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

TL;DR

This paper introduces a novel iterative finite element scheme combining Newton-Raphson and Streamlines-Upwind Petrov-Galerkin methods to accurately simulate nanofluid transport in buoyancy-driven flows, addressing ill-posedness and validating with experimental data.

Contribution

It develops a new numerical approach integrating Newton's method with Streamline-Upwind Petrov-Galerkin regularization for nanofluid transport modeling.

Findings

The method achieves good agreement with experimental results.

Thermophoresis and Brownian motion are crucial near hot and cold walls.

Model limitations in capturing heat transfer impairment are identified.

Abstract

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 Stream Upwind Petrov-Galerkin regularization approach is required to solve properly the ill-posed Buongiorno transport model being tackled as a variational problem under mean value constraint. Non-trivial numerical 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. The numerical experiments demonstrate that by accounting for only the thermophoresis and Brownian motion forces in the concentration transport equation, the model is not able to reproduce the heat transfer impairment due to the presence of suspended nanoparticles in the base fluid. It reveals, however, the significant role that these two terms play in the vicinity of the hot and cold walls.