Effect of Stabilizing Thermal Gradients on Natural Convection in Rectangular Enclosures

1979 ◽  
Vol 101 (2) ◽  
pp. 238-243 ◽  
Author(s):  
S. Ostrach ◽  
C. Raghavan
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Theoretical Calculations ◽  
Vertical Gradient ◽  
Temperature Gradients ◽  
Horizontal Gradient ◽  
Thermal Gradients ◽  
Aspect Ratios ◽  
Different Temperatures ◽  
Prandtl Numbers

An experimental investigation is described of the effect of stabilizing thermal gradients on natural convection in silicone oils in rectangular enclosures with different aspect ratios. The Prandtl numbers are of the order of 105, Grashof numbers range up to 20, and the aspect ratios are 1 and 3. The thermal boundary conditions are established by imposing different temperatures on opposite walls of the enclosure so that there is simultaneous horizontal and vertical heat flow. The effect of stabilizing temperature gradients on flow established by horizontal gradients and the effect of horizontal temperature gradients on a stably stratified fluid are studied for ranges of the parameters. Streamline patterns are observed at steady-state and velocity profiles are calculated from streamline data and extrapolated with approximate theoretical calculations. It is found that the flow generated by a horizontal gradient is retarded by a stabilizing thermal gradient. The reduction is shown as a function of the relevent parameters. For the range of variables investigated complete stabilization of the fluid driven by a horizontal gradient does not seem possible by means of a vertical gradient. The steady state flow patterns obtained do not depend on the manner in which the flow is started, i.e., on the order in which the temperature differences are imposed.

Transient Natural Convection Experiments in Shallow Enclosures

1982 ◽  
Vol 104 (3) ◽  
pp. 533-538 ◽  
Author(s):  
R. Yewell ◽  
D. Poulikakos ◽  
A. Bejan
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Theoretical Prediction ◽  
Thermal Stratification ◽  
Wave Motion ◽  
The Core ◽  
Transient Natural Convection ◽  
Aspect Ratios ◽  
Approach To Steady State ◽  
Rayleigh Numbers

This paper reports experimental observations on transient natural convection in enclosures at high Rayleigh numbers (1.28×109, 1.49×109) and low aspect ratios (0.0625, 0.112). The phenomenon consists of the establishment of thin intrusion layers along the horizontal adiabatic surfaces; in time, the intrusion layers exchange heat with the isothermal core of the cavity, leading to the thermal stratification of the core. The approach to steady state is gradual, contrary to the theoretical prediction of Brunt-Vaisala wave motion (Patterson and Imberger [6]). The measured durations of the observed transients agree very well with theoretical estimates.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

A Numerical Study of Laminar Natural Convection in Shallow Cavities

1981 ◽  
Vol 103 (2) ◽  
pp. 226-231 ◽  
Author(s):  
G. S. Shiralkar ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Numerical Study ◽  
Aspect Ratios ◽  
Shallow Cavities ◽  
Horizontal Cavity ◽  
Side Walls ◽  
Prandtl Numbers

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

Study of Natural Convection in Volumetrically Heated Enclosures for Different Aspect Ratios and Prandtl Numbers

2009 ◽  
Author(s):  
Parameshwar Deshmukh ◽  
Sushanta K. Mitra ◽  
U. N. Gaitonde
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Simple Algorithm ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
Fluid Properties ◽  
Inclination Angles ◽  
Parametric Studies ◽  
Horizontal Cavity ◽  
Prandtl Numbers

Natural convection in volumetrically heated rectangular enclosures is studied in this work. The walls of the enclosure are maintained isothermal. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. The code is benchmarked with the results for a lid-driven cavity and a differentially heated cavity. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 106. For a horizontal cavity, the flow becomes periodically oscillating at Ra = 5×104 and chaotic at Ra = 8×105. With a slight increase in the inclination angle, the oscillations die down and for inclination angles greater than 15°, the flow attain a steady state over a range of Ra. The aspect ratio AR, defined as the ratio of the height to the width of the cavity, is varied from 0.25 to 0.75 (AR < 1: wide cavities) and from 2.0 to 6.0 (AR > 1: long cavities). The values of critical Ra at which the convection sets in the cavity are presented for the range of AR studied here. The corresponding flow regimes are also identified.

Instability of steady natural convection in a vertical fluid layer

1978 ◽  
Vol 84 (4) ◽  
pp. 743-768 ◽  
Author(s):  
R. F. Bergholz
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Fluid Layer ◽  
Travelling Wave ◽  
Linear Stability Theory ◽  
Wave Instability ◽  
Theoretical Predictions ◽  
Different Temperatures ◽  
Prandtl Numbers ◽  
Moderate Range

The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.

Natural Convection in Cubic and Rhomb-Shaped Enclosures

2013 ◽  
Author(s):  
Milorad B. Dzodzo
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Nusselt Numbers ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Velocity And Temperature Fields ◽  
Prandtl Numbers ◽  
Volume Method

Laminar natural convection in cubic and rhomb–shaped enclosures (rhomb angles 59°, 44° and 28.2°) with two opposite vertical walls kept at different temperatures was investigated experimentally and numerically. The enclosures were filled with glycerol and the Rayleigh (Ra) and Prandtl (Pr) numbers ranged from 2,000<Ra<369,000 and 2,680<Pr<7,000. The visualization of the velocity and temperature fields was obtained by using Plexiglass and liquid crystal particles as tracers. The finite volume method based on the finite difference approach was applied for numerical analysis. The velocity and temperature fields and average Nusselt numbers were found as a function of the Reyleigh and Prandtl numbers. Comparison of the average Nusselt numbers for cubic and rhomb-shaped enclosures indicates decrease of heat transfer for the cases when the lower and upper vertical walls of the rhomb-shaped enclosures are at lower and higher temperatures, respectively. This is due to the tendency of fluid stratification in the lower and upper corners.

Heat Transfer by Natural Convection Across Vertical and Inclined Air Layers

1982 ◽  
Vol 104 (1) ◽  
pp. 96-102 ◽  
Author(s):  
S. M. ElSherbiny ◽  
G. D. Raithby ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Practical Interest ◽  
Correlation Equations ◽  
Linear Temperature ◽  
Aspect Ratios ◽  
Different Temperatures ◽  
Air Layers ◽  
Rayleigh Numbers

Measurements of the heat transfer by natural convection across vertical and inclined air layers are reported. The air layer is bounded by flat isothermal plates at different temperatures and around the edges by a perfectly conducting boundary (i.e., one that takes on a linear temperature distribution between the two plates). Measurements are reported for six aspect ratios between 5 and 110, covering a portion of the range of practical interest for windows, solar collectors, etc. Rayleigh numbers were in the range 102 to 2 × 107. The present measurements permitted the role of aspect ratio to be clearly defined. In addition, correlation equations are presented which allow the heat trnasfer across a vertical or inclined air layer to be calculated.

Laminate Delamination Due to Thermal Gradients

1995 ◽  
Vol 117 (4) ◽  
pp. 386-390 ◽  
Author(s):  
J. W. Hutchinson ◽  
T. J. Lu
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Temperature Gradients ◽  
Thermal Gradients ◽  
Steady State Analysis ◽  
Flow Through ◽  
Laminate Thickness ◽  
Fail Safe ◽  
Delamination Cracks

Flaw-induced delamination of orthotropic laminates subject to through-thickness temperature gradients is analyzed. A crack-like flaw impedes heat flow through the laminate, producing thermal stresses and crack tip stress intensities. The focus is on delamination cracks which propagate under steady-state conditions. The steady-state analysis becomes accurate for a crack whose length is about one laminate thickness. Moreover, the analysis provides realistic fail-safe criteria for excluding delamination.

Natural Convection in Modulated Thermal Gradients and Gravity: Numerical Simulation and Experimental Measurements

2003 ◽  
Author(s):  
Y. Shu ◽  
B. Q. Li ◽  
B. R. Ramaprian
Keyword(s):  
Natural Convection ◽  
Modulation Frequency ◽  
Experimental System ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Thermal Gradients ◽  
Molten Metals ◽  
Gravity Forces ◽  
Numerical Predictions ◽  
Prandtl Numbers

This paper presents an investigation on natural convection in a cavity with an imposed modulated thermal gradient or modulated gravity forces. Numerical computations are presented, which are based on the finite element solution of transient Navier-Stokes and energy balance equations, along with appropriate boundary conditions or time-varying gravity forces. To verify the numerical predictions, an experimental system is setup where wall temperatures are oscillated to produce modulated temperature gradients and the velocity fields are measured by a laser-based Particle Image Velocimetry (PIV) system. Computed results compare well with experimental measurements for various conditions. With the mathematical model, so verified by experimental measurements, extensive numerical simulations are carried out to study the effects of modulation frequency and Prandtl numbers on the fluid flow. Results show the strong nonlinear interaction in the intermediate range of modulation frequency. It is also found that with a small Prandtl number typical of molten metals and semiconductor melts, modulated gravity and thermal gradients produce almost the same flow field both in structure and in magnitude.

Lattice Boltzmann Method Simulation on Flow Patterns of Natural Convection in Horizontal Cylindrical Annulus

2013 ◽  
Author(s):  
Mo Yang ◽  
Yuwei Zhou ◽  
Yuwen Zhang ◽  
Enjie Bian ◽  
Zheng Li
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Flow Patterns ◽  
Aspect Ratios ◽  
Cylindrical Annulus ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Good Agreement

The Lattice Boltzmann method is used to simulate the flow patterns of natural convection in horizontal cylindrical annulus for aspect ratios in the range of 0.4≤A≤10 and for Prandtl numbers varying from 0.1 to 0.7. At Pr = 0.3 and A = 2, flow patterns on the whole range of Rayleigh number are mapped indicating the lower and upper critical values for transitions. At Pr = 0.7, the influence of aspect ratio on flow pattern is analyzed acquiring the result that the oscillation flow never happens at A≤3. At A = 2, several Prandtl numbers are calculated at certain Rayleigh number and the conclusion is that the steady upward flow keeps when 0.5≤Pr. The results are found in good agreement with existed studies.

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