Original scientific paper https://doi.org/10.2298/TSCI150118078FIn the present study, natural convection of nanofluids in a concentric horizontal annulus enclosure has been numerically simulated using the lattice Boltzmann method. A water-based nanofluid containing Al 2 O 3 nanoparticle has been studied. Simulations have been carried while the Rayleigh number ranges from 10 3 to 10 5 and solid volume fraction varies between 0 and 0.04. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics such as average and local Nusselt numbers, streamlines, and isotherm patterns for different values of solid volume fraction, annulus gap width ratio and Rayleigh number are investigated and discussed in detail.One of the useful numerical methods that have been used in the recent years is the lattice Boltzmann method (LBM). The LBM has several advantages over other conventional CFD methods due to its particular nature and local dynamics. The major advantages of the LBM are due to the fact that the solution for the particle distribution functions is explicit, easy for parallel computation and implementation of boundary conditions on complex boundaries is simple. It has been used for simulating the flow field in wide ranges of engineering applications such as natural convection [12], nanofluid [13,14], unsteady flow [15][16][17][18][19][20], etc.The aim of this study is to investigate heat transfer characteristics of natural convection in the annulus between horizontal concentric cylinders filled with Al 2 O 3 -water nanofluid.The LBM with single-relaxation-time collision model is employed. The study is carried out at a various range of annulus gap width ratio (0.5 ≤ σ ≤ 5) and solid volume fractions (0% to 4%) at Rayleigh numbers 10 3 -10 5 .
Numerical methodThe LB method implemented here is the same as that employed in Fattahi et al. [12] and Mei et al. [16]. In this work, the most popular model for 2-D problems, the D 2 Q 9 model, which consists of nine distribution functions, has been used.
The LBM for the flow fieldThe LBM solves the microscopic kinetic equation for the particle distribution function f (x, v, t) .These particle distribution functions are normally calculated by solving the following equation: