High Rayleigh Number Laminar Convection in Low Aspect Ratio Enclosures With Adiabatic Horizontal Walls and Differentially Heated Vertical Walls

1982 ◽  
Vol 104 (1) ◽  
pp. 103-110 ◽  
Author(s):  
J. Tichy ◽  
A. Gadgil
Keyword(s):  
Aspect Ratio ◽  
Flow Regime ◽  
Numerical Solutions ◽  
Temperature Profiles ◽  
Approximate Analysis ◽  
Nusselt Numbers ◽  
Numerical Studies ◽  
Vertical Walls ◽  
Laminar Convection ◽  
Rayleigh Numbers

Laminar flow in shallow horizontal cavities (aspect ratio a < < 1) at high Rayleigh numbers (> 106) is investigated using an approximate analysis based on first principles, and also with numerical solutions to the full equations. A Prandtl number of approximately one is assumed. It is found that the flow regime at such high values of Ra is characterized by boundary layers lining both vertical as well as horizontal walls of the enclosure, and is qualitatively different from the flow regimes at lower Rayleigh numbers. The internal region of the core (near to the horizontal centerline) exhibits linear velocity and temperature profiles. Typical isotherms and streamlines characteristic of this flow regime are presented, based on the numerical solutions. The velocity and temperature profiles predicted from the approximate analysis are found to compare well with those obtained from the numerically obtained solutions. The Nusselt numbers predicted from the analysis are also in good agreement with the numerical solutions, and with the limited experimental data in the literature. The various physical processes in this type of flow are discussed based on the findings of the analytical and numerical studies.

scholarly journals An Analytical Model for Natural Convection in a Rectangular Enclosure with Differentially Heated Vertical Walls

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3220
Author(s):  
Alberto Fichera ◽  
Manuel Marcoux ◽  
Arturo Pagano ◽  
Rosaria Volpe
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Heat Fluxes ◽  
Rectangular Enclosure ◽  
Nusselt Numbers ◽  
Pressure Fields ◽  
Vertical Walls ◽  
Temperature And Velocity Fields

This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

NUMERICAL STUDY OF LAMINAR CONVECTION AND THERMOSOLUTAL CONVECTION IN A TWO-DIMENSIONAL TRAPEZOIDAL CAVITY

1994 ◽  
Vol 18 (3) ◽  
pp. 207-224 ◽  
Author(s):  
M. Lacroix
Keyword(s):  
Schmidt Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Thermosolutal Convection ◽  
Governing Equations ◽  
Concentration Gradients ◽  
Height Ratio ◽  
Vertical Walls ◽  
Laminar Convection ◽  
Rayleigh Numbers

Heat transfer driven by temperature gradients and simultaneous temperature and concentration gradients has been studied numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top and insulated vertical walls. Results are presented for a cavity with width-to-mean height ratio of 4, thermal and concentration Rayleigh numbers up to 106 and 5.105 respectively, and top surface inclinations from 0 to 15 deg to the horizontal. The Prandtl and the Schmidt number used are 0.71 and 0.6 respectively. The governing equations are expressed in terms of stream function and vorticity and body-fitted coordinates are used for mapping the sloping top wall. As the inclination of the top surface is increased, the Nusselt and Sherwood numbers decrease. The effect of opposing thermal and concentration gradients on the Nusselt and Sherwood numbers is however more important than the effect of the inclination of the top surface. Theoretical Nusselt and Sherwood numbers are compared with available experimental data.

Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

scholarly journals NUMERICAL STUDIES OF NATURAL CONVECTION IN A SQUARE CAVITY

2006 ◽  
Vol 5 (1) ◽  
pp. 68
Author(s):  
Viviana Cocco Mariani ◽  
Ivan Moura Belo
Keyword(s):  
Boussinesq Approximation ◽  
Square Cavity ◽  
Flow Equations ◽  
Nusselt Numbers ◽  
Numerical Studies ◽  
Numeric Simulation ◽  
Different Temperatures ◽  
Convection Problem ◽  
Volume Method ◽  
Rayleigh Numbers

In the present work a numeric study of thermal and fluid dynamics behavior of natural air convection in a bi-dimensional square cavity is presented, in a laminar flow. The square cavity has two walls heated with different temperatures and two isolated walls, the Boussinesq approximation is used and a constant Prandtl number. The Finite Volume Method is used for the discretization of flow equations. The staggered load of variables is adopted and Power-Law and SIMPLE models are used. The numeric simulation is made up of several Rayleigh numbers, 104 Ra 106, and the results of average Nusselt numbers are compared to values obtained in the literature. Flow and isotherm lines are presented and analyzed. The numerical results presented here in this work agree with the ones available in the literature and can be used by researchers who work in the convection problem numeric simulation area.

Heat Transfer to Curved Surfaces from Heat Generating Pools

1980 ◽  
Vol 102 (3) ◽  
pp. 519-524 ◽  
Author(s):  
J. D. Gabor ◽  
L. Baker ◽  
J. C. Cassulo ◽  
D. J. Erskine ◽  
J. G. Warner
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Curved Surface ◽  
Radius Of Curvature ◽  
Curved Surfaces ◽  
Nusselt Numbers ◽  
Pool Surface ◽  
Vertical Walls ◽  
Upper Pool ◽  
Rayleigh Numbers

Experiments were conducted on heat transfer from internally heated ZnSO4-H2O pools to curved surfaces. These experiments extended existing data for nonboiling pools to higher Rayleigh numbers. The data for convective downward heat transfer from nonboiling pools to a curved surface were reasonably close to the Mayinger correlation extrapolated to higher Rayleigh numbers and lower ratios of pool depth to radius of curvature. Sideward heat transfer to a surface could be described by Nu = 0.7 Ra0.2. Insulating the upper pool surface from the atmosphere had no effect on either sideward or downward heat transfer. An investigation was also made on effects of curvature on heat transfer from boiling pools. Nusselt numbers for sideward heat transfer were proportional to a boiling Reynolds number based on superficial vapor velocity to the 0.275 power and quite close to the correlation for a pool with flat vertical walls. Downward boiling heat transfer to a curved surface was proportional to the Reynolds number to the 0.1 power.

Two-Dimensional Periodic Natural Convection in a Rectangular Enclosure of Aspect Ratio One

1985 ◽  
Vol 107 (4) ◽  
pp. 850-854 ◽  
Author(s):  
D. G. Briggs ◽  
D. N. Jones
Keyword(s):  
Natural Convection ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Lower Boundary ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Vertical Walls ◽  
Rayleigh Numbers

A two-dimensional rectangular cavity of aspect ratio one is studied experimentally using a laser-doppler velocimeter. The enclosure is air filled and consists of two vertical walls at unequal isothermal temperatures and two connecting horizontal walls with temperatures varying linearly between the two vertical surfaces. This study clearly defines the existence of periodic laminar flow regimes detectable at Ra numbers above 0.3 × 107. These periodic variations in velocity are induced by the upper and lower boundary conditions. The envelopes of vertical and horizontal velocity fluctuations are reported as a function of position for Rayleigh numbers of 0.25 × 107, 0.50 × 107, and 0.85 × 107. In addition, the effect of Ra number on frequency of flow is reported.

Experimental and Numerical Studies of Natural Convection in Trapezoidal Cavities

1989 ◽  
Vol 111 (2) ◽  
pp. 372-377 ◽  
Author(s):  
S. W. Lam ◽  
R. Gani ◽  
J. G. Symons
Keyword(s):  
Natural Convection ◽  
Energy Transport ◽  
Convection Heat Transfer ◽  
Experimental Results ◽  
Heat Flow Rate ◽  
Nusselt Numbers ◽  
Numerical Studies ◽  
Surface Inclination ◽  
Experimental Values ◽  
Rayleigh Numbers

Natural convection heat transfer has been studied experimentally and numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top, and insulated vertical walls. Experimental results are presented for a cavity with width-to-mean height ratio of 4, Rayleigh numbers (based on the mean cavity height) from 103 to 107, and top surface inclinations from 0 to 25 deg to the horizontal. For a given top surface inclination, the Nusselt–Rayleigh relationship follows the usual trend, but with an interesting anomaly, in which higher Nusselt numbers than expected are obtained in the range 8 × 103 < Ra < 2 × 105 for inclinations of 0 and 5 deg. Overall, as the inclination of the top surface is increased, the Nusselt number decreases, an effect that becomes greater at higher angles. The proportions of convective heat flow rate into the high side and low side of the cavity were measured and show distinct maxima at particular Rayleigh numbers (which are independent of the top surface inclination angle). The equation Nu = 0.168 [Ra (1 + cos θ)/2]0.278 [(1 − cos θmax)/(cos θ − cos θmax)]−0.199 correlates the experimental results to within 6.9 percent for the ranges 4 × 103 < Ra < 107 and 0 deg ≤ θ ≤ 25 deg, apart from the anomalous region previously indicated. It is suggested that this correlation applies for A ≥ 4. The numerical model uses a false transient ADI finite difference scheme to solve the governing two-dimensional vorticity and energy transport equations. Nusselt numbers computed by the model are in good agreement with the experimental values. The convective flow patterns generated by the model exhibit changes in number and in size of cells for different Rayleigh numbers and different top surface inclinations.

scholarly journals Experimental investigation of natural convection in an enclosure with partial partitions at different angles

2014 ◽  
Vol 18 (4) ◽  
pp. 1133-1144 ◽  
Author(s):  
Osameh Ghazian ◽  
Hossein Rezvantalab ◽  
Mehdi Ashjaee
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Wood Fiber ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Isolated Cells ◽  
Nusselt Numbers ◽  
Vertical Walls ◽  
Rayleigh Numbers ◽  
Partial Partitions

Natural convection heat transfer in a partially partitioned enclosure has been investigated experimentally using Mach-Zehnder Interferometry technique. The top and bottom of the enclosure are insulated while one of the vertical walls is heated isothermally. The partitions are made of wood fiber and are attached to the heated wall with angles changing from 30? to 150? in different experiments. The length of each partition is equal to the width of the enclosure, therefore dividing the enclosure to isolated cells only at 90?. At other angles the cells are interconnected near the cold wall. Rayleigh number based on the enclosure width is changed from 3500 to 32000. Results for the local and the average Nusselt numbers at the heated wall of the enclosure are presented and discussed for various partition angles and Rayleigh numbers. It is found that, at each Rayleigh number, there exists an optimum inclination angle which minimizes the average Nusselt number.

scholarly journals Numerical study of natural convection in an enclosure with discrete heat sources on one of its vertical walls

2019 ◽  
pp. 448-448
Author(s):  
Mehmet Pamuk
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Heat Sources ◽  
Confined Spaces ◽  
Nusselt Numbers ◽  
Discrete Heat Sources ◽  
Computer Chips ◽  
Vertical Walls ◽  
Comparison Of The Results ◽  
Rayleigh Numbers

In this study, natural convection in a fluid-filled rectangular enclosure is analyzed using Comsol? commercial software. The fluid in which natural convection takes place is a dielectric liquid called FC-75. Attached to one of the vertical walls of the enclosure is an array of rectangular protrusions, each representing computer chips mounted on a PCB. The nominal power consumed by each chip is assumed to be 0.35W, 1.07W, 1.65W and 2.35W. This corresponds exactly to the values used in the experiments, which were performed once by the author of this study. The results of the experiment and the numerical study are shown as Nusselt numbers vs. Rayleigh numbers, both being the most important dimensionless parameters of natural convection. A comparison of the results has shown that Comsol? can achieve reliable results in similar problems, eliminating the need to build expensive experimental setups and spending time conducting experiments. The simulation results are aimed to be used in similar designs of electronic circuits in confined spaces.

Sign in / Sign up

Export Citation Format

Share Document