Lattice Boltzmann Simulation of Combined Effects of Radiation and Mixed Convection in a Lid-Driven Cavity with Cooling and Heating by Sinusoidal Temperature Profiles on One Side

Abstract

The coupling between mixed convection and surface radiation in a square cavity, with a vertical wall heated and driven, and the opposite one subjected to a non-uniform temperature that exhibits a sinusoidal spatial variation is studied numerically using the lattice Boltzmann method and air as working fluid. The numerical code is validated against experimental and numerical results available in the literature. The parameters governing the problem are the emissivity of the walls varied from 0 to 1 and the Richardson number varied from 0.01 to 500. The latter is varied either through the Grashof number (the Reynolds number being fixed at 100) or through the Reynolds number (the Grashof number being fixed at ${10}^4$ or ${10}^5$). The results obtained show significant effects of the Richardson number on the overall structure of the flow and heat transfer characteristics. It is also shown that the contribution of radiation to the total heat transfer is not negligible even at low Richardson numbers and this contribution is reinforced by increasing the latter parameter. Useful correlations are presented for the total Nusselt number versus the Richardson number (in the range 1–500) and the emissivity of the walls (in the range 0–1).

Additional information

Notes on contributors

Youssef Dahani

Youssef Dahani is a doctoral student at the Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco. He obtained his Master degree in 2013 in Energetics and Environment at Cadi Ayyad University. His thesis work focuses on the numerical simulation of heat transfer and fluid flow in lid-driven cavities using the Lattice–Boltzmann method.

Mohammed Hasnaoui

Mohammed Hasnaoui is a Professor at Cadi Ayyad University, Faculty of Sciences Semlalia, Marrakesh, Morocco. He received his doctorate degree from the University of Perpignan, France in 1982 and his Ph.D. in mechanical engineering from Ecole Polytechnique of Montreal, Canada in 1991. He is the director of the Laboratory of Fluid Mechanics and Energetics (LMFE), he is a member of the standing committee of JITh and responsible for the Doctoral Formation of Technical Sciences and Engineering. His research activities focus on convective heat transfer in fluid and porous media. He has coauthored more than 300 papers in archival journals and international conferences.

Abdelkhalek Amahmid

Abdelkhalk Amahmid is a Professor of physics at Cadi Ayyad University, Faculty of Sciences Semlalia, Marrakesh, Morocco. He received his doctorate degree from Cadi Ayyad University, Marrakesh, Morocco, in 1999. He has published about 60 research papers in international journals and more than 80 papers in conference proceedings. His research activities focus on convective heat transfer in fluid and porous media.

Abdelfattah El Mansouri

Abdelfattah El Mansouri received the Bachelor and Master degrees from Cadi Ayyad University, Marrakesh, Morocco, in 2011, and 2013, respectively. He is currently a Ph.D. student in the frame of a joint thesis between Cadi Ayyad University and Paris-Saclay University, France. His main areas of research interest are computational fluid dynamics, heat transfer, and renewable energy.

Safae Hasnaoui

Safae Hasnaoui is a cotutelle Ph.D. student enrolled in the frame of a joint thesis between Cadi Ayyad University, Marrakesh (Morocco) and Picardie Jules Verne University, Amiens (France). She received her Master degree in 2013 in Energetics and Environment at Cadi Ayyad University. Her thesis work focuses on heat and mass transfer in the presence of Soret and Dufour effects using the lattice Boltzmann method.