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

01/19/2021
by   M. K. Riahi, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 19

05/09/2022

A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem

We present a high-order hybridized discontinuous Galerkin (HDG) method f...
10/27/2021

Superconvergence of the MINI mixed finite element discretization of the Stokes problem: An experimental study in 3D

Stokes flows are a type of fluid flow where convective forces are small ...
05/24/2020

Variants of the Finite Element Method for the Parabolic Heat Equation: Comparative Numerical Study

Different variants of the method of weighted residual finite element met...
04/12/2022

Sparse grid time-discontinuous Galerkin method with streamline diffusion for transport equations

High-dimensional transport equations frequently occur in science and eng...
05/31/2017

Boundedness-Preserving Implicit Correction of Mesh-Induced Errors for VoF Based Heat and Mass Transfer

Spatial discretisation of geometrically complex computational domains of...
02/20/2017

Heterogeneity Preserving Upscaling for Heat Transport in Fractured Geothermal Reservoirs

In simulation of fluid injection in fractured geothermal reservoirs, the...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.