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

Author

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  • 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)

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.

Suggested Citation

  • Fahir Talay Akyildiz & Fehaid Salem Alshammari & Cemil Tunç, 2024. "Novel Numerical Investigations of Some Problems Based on the Darcy–Forchheimer Model and Heat Transfer," Mathematics, MDPI, vol. 12(11), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1742-:d:1407937
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    References listed on IDEAS

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    1. Ma, Qinguo & Luo, Xiaoxiao & Gao, Jianqiang & Sun, Weiyu & Li, Yongdong & Lan, Tianli, 2022. "Numerical evaluation for cooling performance of a composite measure on expressway embankment with shady and sunny slopes in permafrost regions," Energy, Elsevier, vol. 244(PB).
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