Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM

Abstract

Purpose

The paper aims to focus on modeling of combined mixed convection and volumetric radiation within a vertical channel using a hybrid thermal lattice Boltzmann method (LBM). The multiple relaxation time LBM (MRT-LBM) is used to compute the dynamical field. The thermal field is determined by a finite difference method (FDM), and the simple relaxation time-LBM (SRT-LBM) serves to calculate the radiative part. The geometry considered concerns a vertical channel defined by two diffuse and isothermal walls. The active fluid represents a gray gas participating in absorption, emission and isotropically scattering. The parametrical study conducted aims to highlight the effect of Richardson number (Ri), Planck number (Pl) and the optical thickness (τ) on dynamical and thermal fields. It is found that radiation affects greatly heat transfer.

Design/methodology/approach

MRT-LBM is used to compute the dynamical field. The thermal field is determined by FDM, and SRT-LBM serves to calculate the radiative part.

Findings

This study has shown the strong capability of this approach to simulate similar problems. The Planck number largely affects the streamlines and isotherms distribution. Also, it causes disappearance of reversal flow, undesirable in most industrial applications, for low Planck numbers. The optical thickness causes the disappearance of reversal flow, in the case in which it appears, for lower opacity. However, for higher opacity it leads to a recurrence of reversed flow.

Originality/value

The use of a new original method composed of MRT-LBM to solve the fluid velocity, FDM to handle the temperature equation and extended SRT-LBM to compute the radiative part of the energy equation.

Citation

Derfoufi, S., Moufekkir, F. and Mezrhab, A. (2018), "Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 3, pp. 745-762. https://doi.org/10.1108/HFF-04-2017-0161