Numerical simulation of natural convection between a decentered triangular heating cylinder and a square outer cylinder filled with a pure fluid or a nanofluid using the lattice Boltzmann method

Abstract

Natural convection around a decentered triangular cylinder placed in a square cylinder is studied numerically using the lattice-Boltzmann method. The study is conducted for pure water and water–silver nanofluid. The inner heating triangular cylinder is maintained at a constant and uniform temperature while the vertical/(horizontal) sides of the external cylinder are cooled at constant temperature/(considered adiabatic). The numerical analysis is carried out for three decentered positions of the triangular block toward the left side of the outer square cylinder; these are Left-Bottom (LB), Left-Middle (LM) and Left-Top (LT). The other parameters governing the problem are the Rayleigh number (103≤Ra≤107), the Prandtl number of the pure water (Pr=7) and the volume fraction of nanoparticles (0≤φ≤0.1). The effective thermal conductivity and viscosity of nanofluids are calculated using Maxwell–Garnetts (MG) and Brinkman models, respectively. The results obtained show that fluid flow and heat transfer characteristics are highly affected by the heating cylinder position. The increase of nanoparticles volume fraction has a positive impact on the average Nusselt number for all considered positions of the heating block. Results of the block's positions on the vertical centerline of the outer cylinder are also presented and discussed for comparison purposes. In dominating natural convection regime, it is found out that the bottom/(top) position of the block becomes the most/(least) favorable to heat transfer.