Natural Convection Liquid Cooling of a Substrate-Mounted Protrusion in a Square Enclosure: A Parametric Study

1992 ◽  
Vol 114 (2) ◽  
pp. 401-409 ◽  
Author(s):  
S. B. Sathe ◽  
Y. Joshi
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Flow Behavior ◽  
Air Cooling ◽  
Square Enclosure ◽  
Simple Boundary ◽  
Wide Range ◽  
Solid Region ◽  
Rayleigh Numbers ◽  
Thermal Conductivities

The coupled conduction and natural convection transport from a substrate-mounted heat generating protrusion in a liquid-filled square enclosure is numerically examined. The governing steady two-dimensional equations are solved using a finite-difference method for a wide range of Rayleigh numbers, protrusion thermal conductivities and widths, substrate heights, and enclosure boundary conditions. The results presented apply to liquids with 10≤Pr≤1000. It was established that in many situations it may be inappropriate to specify simple boundary conditions on the solid surface and decouple the conduction within the substrate or the protrusion. Higher Rayleigh numbers, protrusion thermal conductivities, and widths enhanced cooling. A variation in the substrate height did not affect the maximum protrusion temperature; however, the flow behavior was considerably altered. An empirical correlation for the maximum protrusion temperature was developed for a wide range of parametric values. The enclosure thermal boundary conditions changed the heat transfer in the solid region to only a small extent. Immersion cooling in common dielectric liquids was shown to be advantageous over air cooling only if the thermal conductivity of the protrusion was larger than that of the liquid.

scholarly journals Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2788
Author(s):  
Hyun-Sik Yoon ◽  
Yoo-Jeong Shim
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Circular Cylinder ◽  
Flow Structures ◽  
Two Dimensional ◽  
Square Enclosure ◽  
Wide Range ◽  
Secondary Vortices ◽  
Rayleigh Numbers

The present study investigated the natural convection for a hot circular cylinder embedded in a cold square enclosure. The numerical simulations are performed to solve a two-dimensional steady natural convection for three Rayleigh numbers of 103, 104 and 105 at a fixed Prandtl number of 0.7. This study considered the wide range of the inner cylinder positions to identify the eccentric effect of the cylinder on flow and thermal structures. The present study classifies the flow structures according to the cylinder position. Finally, the present study provides the map for the flow structures at each Rayleigh number (Ra). The Ra = 103 and 104 form the four modes of the flow structures. These modes are classified by mainly the large circulation and inner vortices. When Ra = 105, one mode that existed at Ra = 103 and 104, disappears in the map of the flow structures. The new three modes appear, resulting in total six modes of flow structures at Ra = 105. New modes at Ra = 105 are characterized by the top side secondary vortices. The corresponding isotherms are presented to explain the bifurcation of the flow structure.

Lattice Boltzmann Computations of Natural Convection Heat Transfer of Nanofluid in a Square Cavity Heated by Protruding Heat Source

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Mustapha Faraji ◽  
El Mehdi Berra
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Source ◽  
Inclination Angle ◽  
Lattice Boltzmann ◽  
Base Fluid ◽  
Numerical Code ◽  
Convection Flow ◽  
Square Enclosure ◽  
Rayleigh Numbers

Abstract This paper reported the mathematical modeling and numerical simulation of natural convection flow of Cu/water nanofluid in a square enclosure using the lattice Boltzmann method (LBM). The cavity is heated from below by heat source and cooled by the top wall. The vertical walls are adiabatic. After validating the numerical code against the numerical and experimental data, simulations were performed for different Rayleigh numbers (104–0.5 × 107), nanoparticles volume fractions (0–8%), and cavity inclination angle (0 deg–90 deg). The effects of the studied parameters on the streamlines, on isotherms distributions within the enclosure, and on the local and average Nusselt numbers are investigated. It was found that heat transfer and fluid flow structure depend closely on the nanoparticle concentration. Results show differences in stream separation between a base fluid and the nanofluid. Also, adding small nanoparticles fractions, less than 6%, to the base fluid enhances the heat transfer for higher Rayleigh numbers and cavity inclination angle less than 30 deg. It is concluded that the optimal dilute suspension of copper nanoparticles can be applied as a passive way to enhance heat transfer in natural convection engineering applications.

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.

scholarly journals Thermally Optimum Spacing between Inner Plates in Natural Convection Flows in Cavities by Numerical Investigation

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 554 ◽  
Author(s):  
Blas Zamora
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Numerical Investigation ◽  
Thermophysical Properties ◽  
Electronic Equipment ◽  
Passive Devices ◽  
Wide Range ◽  
Optimum Spacing ◽  
Rayleigh Numbers ◽  
Wall Spacing

Buoyancy-driven airflow that included two isothermal inner plates established in a vented cavity is investigated numerically. The thermally optimum wall-to-wall spacing of the immersed channel, as well as its dependence with respect to the relevant governing parameters, are determined. Results are presented as a function of the aspect ratio b/H for a wide range of Rayleigh numbers RaH. A logarithmic correlation for the optimum (b/H)opt as a function of RaH is presented. In addition, since the outlined configuration might be subject to intense heating conditions, the influence of considering variable thermophysical properties is also included in the analysis. In fact, an appreciable influence of the variation of properties on (b/H)opt is also detected for a representative value of RaH = 109. Obtained results can be directly applied to the optimization of electronic equipment cooling, or even to thermal passive devices in buildings.

Natural Convection Inside a Square Cavity Heated From Below and Symmetrically Cooled at Both Sides: Effects of Various Dirichlet Boundary Conditions at the Bottom Wall

2005 ◽  
Author(s):  
Satyajit Roy ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Transfer Rate ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Bottom Wall ◽  
Uniform Heating ◽  
Square Cavity ◽  
Rayleigh Numbers

A numerical study is performed to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over the range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained.

Analysis of Melt Flows in an Electric Heating Furnace for Quartz Glass Synthesis

2018 ◽  
Author(s):  
Qianli Ma ◽  
Haisheng Fang ◽  
Chunli Shang ◽  
Zhongyi Liu ◽  
Jing Wang
Keyword(s):  
Natural Convection ◽  
Flow Field ◽  
Flow Pattern ◽  
Quartz Glass ◽  
Flow Behavior ◽  
Electric Heating ◽  
Heating Furnace ◽  
Rotating Speed ◽  
Wide Range ◽  
Bubble Transport

Flow patterns in molten quartz are highly related to the bubble transport and removal. Understanding the flow behavior in molten quartz is of great importance to the manufacture of high-purity quartz glass. In this paper, a numerical model is set up to simulate the flow field of molten quartz in a typical electric heating furnace. Natural convection and Marangoni convection are examined for their respective effects on the flow pattern of molten quartz. Different heater arrangements will change the flow field by varying temperature distributions. Top heating and bottom heating have the same vortex direction; while side heating induces an opposite direction to them. To improve the flow field in molten quartz, forced convection is introduced by crucible rotation. The influences of rotating speed of crucible on the flow field are studied in a wide range varying from 0 to 100 rad/s. With the increase of rotating speed, a reverse vortex to natural convection shows in molten quartz; and the velocity magnitude increase at a growing speed. To find out the optimal flow pattern for quartz glass manufacture, a qualitative analysis is presented on the reliance of bubble transport behavior on the convection modes. Based on the results, useful suggestions are provided towards increasing the bubble-free area of molten quartz and improving the quality of quartz glass.

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.

scholarly journals A Dimensionless Model for Transient Turbulent Natural Convection in Isochoric Vertical Thermal Energy Storage Tubes

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Reza Baghaei Lakeh ◽  
Richard E. Wirz ◽  
Pirouz Kavehpour ◽  
Adrienne S. Lavine
Keyword(s):  
Natural Convection ◽  
Energy Storage ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Convection Heat Transfer ◽  
Thermal Storage ◽  
Fourier Number ◽  
Turbulent Natural Convection ◽  
Wide Range ◽  
Rayleigh Numbers

In this study, turbulent natural convection heat transfer during the charge cycle of an isochoric vertically oriented thermal energy storage (TES) tube is studied computationally and analytically. The storage fluids considered in this study (supercritical CO2 and liquid toluene) cover a wide range of Rayleigh numbers. The volume of the storage tube is constant and the thermal storage happens in an isochoric process. A computational model was utilized to study turbulent natural convection during the charge cycle. The computational results were further utilized to develop a conceptual and dimensionless model that views the thermal storage process as a hot boundary layer that rises along the tube wall and falls in the center to replace the cold fluid in the core. The dimensionless model predicts that the dimensionless mean temperature of the storage fluid and average Nusselt number of natural convection are functions of L/D ratio, Rayleigh number, and Fourier number that are combined to form a buoyancy-Fourier number.

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