Novel Numerical Investigations of Some Problems Based on the Darcy–Forchheimer Model and Heat Transfer

Fahir Talay Akyildiz, Fehaid Salem Alshammari () and Cemil Tunç
Additional contact information
Fahir Talay Akyildiz: Department of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Fehaid Salem Alshammari: Department of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yıl University, Van 65080, Turkey

Mathematics, 2024, vol. 12, issue 11, 1-21

Abstract: In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct on the basis of a Darcy–Brinkman–Forchheimer model and the electroosmosis-modulated Darcy–Forchheimer flow of Casson nanofluid over stretching sheets with Newtonian heating problems. The approximate solution is represented in terms of Chebyshev delta shaped basis functions. Novel error estimates for interpolating polynomials are derived. Computational experiments were carried out to corroborate the theoretical results and to compare the present method with the existing Chebyshev pseudospectral method. To demonstrate our proposed approach, we also compared the numerical solutions with analytic solutions of the Poisson equation. Computer simulations show that the proposed method is computationally cheap, fast, and spectrally accurate and more importantly the obtained approximate solution can easily be used by researchers in this field.

Keywords: Chebyshev delta shaped collocation method; Chebyshev pseudospectral method; Darcy–Brinkman–Forchheimer model; heat transfer; nanofluid; stretching sheet (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/11/1742/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/11/1742/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:11:p:1742-:d:1407937

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().