Combined Newton–Raphson and Streamlines-Upwind Petrov–Galerkin iterations for nanoparticles transport in buoyancy-driven flow

• Published in: Journal of engineering mathematics Vol. 132; no. 1
• Main Authors: Riahi, M. K., Ali, M., Addad, Y., Abu-Nada, E.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Brownian motion; Computational Mathematics and Numerical Analysis; Enclosures; Finite element method; Galerkin method; Iterative methods; Mathematical analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Nanofluids; Nanoparticles; Numerical analysis; Regularization; Theoretical and Applied Mechanics; Thermophoresis; Transport equations; Finite element method; Navier–Stokes equations; Nanofluid; Nanofluid heat transfer; 35Q35; 35Q79; Newton–Raphson method; Stream-Upwind Petrov–Galerkin; 65M60; Advection-dominated equation; 65Y04
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-021-10205-4

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.