In an irreversible thermodynamics framework, Stokes' second problem was examined for unsteady oscillating flow. The objective was to apply that for a plasma near an illimitable oscillating rigid plane plate under the influence of an unsteady nonlinear applied magnetic field. The Bhatnagar-Gross-Krook (BGK) pattern of the Boltzmann kinetic equation supplemented by Maxwell's equations was investigated. The method of moments was applied with a two-sided distribution function. The exact traveling wave solution was obtained for a system consisting of four non-homogeneous partial differential equations. The velocity, shear stress, viscosity coefficient, generated electric field, applied nonlinear magnetic field, polarization, gyro-radius, and gyro-frequency were calculated. Furthermore, the distinction between the equilibrium velocity distribution function and the perturbed distribution functions was theoretically clarified at distinct time values. The advantage of the Boltzmann equation permitted us to consider irreversible non-equilibrium thermodynamics principles. For that purpose, the calculated distribution functions should be used in the formulae of entropy, entropy flux, thermodynamic forces, and kinetic coefficient. From the analysis of the results, it is found that Boltzmann's H-theorem, thermodynamics laws, and Le Chatelier's principle were consistent with our model for the whole system. The distinct contributions of the forces exerted on the system modified its internal energies; they were expressed via the Gibbs formula. The results demonstrated that the proposed model is capable of describing the behavior of plasma helium gas in the upper atmosphere ionic belts. Based on the analytical calculations, 3D-Graphics illustrating the physical quantities were drawn to predict their conduct, and the results are deeply discussed. INDEX TERMS Plasma materials processing, nuclear and plasma sciences, electrons, atmospheric-pressure plasmas, plasma applications, plasma transport processes, kinetic theory, electrokinetics, fluid dynamics, gases, electromagnetic fields.

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This article analyzes the growth of the vapor bubble in a novel model of power-law nanofluids (Al2O3/H2O) under a new effect of variable surface tension. The governing equations of the rising vapor bubble flow model are formulated and converted to a single equation describing the bubble dynamics behavior. By employing the model of Plesset and Zwick method, we investigate a new model of equations within power-law nanofluids to examine the effect of different physical parameters such as initial superheating liquid, critical bubble radius, and thermal diffusivity on the vapor bubble formation. Furthermore, the effects of surface tension behavior with the initial bubble radius, time, and initial rate of bubble radius are examined. It is found that the growth of the vapor bubble radius increases with the increase of initial superheating liquid, critical bubble radius, and thermal diffusivity. In addition, the connection between shear stress and shear rate is analyzed in detail. Using appropriate values for the physical parameters, the behavior of solutions of the vapor bubble is discussed. Based on the conducted simulation analysis, the behavior of the solutions is found to be more accurate than those in the previous studies. Besides, the obtained results demonstrate that the vapor bubble in power-law nanofluids grows slower than in pure water.

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