Thermodynamic and kinetic investigation of the influence of external centrifugal field and the heat transfer on a confin
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Thermodynamic and kinetic investigation of the influence of external centrifugal field and the heat transfer on a confined neutral gas Taha Zakaraia Abdel Wahid1 · Fatma M. El‑Malky2 Received: 20 January 2020 / Accepted: 20 March 2020 © Springer Nature Switzerland AG 2020
Abstract In the present paper, we offer a new model studying the influence of an external centrifugal field and the heat transfer on a neutral gas confined between two parallel horizontal rigid stationary plane plates. The system of nonlinear differential equations is solved analytically. The temperature and concentration are calculated with a broad range of Knudsen numbers, centrifugal Mach number, and temperatures ratio parameter. We utilized the moment method with suitable boundary conditions. Thermodynamic predictions and internal energy change are examined. Results are applied for laboratory argon gas. Three-dimensional, two-dimensional, and contour plots graphics are drawn, and their manner is discussed. Keywords Kinetic theory · Rarefied gas · Gas centrifuge · Heat transfer · Non-equilibrium distribution functions · BGK model · Exact solutions · Partial differential equations · Moment method · Irreversible non-equilibrium thermodynamics · Internal energy change Mathematics Subject Classification 76P05 · 82B40 · 82B35 · 82B23 · 82B30 · 82C40 · 82C70 · 35J66 List of symbols C Velocity of the gas particles dC Volume element in velocity space, dC = dCx d Cy dCz 𝜑 Distribution function 𝜑0 Local Maxwellian equilibrium distribution function 𝜑1 Distribution function for upward going particles Cy > 0 𝜑2 Distribution function for downward going particles Cy TI
1 Introduction Increasing the separation adequacy of a neutral gas influenced by a centrifugal field is one of the vital objectives in uranium gas isotope separation, which is an essential process. The gas isotope separation has various applications in the nuclear operators, electrical power generator, many medical vital applications, and military weapons. Thermal heat transfer plus centrifugal field, affected on a gas confined between rotating cylinders or in its corresponding approximate model, like Pomraning’s model, is essential for the gas isotope separation process. In the presence of an external centrifuge field applied in a separating isotope, a countercurrent circulating the gas particles is produced by heating the upper rotor cover and cooling the bottom one. This countercurrent is because the heat transfer makes considerable separation possible in a single centrifuge [1]. Pomraning’s model [2–6] acts as if a gas situation between two cylinders can be approximated by a gas situation between two parallel rigid plane plates. In this case, the boundaries move in the opposite direction with equal speeds. The centrifugal force is Vol:.(1234567890)
simulated by affecting a mass force perpendicular to the plates and symmetrical to the distance from the uniformity plane. We can say the outward action is the same as a rigid body. Pomraning’s geometrical model is illustrated in Fi
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