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Journal of Applied Mathematics
Volume 2017, Article ID 7305230, 10 pages
https://doi.org/10.1155/2017/7305230
Research Article

Solvability of the Brinkman-Forchheimer-Darcy Equation

School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana 010000, Kazakhstan

Correspondence should be addressed to Piotr Skrzypacz; zk.ude.un@zcapyzrks.rtoip

Received 26 May 2017; Accepted 19 June 2017; Published 20 July 2017

Academic Editor: Malgorzata Peszynska

Copyright © 2017 Piotr Skrzypacz and Dongming Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy’s range.