Solving Natural Convection Of Darcian Fluid In Porous Media Using Rational Chebyshev Collocation Method

Authors

Mahmoud A. Nassar, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City 11884, Cairo, EgyptFollow
Mohamed A. Ramadan, Mathematics Department and Computer Science, Faculty of Science, Menoufia University, EgyptFollow
Kamal R. Raslan, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City 11884, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, numerical technique is introduced for solving natural convection of Darcian fluid about a vertical full cone embedded in porous media with a prescribed wall temperature or surface heat flux boundary conditions. The power function of distance from the vertex of the inverted cone gives us nonlinear differential equation. Rational Chebyshev collocation method is used to solve the produced third order nonlinear differential equation with boundary conditions transformed to a system of nonlinear equations. The proposed base is specified by its ability of deal with boundary conditions with an independent variable that may tend to infinity with easy manner without divergent. Moreover, we compare the proposed method with other methods to investigate applicability and accuracy.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140514

Recommended Citation

A. Nassar, Mahmoud; A. Ramadan, Mohamed; and R. Raslan, Kamal (2020) "Solving Natural Convection Of Darcian Fluid In Porous Media Using Rational Chebyshev Collocation Method," Applied Mathematics & Information Sciences: Vol. 14: Iss. 5, Article 14.
DOI: http://dx.doi.org/10.18576/amis/140514
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss5/14