0
research-article

An accurate numerical method for solving unsteady isothermal flow of a gas through a semi-infinite porous medium

[+] Author and Article Information
Kourosh Parand

Department of Computer Sciences, Shahid Beheshti University, Tehran, Iran
k_parand@sbu.ac.ir

Mehdi Delkhosh

Department of Computer Sciences, Shahid Beheshti University, Tehran, Iran
mehdidelkhosh@yahoo.com

1Corresponding author.

ASME doi:10.1115/1.4037225 History: Received January 08, 2017; Revised July 01, 2017

Abstract

The Kidder equation, $y''(x)+2xy'(x)/\sqrt{1-\beta y(x)}=0$, $x\in [0,\infty)$, $\beta \in [0,1]$ with $y(0)=1$, and $y(\infty)=0$, is a second order non-linear two-point boundary value ordinary differential equation on the semi-infinite domain, with a boundary condition in the infinite that describes the unsteady isothermal flow of a gas through a semi-infinite micro-nano porous medium and has widely used in the chemical industries. In this paper, a hybrid numerical method is introduced for solving this equation. First, using the quasilinearization method, the equation is converted into a sequence of linear ordinary differential equations (LDEs), and then these LDEs are solved using the rational Legendre functions collocation method. Using $200$ collocation points, we have obtained a very good approximation solution and the value of the initial slope $y'(0)=-1.19179064971942173412282860380015936403$ for $\beta=0.50$, highly accurate to 38 decimal places. The convergence of numerical results is shown.

Copyright (c) 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In