Study Of Three-dimensional Natural Convection Research Articles

Natural convection in a partially heated cylinder: A numerical study

1. Al-Rashed A., Kolsi L., Hussein A.K., Hassen W., Aichouni M., Borjini M.N, 2017, Numerical study of three-dimensional natural convection and entropy generation in a cubical cavity with partially active vertical walls, Case Studies in Thermal Engineering, 10, 100-110. CrossRef Google Scholar

Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers

A systematic numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number (Ra) up to 1010 is performed by using the recently developed coupled discrete unified gas-kinetic scheme. It is found that temperature and velocity boundary layers are developed adjacent to the isothermal walls, and become thinner as Ra increases, while no apparent boundary layer appears near adiabatic walls. Also, the lateral adiabatic walls apparently suppress the convection in the cavity, however, the effect on overall heat transfer decreases with increasing Ra. Moreover, the detailed data of some specific important characteristic quantities is first presented for the cases of high Ra (up to 1010). An exponential scaling law between the Nusselt number and Ra is also found for Ra from 103 to 1010 for the first time, which is also consistent with the available numerical and experimental data at several specific values of Ra.

Numerical study of three-dimensional natural convection and entropy generation in a cubical cavity with partially active vertical walls

Natural convection and entropy generation due to the heat transfer and fluid friction irreversibilities in a three-dimensional cubical cavity with partially heated and cooled vertical walls has been investigated numerically using the finite volume method. Four different arrangements of partially active vertical sidewalls of the cubical cavity are considered. Numerical calculations are carried out for Rayleigh numbers from (103 ≤ Ra ≤ 106), various locations of the partial heating and cooling vertical sidewalls, while the Prandtl number of air is considered constant as Pr=0.7) and the irreversibility coefficient is taken as (φ=10−4). The results explain that the total entropy generation rate increases when the Rayleigh number increases. While, the Bejan number decreases as the Rayleigh number increases. Also, it is found that the arrangements of heating and cooling regions have a significant effect on the fluid flow and heat transfer characteristics of natural convection and entropy generation in a cubical cavity. The Middle-Middle arrangement produces higher values of average Nusselt numbers.

An accurate numerical solution study of three-dimensional natural convection in a box

This paper describes the application of the finite difference method to the simulation of three-dimensional natural convection in a box. The velocity–vorticity formulation is employed to represent the mass, momentum, and energy conservations of the fluid medium. We employ a fractional time marching technique for solving seven field variables involving three velocity, three vorticity and one temperature components. By using the fast Fourier transform (FFT) and a tridiagonal matrix algorithm (TDMA), the velocity Poisson equations are advanced in space along with the continuity equation, thus solving efficiently and easily the diagonally dominant tridiagonal matrix equations. Both vorticity and energy equations are discretized through an explicit method (Adams–Bashforth central difference scheme) as a simplified numerical scheme for solving 3D problems, which otherwise requires enormous computational effort. A natural convection in a box for the Rayleigh number equal to 10 4, 10 5, 10 6 and 10 7 as well as As = L x / L z aspect ratios varying from 0.25 to 4 is investigated. It is shown that the benchmark results for temperature and flow fields could be obtained using the present algorithm.

Numerical simulation of the 3D behavior of thermal buoyant airflows in pentahedral spaces

A numerical study of three-dimensional natural convection in an attic space with heated horizontal base and cooled upper walls is presented. Every previous study pertinent to this subject as of today has assumed that the flow in attics is two-dimensional and restricted to triangular cavities. This problem is examined for fixed aspect ratios holding width to height of 2 and depth to height of 3.33 and Rayleigh numbers ranging from 10 4 to 8 × 10 5. The coupled system of conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. It is categorically found that the flow in the attic is 3D. From the physics of the problem, two steady-state solutions are possible. The symmetrical solution prevails for relatively low Rayleigh numbers. However, as the Ra is gradually increased, a transition occurs at a critical value Ra C. Above this value of Ra C, an asymmetrical solution exhibiting a pitchfork bifurcation arises and eventually becomes steady. Results are presented detailing the occurrence of the pitchfork bifurcation and the resulting flow patterns are described.

Experimental study of three-dimensional natural convection in enclosures with different working fluids

This paper presents an experimental study for buoyancy-induced natural convection in the Rayleigh number range of 8.7 × 10 2−2.0 × 10 9 inside rectangular enclosures wherein the two vertical walls were heated on the right wall and cooled on the left wall, respectively. The remaining four walls are adiabatic. Temperature data were taken for aspect ratios of 1 ⩽ A ⩽ 20 and Prandtl numbers of 0.7 ⩽ Pr 464. To gather detailed information regarding flow and heat transfer measurements, flow visualization as well as qualitative information of thermal fields (only for 8.7 × 10 2 Ra ⩽ 1.5 × 10 4) using holographic techniques were made and analysed. Results are presented for a range of Rayleigh numbers, Prandtl numbers and for various values of the aspect ratio. Furthermore, thermal correlations as a function of Rayleigh numbers and geometrical parameters and working fluids for different flow regimes were developed, which were also qualitatively verified by existing results.

A study of three-dimensional natural convection in high-pressure mercury lamps—III. Arc centering by magnetic field

The present work constitutes the third part of a series of work with the goal of developing a three-dimensional computational model to help understand the various physical mechanisms involved in high-pressure discharge arcs. The effect of an externally applied magnetic field on the convection and temperature characteristics is studied in the present effort. The classic experiment of Kenty is first simulated. It is found that the magnetic field can induce a downward velocity to the hot gas core to offset the buoyancy-induced nonuniformity in the temperature field. Separate pairs of contra-rotating recirculating eddies resulting from the magnetic and buoyancy effects can be identified. Qualitative as well as quantitative agreements between Kenty's experiment and the present prediction are observed. The feasibility of applying the magnetic control to optimize the operation of the modern discharge lamp is then investigated. The model reveals that convection strengthens if either the pressure inside the arc-tube or the magnitude of the magnetic field increases. Furthermore, with the same geometry, the required strength of the magnetic field to center the hot core and maintain a symmetric temperature distribution is linearly proportional to the arc-tube pressure. This finding yields a very useful method for optimizing the discharge lamp design.

A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure

A high-resolution, finite difference numerical study is reported on three-dimensional steady-state natural convection of air, for the Rayleigh number range 10 3 ⩽ Ra ⩽ 10 6, in a cubical enclosure, which is heated differentially at two vertical side walls. The details of the three-dimensional flow and thermal characteristics are described. Extensive use is made of state-of-the-art numerical flow visualizations. The existence of the transverse z-component velocity, although small in magnitude, is clearly shown. Comparison of the present three-dimensional results with the two-dimensional solutions is conducted. The three-dimensional data demonstrate reasonable agreement with the experimental measurements.

A study of three-dimensional natural convection in high-pressure mercury lamps—I. Parametric variations with horizontal mounting

A three-dimensional numerical model utilizing curvilinear coordinates and an efficient solution method has been used to investigate natural convection in horizontal, high-pressure mercury-vapor arctubes. For horizontal arcs, convection velocities are predominantly transverse to the arc axis. The associated upward bowing of the arc column results in non-uniform heating of the quartz wall which can substantially degrade the performance of the modern horizontal metal halide lamp. This investigation shows how the design parameters of the arctube, such as the mercury pressure, the curvature of the curved arctube, the offset electrode distance, and the electrode insertion length affect the temperature distribution in the arctube. Qualitatively, a downward curved arctube can move the hot arc core downward, and offset electrodes can improve temperatures near the ends of the arctube. The evolution of the design improvement of a 400 W high-pressure mercury lamp with the aim of centering the arc and having isotherms conform to the wall is achieved through better quantitative understanding of the transport characteristics.

A study of three-dimensional natural convection in high-pressure mercury lamps—II. Wall temperature profiles and inclination angles

A three-dimensional computational model has been adopted to investigate the natural convection transport of the high-pressure mercury arc discharge in a curved tube. The model solves the combined momentum, continuity, energy, electric field, and simplified radiation transfer equations. The present study investigates the degrees of uniformity of temperature distribution on the tube wall, and the impact of tube inclination angle with respect to gravity on the transport process and the resulting temperature distribution. Good agreements between the predictions and measurements have been obtained. It is found that the gross patterns of gas temperature distribution in mid-plane are rather insensitive to the inclination angle. The wall temperature distribution, however, exhibits substantially greater sensitivity to the inclination angle. This change of characteristics in wall temperature distribution has important effects on the performance of the arctube.

A numerical study of three-dimensional natural convection in a horizontal porous annulus with Galerkin method

A Galerkin scheme is developed to study the three-dimensional natural convection in a fluidsaturated porous annulus heated from the inner surface. In addition to the two-dimensional multiple solutions reported in the authors' previous paper, three-dimensional solutions are obtained; the secondary cells, with streaklines of the three-dimensionally closed co-axial double helices, are found extending along the axial direction in the top region of the annulus. This brings about an increased maximum local heat transfer coefficient, which consequently enhances overall heat transfer compared with that for the twodimensional unicellular flow.