Exact analytical solution of the influence of an external centrifugal field and the heat transfer on a confined gas between two plates in the unsteady state

Abstract

This paper aims to study the non-stationary situation of the effectiveness of an external centrifugal force (ECF) and the heat transfer (HT) on the manner of neutral gas (NG). We solve a system of non-linear non-stationary partial differential equations, which represents an enormous task. Our model is examined to follow the manner of the macroscopic properties of the NG that bounded between two parallel horizontal rigid fixed plane plates (HRFPPs). The moment method and the traveling wave method are utilized. The draw an analogy among the perturbed distribution function (DF), and the equilibrium DF with time is studied. The thermodynamic predictions are calculated. System internal energy change (IEC) is investigated. We applied the results for laboratory helium NG. We detected that in specific conditions, we could compensate for the decreasing of particles’ number adjacent to the lower HRFPP because of the centrifugation process, with other particles adjacent to the higher heated HRFPP. We did that with the help of the reverse heat current from the heated upper HRFPP, which gave us a considerable enhancement and development of gases isotope separation processes. Furthermore, we approved that our model is compatible with the second law of thermodynamics, the rule of Le Chatelier, and the H-Theorem of Boltzmann. Those investigations were done with a non-restricted range of the temperatures ratio factor, the centrifugal Mach number, and the Knudsen numbers. The significance of this study was due to its vast applications in numerous fields, such as in physics, engineering, biomedical, and various commercial and industrial applications.