Irreversible Thermodynamic of a New Model of the Collision Term of the Boltzmann Kinetic Equation Dealing with Gas Mixture affected by a Centrifugal Field

Taha Zakaraia Abdel Wahid

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arXiv · 1811.10887

Irreversible Thermodynamic of a New Model of the Collision Term of the Boltzmann Kinetic Equation Dealing with Gas Mixture affected by a Centrifugal Field

Taha Zakaraia Abdel Wahid

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Abstract

In the present paper, a new model of the collision term, of the Boltzmann Kinetic equation dealing with binary gas mixture affected by a centrifugal field, is introduced. The new model is representing a modification of the BGK (Bhatnagar-Gross-Krook) model of the Boltzmann kinetic equation to be suitable for studying the influence of centrifugal field affected on gases mixture. The scientific achievement of the new model is that it is a very simple model without any mathematical complexity; but without any loss of generality. We shed light upon that the new model is satisfied the conservation of energy, conservation of mass, and conservation of momentum laws, the second law of thermodynamic, and the principle of maximum entropy production that is like the BGK model itself. Complete mathematical model for a centrifugal field, used in Uranium enrichment process affected on gases mixture between two coaxial circular porous rotating cylinders, is presented which is an important application for our new model. We also, introduced the complete irreversible thermodynamics properties of the system for the first time at all, for the best of our knowledge. The entropy, entropy flux, entropy production, thermodynamic forces, kinetic coefficients are presented for our model system. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation. The main important implementation of the model is the uranium enrichment that is used in nuclear energy generation or nuclear weapons, many medical applications and various industrial amazing applications. The flow of a binary gases mixture of UF6, and N2 between rotating cylinders is the first important suggested problem enforcement of the new model.

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Taha Zakaraia Abdel Wahid. 2018-11-27. Irreversible Thermodynamic of a New Model of the Collision Term of the Boltzmann Kinetic Equation Dealing with Gas Mixture affected by a Centrifugal Field. https://arxiv.org/abs/1811.10887

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