In LBM, it is intended to model fluids as a collection of particles, which successively undergo collision and propagation over a discrete lattice mesh. Several lattice Boltzmann models have been proposed for the incompressible Navier–Stokes equations. A collision model was proposed by Bhatnagar et al. [13] to simplify the analysis of

the lattice Boltzmann equation, which leads to the so-called lattice BGK model. Remarkable efforts have been conducted by many researchers that made this numerical method more attractive for fluid dynamics modeling, e.g., [14, 15]. For more details about Fulvestrant purchase LBM and its application, kindly refer to the aforementioned publications. Most of the researches cited above considered the heat transfer enhancement by adding either the fin or using nanofluids. The main objective of this study is to examine both of these effects on the heat transfer performance. In general, previous works were performed to investigate different cases of nanofluid flow and

heat transfer in channels with mounted objects by focusing on changing geometries, arrangement, and dimensions of the objects. However, more efforts are needed in order to optimize the controlling parameters for best heat transfer enhancement. Methods Problem definition The geometry of the problem mTOR inhibitor is shown in Figure 1. A cold mixture of base fluid (water) and the nanoparticles (alumina) is forced to flow into a channel that is heated from its bottom and kept at a constant high temperature, while the top wall is insulated. The channel aspect ratio is fixed at L/H = 15. The Prandtl number

is taken as 7.02, and the Reynolds numbers are 10, 50, and 100, whereas the extended surfaces’ height to space ratio l/S is 0.2, and the ratio between the objects’ height to the channel’s height l/H is 0.2. Figure 1 A schematic plot of flow in a channel. The flow is assumed as Newtonian, laminar, two-dimensional, and incompressible. In addition, it is assumed that the cold mixture of base fluid (water) and the solid spherical nanoparticles (alumina) is in thermal equilibrium, and it flows at the same velocity as a homogenous mixture. Numerical simulation The D2Q9 LBM model is used to simulate fluid flow in two-dimensional channel with uniform grid size of δx × δy. The lattice Boltzmann Methamphetamine equation (known as LBGK equation) with single relaxation time can be expressed as [13] (1) which can be reformulated as (2) where and τ f as the single relaxation time of the fluid, f i represents the particle distribution function, e i is the particle streaming velocity, and is the local equilibrium distribution function. For D2Q9 model is given by [8] (3) where ρ is the density of the fluid and ω i is the weight function, which has the values of , for i = 1 to 4, and for i = 5 to 8. The macroscopic fluid flow velocity in lattice units is represented by u.