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Numerical and Analytical Solution of Gas Flow Through a Micro-Nano Porous Media: A Comparison

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Abstract:

In this paper, we study a non-linear two-point boundary value problem (BVP) on semi-infinite interval that describes the unsteady gas equation. The solution of the mentioned ordinary differential equation (ODE) is investigated by means of the Hermite functions collocation method and the Homotopy analysis method (HAM). The Hermite functions collocation method reduces the solution of above-mentioned problem to the solution of a system of algebraic equations and finds its the numerical solution. The homotopy analysis method is also one of the most effective methods in obtaining series solutions for these types of problems and finds their analytic solution. Through the convergence of these methods we determine the accurate initial slope y′(0) with good capturing the essential behavior of y(x). Numerical and analytical evaluations and comparisons with the results obtained are also discussed at the last part of the paper.

Keywords: COLLOCATION METHOD; HERMITE FUNCTIONS; HOMOTOPY ANALYSIS METHOD; MICRO-NANO POROUS MATERIALS; NONLINEAR ODE; UNSTEADY GAS EQUATION

Document Type: Research Article

DOI: http://dx.doi.org/10.1166/jctn.2011.1922

Publication date: October 1, 2011

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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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