Three-Dimensional Natural Convective Flow in a Rectangular Enclosure With a Rectangular Heated Section on One Vertical Wall and With the Other Vertical Walls Cooled

2008 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Abdulrahim Kalendar ◽  
Thomas M. Simko
Keyword(s):  
Convective Flow ◽  
Vertical Wall ◽  
Three Dimensional ◽  
The Other ◽  
Heated Wall ◽  
Governing Equations ◽  
Vertical Sidewall ◽  
Rectangular Enclosure ◽  
Wide Range ◽  
Vertical Walls

Three-dimensional natural convective flow in a rectangular enclosure with vertical sidewalls and horizontal top and bottom surfaces has been considered. A heated rectangular element is mounted in the middle of one vertical wall of the enclosure, the remainder of this wall being adiabatic. The remaining vertical walls are cooled to a uniform low temperature. The horizontal top and bottom walls are adiabatic. The flow has been assumed to be steady and laminar. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. Radiation effects have been neglected. The numerical solution was obtained using the governing equations written in terms of dimensionless variables. The enclosure height, H′, was used as the characteristic length scale and the difference between the temperatures of the hot wall section and the cooled walls were used as the characteristic temperature scale. The dimensionless governing equations have been solved using FIDAP, a commercial software package that employs the finite element method. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless height of the heated wall section compared to the overall enclosure height; the dimensionless width of the heated wall section compared to its height; the dimensionless width of the enclosure between the vertical sidewall on which the heated wall section is mounted and the opposite vertical sidewall, and the dimensionless width of the enclosure between the other two vertical sidewalls. Because of the application being considered, results have only been obtained for Pr = 0.7. Attention has been restricted to the case where the dimensionless width of the enclosure between the vertical sidewall on which the heated wall section is mounted and the opposite vertical sidewall is 0.5 and where the dimensionless width of the enclosure between the other two vertical sidewalls is 1.0. A wide range of the other parameters has been considered particular attention having been given to the effect of the dimensionless width of the heated wall section compared to its height on the mean Nusselt number for the heated wall section.

Laser-Doppler Measurements of the Velocity Along a Heated Vertical Wall of a Rectangular Enclosure

1983 ◽  
Vol 105 (4) ◽  
pp. 782-788 ◽  
Author(s):  
H. Ozoe ◽  
M. Ohmuro ◽  
A. Mouri ◽  
S. Mishima ◽  
H. Sayama ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Laser Doppler ◽  
Central Core ◽  
Heated Wall ◽  
Critical Test ◽  
Three Dimensional Flow ◽  
Rectangular Enclosure ◽  
First Time

The horizontal and vertical velocity profiles near a heated vertical wall of rectangular enclosure were measured for the laminar regime of natural convection with a laser-Doppler anemometer. The horizontal temperature profiles near the heated wall were measured with a thermocouple. An almost perfect two-dimensional mode of flow was confirmed for the central regime of the box. A minimum in the temperature profile between the hot wall and the thermally stratified central core resulted in a downward flow just outside the boundary layer of upward flow, but the central core was stagnant. Visualization of the flow with a phenolphtalein tracer confirmed the two-dimensionality of the flow along the vertical heated wall and revealed a zone of three-dimensional flow in the form of spiral streaklines along the insulated top plate toward the opposing cooled vertical wall. Measurements such as these provide for the first time the basis for a critical test of the accuracy of numerical solutions.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

Effect of Sinusoidal Oscillatory Flow on a Vertical Wall-Mounted Cylinder

2020 ◽  
Author(s):  
HaKun Jang ◽  
Celalettin Emre Ozdemir ◽  
Mayank Tyagi ◽  
Jun-Hong Liang
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Finite Depth ◽  
Horseshoe Vortex ◽  
Vortex Structures ◽  
Navier Stokes ◽  
Wide Range ◽  
Sinusoidal Flow

Abstract The purpose of this study is to numerically investigate the bed shear stress and near-bed mixing due to coherent vortex structures in the vicinity of a vertically wall-mounted circular cylinder subject to an imposed finite-depth oscillatory sinusoidal flow. Previous studies reveal that the Keulegan–Carpenter (KC) number influences the formation of lee-side wake vortex structures as well as the horseshoe vortex in front of a cylinder. Therefore, parametric studies in a moderately wide range of KC from 5 to 20 are numerically performed. In the present study, Direct Numerical Simulation (DNS) is conducted using the open-source software, OpenFOAM, that solves the three-dimensional unsteady incompressible Navier-Stokes equations using finite volume method. Nondimensional parameters used in the simulations are carefully chosen to represent the real physics. The numerical solutions are first validated using an analytical solution for the oscillating Stokes flow and the results are then systematically and quantitatively compared with the experimental measurements. The results show that the lee-side wake is significantly influenced by KC, and distinctive types of the lee-side wake are generated and classified based on KC. It is also found that both KC and the ratio of the thickness of the Stokes boundary layer to the water depth are heavily associated with the stability of the lee-side wake. In addition, the simulated size and lifespan of the horseshoe vortex agree well with the experimental data.

Free Convective Flow in a Two Enclosure Arrangement With a High Aspect Ratio Side Enclosure Joined to a Large Square Enclosure

2000 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Vertical Wall ◽  
Heated Wall ◽  
Free Convective Flow ◽  
Square Enclosure

Abstract A numerical study of free convective flow in a vertical joined two-enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is separated from a larger square enclosure by a vertical dividing wall which is impermeable but offers no resistance to heat transfer. The vertical wall of the main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. All remaining walls in both enclosures are adiabatic. The situation considered is an approximate model of a window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number and the dimensionless width of the side enclosure on the Nusselt number have been investigated. The results show that there is a minimum in the Nusselt number variation with side enclosure width for a fixed Rayleigh number. The effect of Rayleigh number on the conditions under which this minimum occurs and on the value of the minimum Nusselt number has been investigated.

scholarly journals NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra

2006 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
E. L. M. Padilla ◽  
R. Campregher ◽  
A. Silveira-Neto
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Governing Equations ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Horizontal Annuli ◽  
Rayleigh Numbers ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.

Heat Transfer in Air Enclosures of Aspect Ratio Less than One

1981 ◽  
Vol 103 (4) ◽  
pp. 617-622 ◽  
Author(s):  
V. Sernas ◽  
E. I. Lee
Keyword(s):  
Heat Transfer ◽  
Vertical Wall ◽  
The Other ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Rates ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Adiabatic Boundary Condition ◽  
Better Than

The heat transfer rates inside rectangular air enclosures of aspect ratios between 0.1 and 1.0 were investigated interferometrically for a Grashof number range between 2.64 × 106 and 5.45 × 106. The enclosures were composed of dissimilar temperature vertical walls and two types of ceilings and floors. One type was made from constant temperature plates kept at the vertical wall temperatures, and the other type was made of low thermal conductivity polyurethane foam rubber. The heat transfer characteristics and flow patterns within these two types of enclosures were found to be significantly different. For aspect ratios between 0.4 and 1.0 the isothermal ceiling and floor approximate an adiabatic boundary condition much better than foam because much less heat was interchanged between the floor (or ceiling) and the air in the enclosure.

Effect of the Inclination on Three-Dimensional Incompressible Fluid Flow in a Discretely Heated Cavity

2013 ◽  
Vol 597 ◽  
pp. 3-8
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida ◽  
Slawomir Smolen ◽  
Touria Mediouni
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Vertical Wall ◽  
Three Dimensional ◽  
The Other ◽  
Uniform Temperature ◽  
Incompressible Fluid Flow ◽  
Electronic Components ◽  
Flow And Heat Transfer

Natural convection in inclined cubic cavity, discretely heated, is studied numerically using a three-dimensional finite volume formulation. Two heating square portions are placed on the vertical wall of the enclosure, while the rest of the considered wall is adiabatic. These sections, similar to the integrated electronic components, generate a heat flux q". The opposite vertical wall is maintained at a cold uniform temperature Tc and the other walls are adiabatic. The fluid flow and heat transfer in the cavity are studied for different sets of the governing parameters, namely the Rayleigh number Ra (103 ≤ Ra ≤ 107), the cavity inclination γ (- 45° ≤ γ ≤ 45°) and the position of the heating sections λ (0.3 ≤ λ ≤ 0.7). The dimensions of the heater sections, ε = D / H and the longitudinal aspect ratio of the cavity Ax = H / L are respectively fixed to 0.35 and 1.

scholarly journals Numerical Simulation for Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step

2004 ◽  
Author(s):  
J. G. Barbosa Saldana ◽  
N. K. Anand ◽  
V. Sarin
Keyword(s):  
Convective Flow ◽  
Three Dimensional ◽  
Step Length ◽  
Expansion Ratio ◽  
The Other ◽  
Step Height ◽  
Streamwise Direction ◽  
Backward Facing Step ◽  
Thermal Features ◽  
Mixed Convective Flow

Laminar mixed convective flow over a three-dimensional horizontal backward-facing step heated from below at a constant temperature was numerically simulated using a finite volume technique and the most relevant hydrodynamic and thermal features for air flowing through the channel are presented in this work. The channel considered in this work has an aspect ratio AR = 4, and an expansion ratio ER = 2, while the total length in the streamwise direction is 52 times the step height (L = 52s) and the step length is equal to 2 times the step height (l = 2s). The flow at the duct entrance was considered to be hydro-dynamically fully developed and isothermal. The bottom wall of the channel was subjected to a constant high temperature while the other walls were treated to be adiabatic. The step was considered to be a thermal conductive block.

Influence of Coil Inclined around Y Axis on Thermomagnetic Convection of Air in a Porous Cubic Enclosure under Zerogravity

2011 ◽  
Vol 354-355 ◽  
pp. 24-28 ◽  
Author(s):  
Chang Wei Jiang ◽  
Xian Feng Zhu ◽  
Er Shi ◽  
Zhen Zhou
Keyword(s):  
Heat Transfer ◽  
Magnetic Force ◽  
Vertical Wall ◽  
Simple Algorithm ◽  
Darcy Number ◽  
The Other ◽  
Governing Equations ◽  
Left Hand ◽  
Thermomagnetic Convection ◽  
Volume Method

Thermomagnetic convection of air in a porous cubic enclosure with a electric coil inclined around the Y axis is numerically investigated under zerogravity environment. The porous cubic enclosure is heated isothermally from left-hand side vertical wall and cooled isothermally from opposing wall while the other four walls are thermally insulated. The governing equations in primitive variables are discretized by the finite-volume method and solved by the SIMPLE algorithm. The results show that the overall heat transfer is enhanced gradually with the increase of magnetic force number and Darcy number. The resulted convection is symmetrical in terms of the angle at yeuler =0 when the range of inclination angle is from -90 to 90.

Influence of Coil Inclined around X Axis on Thermomagnetic Convection of Air in a Porous Cubic Enclosure under Zerogravity

2011 ◽  
Vol 354-355 ◽  
pp. 174-178 ◽  
Author(s):  
Chang Wei Jiang ◽  
Ming Zhang ◽  
Xian Feng Zhu
Keyword(s):  
Inclination Angle ◽  
Magnetic Force ◽  
Vertical Wall ◽  
Simple Algorithm ◽  
Darcy Number ◽  
The Other ◽  
Governing Equations ◽  
Left Hand ◽  
Thermomagnetic Convection ◽  
Volume Method

Thermomagnetic convection of air in a porous cubic enclosure with an electric coil inclined around the X axis is numerically investigated under zerogravity environment. The porous cubic enclosure is heated isothermally from left-hand side vertical wall and cooled isothermally from opposing wall while the other four walls are thermally insulated. The governing equations in primitive variables are discretized by the finite-volume method and solved by the SIMPLE algorithm. The results show that the overall heat transfer is enhanced gradually with the increase of magnetic force number and Darcy number. The resulted convection is symmetrical in terms of the inclination angle at xeuler =45 when the range of inclination angle is from 0 to 90 .

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