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This paper discussed a new mathematical model of the Boltzmann equation for a gas mixture influenced by a centrifugal force. We do that to study the performance of the particles’ non-equilibrium unsteady distribution function of a gas confined between two parallel rigid concentric cylinders. This examination is done in a non-restricted range of Knudsen number and a non-restricted range of a centrifugal Mach number. For this approach, an exact analytical moments equation of the new kinetic mathematical model is presented for two-sided non-equilibrium distribution Maxwellian functions. Our new mathematical model is a significant modification and a considerable development of the BGK (Bhatnagar-Gross-Krook) model of the Boltzmann equation to be appropriate for investigating the effect of the centrifugal force on a neutral gas mixture. The new mathematical model’s scientific achievement is that it represents an uncomplicated mathematical model that has no mathematical complication. On the other hand, the mathematical model does not lose any of its generality. The mathematical model formula is citable for any coordinate system. Nevertheless, we will focus here on the mathematical model related to the cylinder coordinate. We shed light upon the new mathematical model satisfaction of the conservation laws of energy, mass, and momentum, thermodynamics second law, and Boltzmann H-theorem. The new mathematical model for a centrifugal force, utilized in the Uranium enrichment process and affecting on the neutral gas mixture between two concentric circular rigid cylinders, is discussed as a significant application for the new mathematical model. We also introduced the irreversible non-equilibrium thermodynamics mathematical formulas of the system related to the new mathematical model for the first time at all. The ratios between the various participations of the internal energy modifications are calculated. The flow of a neutral binary gas mixture of (UF6 and N2) between rotating cylinders is the first suggested problem enforcement of the new mathematical model.

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