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Abdel Wahid T.Z.,Monoufiya University
Journal of Non-Equilibrium Thermodynamics | Year: 2012

This article presents an exact and enhanced solution of the study in the previous paper [Can. J. Phys., 88 (2010), 501-511]. For this purpose, I use the traveling wave solution method instead of the small parameter method, which enables us to have the full exact solution without any cut-off from the value of variables. In addition, I use the accurate formula of the electron- electron collision frequency. I persist in avoiding the discontinuity in the solution caused by the Laplace transformation results, which is included in the previous study. In the present work, the kinetic and the irreversible thermodynamic properties of the charged gas are presented from the molecular viewpoint. Our study is based on the solution of the BGK (Bhatnager- Gross-Krook) model of the Boltzmann kinetic equation, with the precision value of the electron-electron collision frequency. The BGK model equation coupled with Maxwell's equations for electrons near a moving rigid plane are solved. The distinction and comparisons between the perturbed and the equilibrium velocity distribution functions are illustrated. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma. © de Gruyter 2012. Source


Abourabia A.M.,Monoufiya University | Wahid T.Z.A.,Monoufiya University
Canadian Journal of Physics | Year: 2010

In the framework of irreversible thermodynamics, the characteristics of the Rayleigh flow problem of a rarified electron gas extracted from neutral atoms is examined and proved to obey the entropic behavior for gas systems. A model kinetic equation of the BGK (Bhatnager-Gross-Krook) type is solved, using the method of moments with a two-sided distribution function. Various macroscopic properties of the electron gas, such as the mean velocity, the shear stress, and the viscosity coefficient, together with the induced electric and magnetic fields, are investigated with respect to both distance and time. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. We restrict our study to the domain of irreversible thermodynamics processes with small deviation from the equilibrium state to estimate the entropy, entropy production, entropy flux, thermodynamic force, and kinetic coefficient and verify the celebrated Boltzmann H-theorem for non-equilibrium thermodynamic properties of the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are predicted via Gibbs' equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma. Source


Abourabia A.M.,Monoufiya University | Abdel Wahid T.Z.,Monoufiya University
Canadian Journal of Physics | Year: 2012

In the present study, the kinetic and the irreversible thermodynamic properties of a binary gas mixture, under the influence of a thermal radiation field, are presented from the molecular viewpoint. In a frame comoving with the fluid, the Bhatnagar-Gross-Krook model of the kinetic equation is analytically applied, using the Liu-Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the binary gas mixture, such as the temperature and the concentration. The distinction and comparisons between the perturbed and equilibrium distribution functions are illustrated for each gas mixture component. From the viewpoint of the linear theory of irreversible thermodynamics we obtain the entropy, entropy flux, entropy production, thermodynamic forces, and kinetic coefficients. We verify the second law of thermodynamics and celebrated Onsagers reciprocity relation for the system. The ratios between the different contributions of the internal energy changes, based upon the total derivatives of the extensive parameters, are estimated via Gibbs formula. The results are applied to the argon-neon binary gas mixture, for various values of both the molar fraction parameters and radiation field intensity. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed. © 2012 Published by NRC Research Press. Source


Abourabia A.M.,Monoufiya University | Tolba R.E.,Monoufiya University
European Physical Journal Plus | Year: 2012

The Rayleigh flow problem is studied in the framework of the Bhatnager-Gross-Krook (BGK) approximation to the Boltzmann equation supplemented by Maxwell’s equations. The behavior of a rarefied electron gas extracted from noble gases is investigated, considering the method of moments with a two-sided distribution function of Liu and Lees type. Exact solutions of the fourth-order linear homogeneous differential equations, based on the method of the separation of variables for both the mean flow velocity and the shear stress are obtained in terms of the coordinate y and time t with suitable boundary conditions. The advantage of dealing with the Boltzmann equation permits to consider the principles of the irreversible thermodynamics near-equilibrium, by substituting the calculated distribution functions in the formulae of Boltzmann’s H-theorem to evaluate entropy and entropy production. The different contributions of the forces exerted on the system change its internal energies. They are expressed via the Gibbs formula within which the diamagnetic properties of the system are predicted. © 2012, Società Italiana di Fisica and Springer. Source


Abourabia A.M.,Monoufiya University | Wahid T.Z.A.,Monoufiya University
Journal of Non-Equilibrium Thermodynamics | Year: 2011

A new approach for studying the influence of a thermal radiation field upon a rarefied neutral gas is introduced. We insert the radiation field effect in the force term of the Boltzmann equation. In a frame co-moving with the fluid, the BGK (BhatnagerGrossKrook) model kinetic equation is applied analytically. The one-dimensional steady problem is studied using the LiuLees model. We apply the moment method to follow the behavior of the macroscopic properties of the gas, such as the temperature and concentration. They are substituted into the corresponding two-stream Maxwellian distribution functions, permitting the investigation of the non-equilibrium thermodynamic properties of the system (gas + heated plate). The entropy, entropy flux, entropy production, thermodynamic forces and the kinetic coefficients are obtained. We verify the celebrated Onsager reciprocity relations for the system. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. The results are applied to the Helium gas for various radiation field intensities due to different plate temperatures. Figures illustrating the calculated variables are drawn to predict their behavior and the results are discussed. © de Gruyter 2011. Source

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