ItemArticle

DarcyForchheimerBrinkman flow of a Newtonian fluid through an enclosure with two straight boundaries and one curved boundary

Title
DarcyForchheimerBrinkman flow of a Newtonian fluid through an enclosure with two straight boundaries and one curved boundary
Creator
Sam, Neha Elizabeth; Nagouda, Smita S.; Siddheshwar, P.G.
Description
The study examines the flow and heat transfer of a Newtonian fluid in a porous medium inside an enclosure with two straight boundaries and one curved boundary. This setup is important for heat storage and energy systems. The aim of this study is to solve the Brinkman-Forchheimer (BF) equation in an enclosure with two straight and one curved boundary. The research also looks to perform a thorough heat transfer analysis to improve the understanding of thermal behaviour in porous medium BF flow. Additionally, the study calculates the Nusselt number using a compatibility condition to ensure the results are physically consistent. Finally, it fits the Nusselt number as a function of the shape factor (s) and the Forchheimer number (F). This helps in capturing the trends in convective heat transfer behaviour within the medium.The main assumptions include a steady, fully developed flow in the z-direction with a constant axial pressure gradient -, and zero axial velocity (w = 0) on all boundaries. The domain in three-dimensions is defined in cartesian coordinates (x,y,z), with on the curved boundary,ensuring the spatial constraint of the geometry. The quasi-linearisation method is used to linearise the governing equations, resulting in a system of linear algebraic equations that is subsequently solved using the alternate direction implicit (ADI) method with an accuracy of. The findings show that an increase in the shape factor (s) results in a plug flow behaviour and better heat retention, as in higher temperature profiles and centreline velocities. In contrast, higher Forchheimer numbers causes a drop in both velocity and temperature due to increased flow resistance. But as F goes up, the Nusselt number always increases, meaning heat is better transferred through convection. The study also shows that hot spots and heat islands form inside the enclosure, especially when the shape factor is higher, because the heat builds up more quickly when there is less resistance, which is an essential thing to think about for things like heat storage systems, where it is crucial to have better thermal efficiency. The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.
Source
International Journal of Applied and Computational Mathematics;Volume;11;Issue;5;Article No.;195;
Date
01-01-2025
Publisher
Springer
Subject
ADI scheme; BrinkmanForchheimer(BF) flow; Finite difference method (FDM); Linear and curved boundary; Quasi-linearization
Coverage
Sam N.E., Department of Mathematics, Center for Mathematical Needs, CHRIST University, Karnataka, Bangalore, 560029, India; Nagouda S.S., Department of Mathematics, Center for Mathematical Needs, CHRIST University, Karnataka, Bangalore, 560029, India; Siddheshwar P.G., Department of Mathematics, Center for Mathematical Needs, CHRIST University, Karnataka, Bangalore, 560029, India
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 23495103;
Format
online
Language
English
Type
Article

Citation

Sam, Neha Elizabeth; Nagouda, Smita S.; Siddheshwar, P.G., “DarcyForchheimerBrinkman flow of a Newtonian fluid through an enclosure with two straight boundaries and one curved boundary,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 19, 2026, https://archives.christuniversity.in/items/show/22078.

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