Bejan number has been actually used in the definition of diffusive phenomena, such as convection and diffusion through porous media. Is it reasonable to enlarge its domain to the much larger domain of general fluid dynamics? If this extension will be evaluated possible, what are the potential implications for the future of scientific research? Can be the ambiguity between Hagen number and Bejan number be resolved? Can be the ambiguity between the diffusive definition and the entropy generation definition of Bejan number be solved? Can it be possible to state the equivalence between the two alternative formulations? Is it possible to define fluid dynamic and diffusive problems according to a unified vision in the domain of thermodynamics? What are the implications concerning analysis and optimisation of fluid dynamics phenomena by new equations that couples first and the second law of thermodynamics? Could it have the role of producing an effective unification of a larger multidisciplinary domain?

A new dimensionless approach to general fluid dynamics problems that accounts both the first and the second law of thermodynamics