A Numerical Study of Natural Convective Flow in a Narrow Open Top Enclosure With a Linearly Varying Side-Wall Temperature Attached to a Large Square Enclosure

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
David Scott
Keyword(s):  
Numerical Study ◽  
Side Wall ◽  
Approximate Model ◽  
Maximum Temperature ◽  
Vertical Side ◽  
Square Enclosure ◽  
Fluid Properties ◽  
Horizontal Wall ◽  
Side Walls ◽  
Adiabatic Surface

Abstract Natural convective flew in a large square enclosure with a narrow rectangular enclosure mounted symmetrically on the upper surface of this main enclosure has been considered. The horizontal bottom and vertical side-walls of the main enclosure are assumed to be at a uniform high temperature and the vertical side-walls of the narrow top enclosure are assumed have a temperature that varies linearly with height above the main enclosure. The top horizontal wall of the upper enclosure is assumed to be adiabatic The situation consider is an approximate model of that which arises when measurements have to be made in a large enclosure containing a hot fluid and in which the measuring instrument is mounted in a small enclosure which is open at one end to the main tank and which has the instrument mounted at the opposite closed end. In order to ensure that the instrument is not exposed to a temperature that is above its operational limit, the walls of this small enclosure are cooled. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form and the resultant dimensionless equations have been solved using a finite-element method. Results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number and dimensionless height and width of the top enclosure on the maximum temperature of the top adiabatic surface have been investigated. The results show that provided the aspect ratio of the upper enclosure is kept large, overheating of the upper adiabatic surface of the top enclosure is not likely to occur.

A NUMERICAL STUDY OF FREE CONVECTIVE HEAT TRANSFER FROM A HEATED HALF-CYLINDER IN AN ENCLOSURE

1995 ◽  
Vol 19 (3) ◽  
pp. 285-300
Author(s):  
P.H. Oosthuizen ◽  
J.T. Paul
Keyword(s):  
Heat Transfer ◽  
Numerical Study ◽  
Boussinesq Approximation ◽  
Approximate Model ◽  
Governing Equations ◽  
Free Convective Flow ◽  
Wide Range ◽  
Fluid Properties ◽  
Different Temperatures ◽  
Side Walls

Two-dimensional free convective flow in an enclosure which has a heated half-cylinder on the floor has been numerically studied. The half-cylinder is kept at a uniform high temperature. The enclosure has horizontal upper and lower walls and inclined side-walls. The side-walls are also kept at uniform temperatures and the top and bottom surfaces are adiabatic. In general, the side-walls have been assumed to be at different temperatures. The situation considered is an approximate model of that which occurs in some simple crop dryers. The flow has been assumed to be steady and laminar. Fluid properties have been assumed constant except for the density change with temperature which has been treated using the Boussinesq approximation. The governing equations have been written in dimensionless form and solved using a finite element method. Results have been obtained for a wide range of the governing parameters for a Prandtl number of 0.7, i.e. for air, and the effects of these governing parameters on the heat transfer rate has been studied.

A 2D-PIV Study on Natural Convective Heat Transfer in a Square Enclosure With Partially Active Side Walls

2009 ◽  
Author(s):  
Massimo Paroncini ◽  
Francesco Corvaro ◽  
Alessia Montucchiari
Keyword(s):  
Holographic Interferometry ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Number Range ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Side Walls ◽  
Dynamic Structures ◽  
Rayleigh Numbers

The present study is an experimental and numerical analysis on the natural convection of air in square enclosures with partially active side walls. The experimental equipment is based on two different systems: an holographic interferometer and a 2D-PIV. The test cell is a square enclosure filled of air with vertical partially active side walls at different temperatures. The hot and cold regions on these sides are located in the middle of the cavity. The remaining vertical walls are made up of glass to allow an optical access to the cavity. The top and bottom surfaces of the enclosure are made up of plexiglas to reduce heat leakages. The experimental study is carried out both through the holographic interferometry, in order to obtain the average Nusselt numbers at different Rayleigh numbers, and through the 2D-PIV, in order to analyse the dynamic behaviour of the phenomenon at the same Rayleigh numbers. The average Nusselt numbers are obtained measuring the temperature distribution in the air layer trough the real-time and double-exposure holographic interferometry; the dynamic structures are the velocity vector distribution, the streamlines and the velocity maps. Finally these experimental data are compared to the results obtained through a numerical study carried out using the finite volume code, Fluent 6.2.3. The aim of this comparison is the validation of the numerical procedure. In this way it is possible to use the numerical code to enlarge the Rayleigh number range.

MELTING ABOUT A HEATED CYLINDER IN AN ICE-FILLED SQUARE ENCLOSURE WITH AN ISOTHERMALS FREE SURFACE

1999 ◽  
Vol 23 (3-4) ◽  
pp. 409-423
Author(s):  
P.H. Oosthuizen ◽  
J.T. Paul
Keyword(s):  
Free Surface ◽  
Numerical Study ◽  
Experimental Studies ◽  
Freezing Temperature ◽  
Lower Surface ◽  
Uniform Temperature ◽  
Square Enclosure ◽  
Heated Cylinder ◽  
Finite Element Procedure ◽  
Side Walls

A numerical study of the flow about and heat transfer from a heated cylinder centrally positioned in a square enclosure containing ice has been undertaken. The cylinder is heated to a uniform temperature that is higher than the freezing temperature of water and melting, therefore, occurs in the vicinity of the cylinder. The two side-walls of the enclosure are kept at a uniform temperature that is below the freezing temperature. The conditions considered here are such that there can be significant natural convection in the water near the cylinder. The lower surface of the enclosure is assumed to be adiabatic. The liquid has a free surface which is assumed to be flat. In most previous numerical studies of such a situation it has been assumed that the free surface is adiabatic. In experimental studies of the is type of flow, however, the free surface is often effectively cooled. In order to evaluate the effect of this, it has here been assumed that the free surface is at the uniform temperature that is below the freezing temperature but that is, in general, higher than that of the cooled side-walls. The governing equations have been expressed in dimensionless form and solved using a finite element procedure. The effect of the various governing parameters on the mean cylinder Nusselt number and on the thickness of the melted region about the cylinder have mainly been considered. The effect of the assumed free-surface temperature has, in particular, been studied.

scholarly journals Thermal Convection Inside Three-Dimensional Differentially Heated Cavity Under Laminar and Transitional Flow Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 31-34
Keyword(s):  
Three Dimensional ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Vertical Side ◽  
Square Enclosure ◽  
Fortran Code ◽  
Buoyancy Driven Flows ◽  
Flow Phenomena ◽  
Side Walls

The study presents the heat transfer phenomena of steady buoyancy driven flows inside a three-dimensional square enclosure. The thermal boundary condition of this enclosure are the vertical side walls are maintained at constant temperature difference and all the other walls are adiabatic. Reynolds averaged Navier stokes (RANS) equations are used to model the flow phenomena inside the enclosure, these equations are discretized using finite difference method (FDM) based Fortran code which was developed in house. The study is done for varying Grashof numbers 105 ≤ Gr ≤ 107 and a constant Prandtl number 6.2. The results indicated that as the Grashof number increases the temperature along the enclosure decreases by 24.2% and the rate of transfer of heat inside the enclosure increased by 26%.

NUMERICAL STUDY ON NATURAL CONVECTION OF A GROWING CRYSTAL IN SOLUTION LAYER CAVITY

2009 ◽  
Vol 09 (03) ◽  
pp. 273-281
Author(s):  
SHUICHI TORII ◽  
WEN-JEI YANG
Keyword(s):  
Numerical Study ◽  
Side Wall ◽  
Circulation Pattern ◽  
Two Dimensional ◽  
Governing Equations ◽  
Vertical Side ◽  
Finite Difference Technique ◽  
Flow Transport ◽  
Solution Layer ◽  
Thermal Fluid Flow

Numerical study is performed on the thermal fluid-flow transport phenomena in a disk-shape cavity. Consideration is given to the movement and growth of the crystal in solution layer. Here the lysozyme is employed as the crystal. The mechanism is numerically investigated by solving the two-dimensional governing equations through discretization by means of a finite-difference technique and simultaneously the crystal movement is predicted by the Basset–Boussinesq–Oseen (BBO) equation. It is found that (i) the crystal circulates in the cavity with fluid current and shows the circulation pattern of a donut shape, like the flow in a typical Benard cell, (ii) when the particle makes the second circulation with a larger loop, it falls on to the bottom near the vertical side-wall, and (iii) the size of the falling particle becomes larger as the Rayleigh number, i.e. the temperature difference between the heat sink and the vertical side-wall is increased.

Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall(s)

2007 ◽  
Author(s):  
E. Natarajan ◽  
Tanmay Basak ◽  
S. Roy
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Vertical Wall ◽  
Side Wall ◽  
Convection Flow ◽  
Left Wall ◽  
Wide Range ◽  
Stream Functions ◽  
Side Walls

The present numerical study deals with natural convection flow in a trapezoidal cavity when the bottom wall is uniformly heated and the vertical wall(s) are linearly heated and cooled whereas the top wall is well insulated. Nonlinear coupled partial differential equations governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Parametric study for the wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 105 and Prandtl number (Pr), 0.07 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For linearly heated side walls symmetry is observed while representing the flow patterns in terms of stream functions whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. Local Nusselt number becomes negative at the side wall for linearly heated side walls and at the left wall for linearly heated left wall and cooled right wall indicating the reversal of heat flow. The effect of Prandtl number in the variation of average Nusselt numbers is more significant for Prandtl numbers in the range 0.07 to 0.7 than 10 to 100.

scholarly journals How universal is the vibration-velocity controlled granular convection?

2021 ◽  
Vol 249 ◽  
pp. 03019
Author(s):  
Mika Umehara ◽  
Ko Okumura
Keyword(s):  
Side Wall ◽  
Experimental System ◽  
Wall Friction ◽  
Vibration Velocity ◽  
High Reproducibility ◽  
Vertical Side ◽  
Granular Dynamics ◽  
A Cell ◽  
Brazil Nut Effect ◽  
Side Walls

Recently, a number of articles have reported that granular convection induced by continuous vibration is controlled by vibration velocity, in contrast with some previous studies. We have reported such an example for the Brazil nut effect when the vibration is given discontinuously, using a one-layer granular bed in a cell with down-facing side walls. Here, we report the effect of vibration phase and wall friction using the same experimental system, to confirm rising motion of an intruder induced by granular convection is again governed by vibration velocity. We compare two different cases of vibration phase for giving intermittent vibration cycles, and found one, in which granular packing is well established before grains start to lose contacts due to vibration, provides distinctly high reproducibility. We further control the side wall friction using a microfabrication technique, and found that significantly high reproducibility is attained in a cell with vertical side walls when a millimeter texture is introduced on the side walls. Our results indicate that the granular convection is universally controlled by vibration velocity. The present study opens a way to conduct highly reproducible experiments on granular dynamics, which is indispensable for deep physical understanding of granular flow and segregation.

Numerical Investigation on Mixed Convection in a Horizontal Channel Heated From Below

2007 ◽  
Author(s):  
Giuseppe Foglia ◽  
Nicola Lanzaro ◽  
Oronzio Manca ◽  
Sergio Nardini
Keyword(s):  
Mixed Convection ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Horizontal Channel ◽  
Uniform Heat Flux ◽  
Vertical Side ◽  
Parallel Wall ◽  
Horizontal Wall ◽  
Side Walls ◽  
Rayleigh Numbers

In this work mixed convection in a horizontal channel with the lower wall heated at uniform heat flux is studied numerically. A three dimensional problem is modeled and solved by means of the FLUENT code. The domain is made of a principal channel and two channels with adiabatic walls, one upstream the principal channel and the other downstream. The principal channel is formed by a uniformly heated horizontal wall, a parallel wall located above and two adiabatic vertical side walls. The aim of this paper is to investigate the effect of Reynolds and Rayleigh numbers on thermal and fluid dynamic behavior in mixed convection in a horizontal channel heated from below. The analysis is carried out in transient regime in order to evaluate the thermal and fluid dynamic parameters as functions of the time. The Reynolds and Rayleigh numbers investigated are between 5 and 500 and 1.37×106 and 2.75×106 respectively. The corresponding Richardson number, Ri = Gr/Re2, holds values in the range 7.76 – 1.55 × 105. Wall temperature distributions and profiles along longitudinal and transversal coordinates are reported for different time values. Air velocity and temperature in the principal channel are presented along the longitudinal and transversal sections for some time values.

scholarly journals Thermal Convection Inside Three-Dimensional Differentially Heated Cavity Under Laminar and Transitional Flow Conditions

2020 ◽  
Vol 9 (4) ◽  
pp. 31-34
Keyword(s):  
Three Dimensional ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Vertical Side ◽  
Square Enclosure ◽  
Fortran Code ◽  
Buoyancy Driven Flows ◽  
Flow Phenomena ◽  
Side Walls

The study presents the heat transfer phenomena of steady buoyancy driven flows inside a three-dimensional square enclosure. The thermal boundary condition of this enclosure are the vertical side walls are maintained at constant temperature difference and all the other walls are adiabatic. Reynolds averaged Navier stokes (RANS) equations are used to model the flow phenomena inside the enclosure, these equations are discretized using finite difference method (FDM) based Fortran code which was developed in house. The study is done for varying Grashof numbers 105 ≤ Gr ≤ 107 and a constant Prandtl number 6.2. The results indicated that as the Grashof number increases the temperature along the enclosure decreases by 24.2% and the rate of transfer of heat inside the enclosure increased by 26%.

Numerical Study of Forced Convection in Different Fluids From Stationary Heated Cylinders in a Square Enclosure

2018 ◽  
Author(s):  
Srishti Mishra ◽  
Mukul Tomar ◽  
Adeel Ahmad ◽  
Satvik Jain ◽  
Naveen Kumar
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Transfer Rate ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Flow Characteristics ◽  
Governing Equations ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Fluid Properties

This paper performs a numerical study of forced convection heat transfer in a square enclosure with four identical stationary cylinders with single inlet and outlet ports. The ratio of the diameter of the cylinder to the length of the enclosure is kept constant at 0.1 with a fixed spacing between the cylinders. The enclosure walls are adiabatic while the cylinders are maintained at a constant temperature. The governing equations are solved for laminar, steady state and incompressible flow for different fluids namely air, water, and ethylene glycol. The study aims to determine the effect of varying Reynolds number (5 ≤ Re ≤ 100) and fluid properties (0.7 ≤ Pr < 200) on heat transfer rate and flow characteristics. The results of the study are presented in terms of streamlines, isotherm contours, and surface-averaged Nusselt numbers. The 2-D modeling and simulation have been conducted using ANSYS 16.0.

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