In this paper, a numerical study of forced convection on a backward facing step containing a single-finned fixed cylinder has been performed, using a ferrofluid and external magnetic field with different inclinations. The partial differential equations, which determine the conservation equations for mass, momentum and energy, were solved using the finite element scheme based on Galerkin’s method. The analysis of heat transfer characteristics by forced convection was made by taking different values of the Reynolds number (Re between 10 and 100), Hartmann number (Ha between 0 and 100), nanoparticles concentration (φ between 0 and 0.1) and magnetic field inclination (γ between 0° and 90°); also, several fin positions α [0°–180°] were taken in the counter clockwise direction by a step of 5. After analysing the results, we concluded that Hartmann number, nanoparticles concentration, Reynolds number and magnetic field angles have an influence on the heat transfer rate. However, the fin position on the cylinder has a big impact on the Nusselt number and therefore on heat transfer quality. The best position of the fin is at (α = 150°), which gives the best Nusselt number and therefore the best heat transfer, but the fin position at (α = 0°) remains an unfavourable case that gives the lowest Nusselt values.
This paper deals with a numerical investigation in order to predict correctly the combined effects of aiding thermal buoyancy and rheological flow behavior of power-law fluids on downward flow and heat transfer rate inside of 180° curved duct. The governing equations involving the momentum, continuity and the energy are solved in two-dimensions using the package called ANSYS-CFX. The computational results are depicted and discussed for the range of conditions as:Re= 40 to 1000,Ri= 0 to-1 andn= 0.4 to 1.2 at fixed value of Prandt number ofPr= 1. To interpret the found results, the flow structure and temperature field are shown in form of streamlines and isotherm contours. The average Nusselt number of the inner and outer walls of curved channel is calculated to determine the role of Reynolds number, Richardson number and power-law index. It is found that increase in strength of aiding buoyancy creates a counter rotating region in angle of 90 degrees of the duct.
A two-dimensional numerical simulation is carried out to understand the combined effects of thermal buoyancy strength and rheological flow behavior of non Newtonian power-law fluids on laminar flow and heat transfer rate through a 180° curved duct. The governing equations including the full Navier-Stokes, the continuity and the energy are solved using the commercial code ANSYS-CFX. The numerical results are presented and discussed for the range of conditions as: Re = 40 to 1000, Ri = 0 to 1 and n = 0.4 to 1.2 for fixed value of Prandt number of Pr = 1. In order to analyze the obtained results, the representative streamlines and isotherm patterns are presented. The average Nusselt number of the inner and outer walls of duct is computed to determine the role of Reynolds number, Richardson number and power-law index on flow and heat transfer. It is found that increase in Richardson number creates alternative vortices on duct walls. Moreover, the alternative vortices enhance the heat transfer rate for shear thinning, Newtonian and shear thickening fluids.
The present numerical study is based on the forced magnetohydrodynamic (MHD) convection of a ferrofluid through a backward facing step (BFS). A cylinder with two fixed fins and fixed dimensions is implanted inside fluid. The dimensionless governing equations have been solved using the multigrid finite element method. Several parameters were considered, such as the Hartmann number 0≤ Ha ≤100, the magnetic field inclination angle 0°≤ ɣ ≤90°, the Reynolds number 10≤ Re ≤200, the nanoparticle volume fraction 0%≤ φ ≤10%, and the fins inclination angle 0°≤ a ≤180°. The results have shown that the presence of the fins improves the heat transfer, especially at the position a = 90° where the Nuave number increases with a ratio of 113% for Re = 200.
Abstract. Fluid flows through curved pipes are frequently encountered in various industrial or biomedical applications. These flows, under the effect of the centrifugal force resulting from the curvature of the pipe, causes an instability phenomenon known as Dean instability, which results in the appearance of two or more counter-rotating vortex cells. The objective of this work is to determine numerically the effect of geometric parameters and rheological behavior of the fluid, including the index of behavior on the occurrence and development of the instability of Dean in a 180° curved duct. The governing equations including the full Navier-Stokes, the continuity and the Momentum are solved in three dimensions using the commercial code ANSYS-CFX, under the conditions of laminar, stationary and incompressible flow. In the first part, the results of the flow of a shear thinning fluid and a shear thickening fluid for a Dean number Dn = 125 and a radius of curvature Rc = 15.1 are presented. These calculation results gave a good agreement with the measured values extracted from the literature. The second part concerns the influence of the curvature ratio and the rheological behaviour of the fluid, the presence of two stationary secondary recirculations, as well as the appearance and the development of two additional vortices are highlighted. The main point observed is that the decrease in the curvature radius increases the instability of the flow through the pipe and this increases the number of vortex cells (Dean vortex). The velocity of the flow and its rheological nature are essential parameters for the reduction of instability in the canal.
A backward facing duct are present in various industrial applications especially those focused on heat transfer. The flow through a curved backward facing duct especially in the presence of nanofluid presents complexities compared to a straight backward facing step (BFS) duct. Therefore, the present numerical study deals a nanofluid flow (Fe3O4-H2O) forced convection in a curved backward facing duct. The objective of this investigation is to visualize at different curvature angles g (0°, 30°, 45°, 60°, 90°) imposed on the top wall of the duct, the effect of Hartmann number Ha (0, 50, 100), magnetic field inclination angle γ (0°, 60°, 90°), Reynolds number Re (10, 100, 200) and nanoparticle volume fraction φ (0 %, 0.05 %, 0.1 %). The dimensionless governing equations are solved using the multigrid finite element method. The results showed that the heat transfer was enhanced at the curved angle g = 90° for large Hartman numbers, thus, the average Nusselt number increased with a ratio of 240.74 % in the case of Hartmann number (Ha = 100).
In this paper, a study is conducted to determine numerically the effect of the nanoparticles nature (Al2O3, CuO, and Fe3O4) on the thermo-magnetohydrodynamic behavior of a nanofluid in a square cavity with a circular obstacle. The left wall of this cavity is movable and provided with a cold temperature (Tc) and the right wall is exposed to a hot temperature (Th). However, the upper and lower walls are considered adiabatic. The purpose of this paper is to highlight the effect of aluminum dioxide, copper oxide, and iron trioxide nanoparticles on the thermal and hydrodynamic behavior under the influence of different volume fractions(0 ≤ φ ≤ 0.1), different Hartmann numbers (0 ≤ Ha ≤ 75) and Richardson number (0 ≤ Ri ≤5). The system of governing équations was solved by the finite element method adopting the Galerkine discretization. The obtained results showed that the CuO nanoparticles improve the heat transfer at the fluid and obstacle, in addition, the increase of Hartmann number reduces the heat capacity, especially with the use of Fe3O4 nanoparticles. This study falls within the context of improving the cooling rate of industrial equipment.
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