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Combined Newton–Raphson and Streamlines-Upwind Petrov–Galerkin iterations for nanoparticles transport in buoyancy-driven flow
Open accessAbstract
The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the Navier–Stokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection-dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines Newton’s method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that the Stream-Upwind Petrov–Galerkin regularization approach is required to solve properly the transport equation in Buongiorno’s model, in the Finite Element framework. Indeed, we formulate this ill-posed equation as a variational problem under mean value constraint. Numerical analysis and computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature.
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“On the other hand, a more advanced two-phase model taking into account the Brownian diffusion and thermophoresis diffusion slip mechanisms as originally proposed by Buongiorno45, then further improved for numerical stability by Riahi et al.48, and upgraded by Amidu et al.47 to also include nanoparticles sedimentation effects, would be more suitable for such multi-cycle simulations.”
From A critical assessment of nanoparticles enhanced phase change materials (NePCMs) for latent heat energy storage applications (2023) · cites this paper as [48]
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Cited by
Amidu, M. A., Ali, M., Alkaabi, A. K., & Addad, Y. (2023) · Scientific Reports · doi:10.1038/s41598-023-34907-0 · Cited by 101
Self-citation
Metadata
- Authors
- Riahi, M. K., Ali, M., Addad, Y., & Abu-Nada, E.
- Affiliations
- Khalifa University of Science and Technology (AE)
- Corresponding author
- Riahi, M. K.
- Venue
- Journal of Engineering Mathematics
- Published
- 2022-01-19
- Volume
- 132
- Issue
- 1
- ISSN
- 0022-0833 (ISSN-L)
- 1573-2703
- OpenAlex
- W4226161547
- Cited by
- 20
- References
- 56
- Citations by year
- 2026: 2 · 2024: 4 · 2023: 8 · 2022: 6
- FWCI
- 1.31
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- www.springer.com/tdm (vor)
- Locations
- Journal of Engineering Mathematics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Nanofluid Flow and Heat Transfer
- Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Methods in Computational Mathematics
- Physical Sciences › Engineering › Computational Mechanics › Heat Transfer and Numerical Methods
- Keywords
- nanofluids, Buongiorno model, natural convection, enclosure, variable material properties, Newton's method, SUPG, advection-dominated transport, nanoparticle concentration, thermophoresis, Brownian motion, finite element discretization, variational formulation
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