A Numerical Study of Local and Average Natural Convection Nusselt Numbers for Simultaneous Convection Above and Below a Uniformly Heated Horizontal Thin Plate

1997 ◽  
Vol 119 (1) ◽  
pp. 102-108 ◽  
Author(s):  
B. Chambers ◽  
Tien-Yu T. Lee
Keyword(s):  
Natural Convection ◽  
Power Law ◽  
Numerical Study ◽  
Lower Surface ◽  
Plate Edge ◽  
Nusselt Numbers ◽  
Plate Center ◽  
Heated Plates ◽  
Rayleigh Numbers ◽  
Plate Width

Numerical simulations were conducted to determine local and average natural convection Nusselt numbers for uniformly heated horizontal plates with convection occurring simultaneously from upper and lower surfaces. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 86 to 1.9 × 108. Upper surface Nusselt numbers were found to be smaller than corresponding lower surface Nusselt numbers. The local Nusselt number was largest at the plate edge and decreased towards the plate center for both surfaces. This variation followed approximately a minus 1/3-power law variation with the non-dimensionalized x coordinate on the upper surface for modified Rayleigh numbers greater than 104, and a minus 1/9-power law variation on the lower surface for all modified Rayleigh numbers. Comparative simulations were also performed for upward and downward facing uniformly heated plates (single sided convection). For these cases, Nusselt numbers on the upward facing plates were larger than for downward facing plates.

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.

ANALYSIS OF NATURAL CONVECTION HEAT TRANSFER BETWEEN TWO HORIZONTAL CYLINDERS AND THEIR ENCLOSURE

1992 ◽  
Vol 16 (1) ◽  
pp. 17-32 ◽  
Author(s):  
M. Lacroix
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Nusselt Numbers ◽  
Horizontal Cylinders ◽  
Rayleigh Numbers

A numerical study has been conducted for natural convection heat transfer for air around two horizontal heated cylinders placed inside a rectangular enclosure cooled from the side. Three cylinder spacings were investigated. The local and overall Nusselt numbers were determined over the range of Rayleigh numbers from 104 to 106. It is found that the thermal performance of the unit is strongly influenced by the Rayleigh number and, to a lesser extent, by the cylinder spacing. A correlation is suggested for the overall Nusselt number.

scholarly journals Numerical Study of Heat Transfer by Natural Convection in Concentric Hexagonal Cylinders Charged with a Nanofluid

2022 ◽  
Vol 17 ◽  
pp. 19-28
Author(s):  
Taloub Djedid ◽  
Bouras Abdelkrim ◽  
Zied Driss
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Volume Fraction ◽  
Numerical Study ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Fixed Temperature ◽  
Nusselt Numbers ◽  
Volume Method ◽  
Rayleigh Numbers

In this document, a numerical study of the natural convection of steady-state laminar heat transfer in a horizontal ring between a heated hexagonal inner cylinder and a cold hexagonal outer cylinder. A Cu - water nanofluid traverses this annular space. The system of equations governing the problem was solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. The interior and exterior sides from the two cylinders are maintained at a fixed temperature. We investigated the impacts of various thermal Rayleigh numbers (103≤ Rat ≤2.5x105), and the volume fraction from the nanoparticles (0≤ Ø ≤0.12) on fluid flow and heat transfer performance. It is found that in high thermal Rayleigh numbers, a thin thermal boundary layer is illustrated at the flow that heavily strikes the ceiling and lower from the outer cylinder. In addition, the local and mean Nusselt number from a nanofluid are enhanced by enhancing the volume fraction of the nanoparticles.The results are shown within the figure of isocurrents, isotherms, and mean and local Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.

scholarly journals Natural convection air flow in vertical upright-angled triangular cavities under realistic thermal boundary conditions

2016 ◽  
Vol 20 (5) ◽  
pp. 1407-1420 ◽  
Author(s):  
Jaime Sieres ◽  
Antonio Campo ◽  
José Martínez-Súarez
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Aperture Angle ◽  
Temperature Fields ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Horizontal Wall ◽  
Rayleigh Numbers

This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle ? is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles ? (= 15?, 30? and 45?) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.

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.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103<Ra<4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

Mixed Convection in a Horizontal Porous Duct With a Sudden Expansion and Local Heating From Below

1999 ◽  
Vol 121 (3) ◽  
pp. 653-661 ◽  
Author(s):  
Y. Yokoyama ◽  
F. A. Kulacki ◽  
R. L. Mahajan
Keyword(s):  
Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Local Heating ◽  
Lower Surface ◽  
Porous Matrix ◽  
Sudden Expansion ◽  
Nusselt Numbers ◽  
Matrix Heat ◽  
Heating From Below

Results are reported for an experimental and numerical study of forced and mixed convective heat transfer in a liquid-saturated horizontal porous duct. The cross section of the duct has a sudden expansion with a heated region on the lower surface downstream and adjacent to the expansion. Within the framework of Darcy’s formulation, the calculated and measured Nusselt numbers for 0.1 < Pe < 100 and 50 < Ra < 500 are in excellent agreement. Further, the calculated Nusselt numbers are very close to those for the bottom-heated flat duct. This finding has important implications for convective heat and mass transfer in geophysical systems and porous matrix heat exchangers. The calculations were also carried out for glass bead-packed beds saturated with water using non-Darcy’s formula. The streamlines in the forced convection indicate that, even with non-Darcy effects included, recirculation is not observed downstream of an expansion and the heat transfer rate is decreased but only marginally.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

scholarly journals Finite Volume Simulation of Natural Convection for Power-Law Fluids with Temperature-Dependent Viscosity in a Square Cavity with a Localized Heat Source

2021 ◽  
Vol 39 (5) ◽  
pp. 1405-1416
Author(s):  
Hamza Daghab ◽  
Mourad Kaddiri ◽  
Said Raghay ◽  
Ismail Arroub ◽  
Mohamed Lamsaadi ◽  
...  
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Finite Volume ◽  
Power Law ◽  
Numerical Study ◽  
Staggered Grid ◽  
Cooling Performance ◽  
Coupled Equations ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, numerical study on natural convection heat transfer for confined thermo-dependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 ≤ Ra ≤ 106), power-law index (0.6 ≤ n ≤ 1.4), Pearson number (0 ≤ m ≤ 20) and length of the heat source (0.2 ≤ W ≤ 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length.

scholarly journals Numerical study of the coupled natural convection with surface radiation in a cylindrical annular enclosure

2020 ◽  
Vol 330 ◽  
pp. 01029
Author(s):  
Mohamed Amine MEDEBBER ◽  
Abderrahmane AISSA ◽  
Belkacem OULD SAID ◽  
Noureddine RETIEL ◽  
Mohammed EL GANAOUI
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Surface Radiation ◽  
Navier Stokes ◽  
Simpler Algorithm ◽  
Energy Equations ◽  
Volume Method ◽  
Rayleigh Numbers ◽  
Total Average

The interaction of natural convection with thermal radiation of black surfaces in a cylindrical enclosure filled with air has been numerically investigated. The steady-state continuity, Navier-Stokes and energy equations were discretized using the control volume method and solved numerically via the SIMPLER algorithm. Effects of Rayleigh number (Ra), wall emissivity (εp) and height ratio parameter (X) are studied. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The total average Nusselt number has also been discussed for valuating heat transfer through the enclosure.

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