Eur. Phys. J. Appl. Phys. (2017) 78: 34803
https://doi.org/10.1051/epjap/2017170087

Regular Article

Study on an antagonist differentiated heated lid driven-cavity enclosing a tube: lattice Boltzmann method^*

¹ LMT/ENS-Cachan/CNRS/Université Paris Saclay, 61 avenue du Présdent Wilson, 94235 Cachan, France
² Key Lab of Refrigeration Technology, Tianjin University of Commerce, 300134, Tianjin, P.R. China
³ école Polytechnique de Montréal, Montréal QC H3T 1J4, Canada

^a e-mail: ma@lmt.ens-cachan.fr

Received: 5 March 2017
Revised: 21 March 2017
Accepted: 5 April 2017
Published online: 19 May 2017

Abstract

The method of lattice-Boltzmann multiple relaxation time (MRT) is commonly applied to study the conversion system consisting in a combination of forced convection and natural convection occurred in a cavity. Moving the top surface horizontally at a fixed speed, while two vertical walls are applied with constant different temperatures, assuming adiabatic case on both bottom and top walls. We consider a “non-cooperating” situation, where dynamics and buoyancy forces counterbalance. The cavity contains a circular cylinder placed at various positions. Boundary conditions for velocity and temperature have been applied to handle the non-Cartesian boundary of the cylinder. In lattice Boltzmann methods we adopt the double distribution model for calculating both the thermal and hydrodynamic fields. The D₂Q₅ and D₂Q₉ lattice are chosen to perform the simulations for a wide range of Reynolds and Rayleigh numbers. By calculating the average Nusselt number, we also investigated the influence of different obstacle positions on characteristics of flow and heat transfer. The results show the influence of the obstacle position on the dimensionless numbers, so as to effect the heat transfer behaviors inside the cavity. It is also indicates that the governing parameters are also related to driven power for the upper surface sliding.