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Solving the Unsteady Isothermal Gas Through a Micro-Nano Porous Medium via Bessel Function Collocation Method

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In this study, a new numerical algorithm is introduced to solve the unsteady isothermal flow of a gas through a semi-infinite micro-nano porous medium. The unsteady gas equation is a second-order non-linear two-point boundary value ordinary differential equation (ODE) on the semi-infinite domain, with a boundary condition in the infinite. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, that is convergent for any x ∈ R. In this work, we aim to solve the problem on the semi-infinite domain without any domain truncation, variable transformation in basis functions or transformation of the domain of the problem to a finite domain. In this work, we reduce the solution of a nonlinear problem to the solution of a system of the nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method, and also.

Keywords: BESSEL FUNCTIONS OF THE FIRST KIND; COLLOCATION ALGORITHM; NONLINEAR ODE; SEMI-INFINITE INTERVAL; UNSTEADY ISOTHERMAL FLOW OF A GAS

Document Type: Research Article

Publication date: January 1, 2014

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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