Comments on the Article Titled ‘The Starting Flow in Ducts Filled with a Darcy-Brinkman Medium,’ Transport in Porous Media, 75, 55–62, 2008

Content Provider	Semantic Scholar
Author	Alkam, M. K. Al-Nimr, Moh'd A.
Copyright Year	2010
Abstract	In a recent article published at Transport in Porous media (Wang 2008), analytical solutions have been obtained for the transient forced convection fluid flow in channels filled with porous media. Three geometrical configurations have been considered, namely, circular, rectangular, and parallel plate ducts. Two of these configurations have been visited earlier by Al-Nimr and Alkam (2000), specifically, parallel plate and circular ducts. In their study, Al-Nimr and Alkam presented analytical closed form solutions for five basic fluid flow problems in porous media. These five basic cases included: (1) transient flow in porous tubes and annuli, (2) transient flow in porous tubes with suction and injection, (3) rotating liquid in porous cylindrical and annular containers, (4) steady asymptotic suction flow in a porous domain, and (5) free-convection flow in porous slabs confined between heated plates. In his study, Wang (2008) has claimed that the solution presented by Al-Nimr and Alkam (2000) for the case of transient fluid flow in porous tubes is incorrect. The present short comment is a rebuttal to Wang’s claim and it aims to prove that Al-Nimr and Alkam’s solution is correct. In the discussion section of his article, Wang reported: “Al-Nimr and Alkam (2000) attempted to solve the transient circular tube problem by an expansion in modified Bessel functions. But these functions have neither eigenvalues nor orthogonality. Thus their solution is incorrect. The correct solution, presented here, should be expressed in terms of Bessel functions J0”. In response to this statement, the basic ordinary differential equation obtained by the separation of variables for the transient momentum equation is a special case of the Sturm–Liouville problem; hence, the solutions of this equation are considered eigenfunctions and the solutions have eigenvalues. Also, the orthogonality of these solutions over a weight function is guaranteed. In order to prove that, let us start with Eq. 6 of Al-Nimr and Alkam (2000) that is rewritten below:
Starting Page	361
Ending Page	363
Page Count	3
File Format	PDF HTM / HTML
DOI	10.1007/s11242-009-9411-4
Volume Number	81
Alternate Webpage(s)	https://page-one.springer.com/pdf/preview/10.1007/s11242-009-9411-4
Alternate Webpage(s)	https://doi.org/10.1007/s11242-009-9411-4
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article