Experimental Investigation of Free Convection in a Vertical Rod Bundle—A General Correlation for Nusselt Numbers

1985 ◽  
Vol 107 (3) ◽  
pp. 611-623 ◽  
Author(s):  
M. Keyhani ◽  
F. A. Kulacki ◽  
R. N. Christensen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Free Convection ◽  
Power Dissipation ◽  
Unit Length ◽  
Outer Cylinder ◽  
Working Fluid ◽  
Curvature Effects ◽  
Nusselt Numbers ◽  
Wide Range

Free convection in two vertical, enclosed rod bundles has been experimentally investigated for a wide range of Rayleigh numbers. A uniform power dissipation per unit length is supplied to each rod, and the enclosing outer cylinder is maintained at constant temperature. Nusselt numbers for each rod, as well as an overall value for each bundle, have been obtained as a function of Rayleigh number. Comparison of the results for air and water as the working fluid indicate that, for a fixed Rayleigh number, an increase in the Prandtl number produces a reduction in the Nusselt number. This is contrary to what has been reported for vertical cavities and is attributed to curvature effects. Furthermore, the data reveal the interesting fact that it is quite possible for the individual rods in the bundle to exchange energy with the working fluid via different but coexisting regimes at a given power dissipation. Also, as the Rayleigh number is increased, the rods each tend to assume nearly the same heat transfer coefficient. Finally, a correlation for the overall convective Nusselt number is developed in terms of Rayleigh number and geometric parameters.

Free Convection in a Vertical Annulus With Constant Heat Flux on the Inner Wall

1983 ◽  
Vol 105 (3) ◽  
pp. 454-459 ◽  
Author(s):  
M. Keyhani ◽  
F. A. Kulacki ◽  
R. N. Christensen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Free Convection ◽  
Thermal Radiation ◽  
Outer Cylinder ◽  
Working Fluid ◽  
Spent Fuel ◽  
Transfer Coefficients ◽  
Vertical Annulus

Heat transfer measurements are presented for free convection in a vertical annulus wherein the inner cylinder is at constant surface heat flux and the outer cylinder is at constant temperature. Overall heat transfer data are corrected for thermal radiation in the annulus. Rayleigh numbers span the conduction, transition and boundary layer regimes of flow, and average heat transfer coefficients are obtained with air and helium as the working fluids. The range of Rayleigh number is 103 < Ra < 2.3 × 106; the radius ratio is 4.33; and the aspect ratio (cylinder length divided by annular gap) is 27.6. Energy transferred by thermal radiation varies with Rayleigh number and working fluid. With air, thermal radiation can account for up to 50 percent of the heat transfer. With helium, radiation can account for up to 30 percent of the heat transfer rate. The results of the study provide data relevant to the design and performance assessment of spent fuel packages as part of the National Waste Terminal Storage Program for nuclear waste isolation.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

scholarly journals Effect of Rayleigh Number on Internal Eccentricity in a Heated Horizontal Elliptical Cylinder to its Coaxial Square Enclosure

2020 ◽  
Vol 25 (3) ◽  
pp. 17-29
Author(s):  
Abdelkrim Bouras ◽  
Djedid Taloub ◽  
Zied Driss
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Commercial Code ◽  
Volume Method ◽  
Rayleigh Numbers

AbstractThis paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure’s sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

A Short Method to Compute Nusselt Numbers in Rectangular and Annular Channels With any Ratio of Constant Heat Rate

2010 ◽  
Author(s):  
Alexandre Malon ◽  
Thierry Muller
Keyword(s):  
Differential Equation ◽  
Nusselt Number ◽  
Heat Rate ◽  
Equation System ◽  
Radius Ratio ◽  
Differential Equation System ◽  
Simple Method ◽  
Nusselt Numbers ◽  
Annular Channels ◽  
Wide Range

An analytic investigation of the thermal exchanges in channels is conducted with the prospect of building a simple method to determine the Nusselt number in steady, laminar or turbulent and monodimensional flow through rectangular and annular spaces with any ratio of constant and uniform heat rate. The study of the laminar case leads to explicit laws for the Nusselt number while the turbulent case is solved using a Reichardt turbulent viscosity model resulting in easy to solve one-dimensional ordinary differential equation system. This differential equation system is solved using a Matlab based boundary value problems solver (bvp4c). A wide range of Reynolds, Prandtl and radius ratio is explored with the prospect of building correlation laws allowing the computing of Nusselt numbers for any radius ratio. Those correlations are in good agreement with the results obtained by W.M. Kays and E.Y. Leung in 1963 [1]. They conduced a similar analysis but with an experimental basis, they explored a greater range of Prandtl but only a few discreet radius ratio. The correlations are also compared with a CFD analysis made on a case extracted from the Re´acteur Jules Horowitz.

scholarly journals Prediction of Natural Convection Heat Transfer Phenomena of Nanofluids in Corrugated Annulus

2020 ◽  
Author(s):  
Sattar Aljobair ◽  
Akeel Abdullah Mohammed ◽  
Israa Alesbe
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Outer Cylinder ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract The natural convection heat transfer and fluid flow characteristic of water based Al2O3 nano-fluids in a symmetrical and unsymmetrical corrugated annulus enclosure has been studied numerically using CFD. The inner cylinder is heated isothermally while the outer cylinder is kept constant cold temperature. The study includes eight models of corrugated annulus enclosure with constant aspect ratio of 1.5. The governing equations of fluid motion and heat transfer are solved using stream-vorticity formulation in curvilinear coordinates. The range of solid volume fractions of nanoparticles extends from PHI=0 to 0.25, and Rayleigh number varies from 104 to 107. Streamlines, isotherms, local and average Nusselt number of inner and outer cylinder has been investigated in this study. Sixty-four correlations have been deduced for the average Nusselt number for the inner and outer cylinders as a function of Rayleigh number have been deduced for eight models and five values of volume fraction of nano particles with an accuracy range 6-12 %. The results show that, the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. Also, increase the number of undulations in unsymmetrical annuli reduces the heat transfer rates which remain higher than that in symmetrical annuli. There is no remarkable change in isotherms contour with increase of volume fraction of nanofluid.

scholarly journals Laminar Free Convection From a Heated Square Cylinder in Bingham Plastic Fluids

2021 ◽  
Author(s):  
Bairi Levi Rakshith
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Cylinder Surface ◽  
Square Cylinder ◽  
Governing Equations ◽  
Bingham Plastic ◽  
Bingham Number ◽  
Wide Range ◽  
Nusselt Number Distribution ◽  
Plastic Fluids

The free convection phenomenon from a heated square cylinder submerged in Bingham Plastic fluids is numerically investigated. The governing equations are solved for a wide range of physical dimensionless parameters, such as Rayleigh number (10^2 ≤ Ra ≤ 10^5), Prandtl number (10 ≤ Pr ≤ 100) and Bingham number (0 ≤ Bn ≤ 10^7). The heat transfer characteristics are investigated in terms of local Nusselt number distribution over the surface of the cylinder surface average Nusselt number. Streamlines, isothermal contours, yielded and unyielded regions are visualized in detail.

Numerical computation of natural convection inside a curved-shape nanofluid-filled enclosure with nonuniform heating of the bottom wall

2019 ◽  
Vol 30 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Abdellaziz Yahiaoui ◽  
Mahfoud Djezzar ◽  
Hassane Naji
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Pure Water ◽  
Bottom Wall ◽  
Working Fluid ◽  
Nonuniform Heating ◽  
Square Enclosure ◽  
Nusselt Numbers

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H2O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature [Formula: see text], the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 103, 104, 105, the Prandtl number is fixed at 6.2, and the volume fraction [Formula: see text] is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

An Interferometric Study of Combined Free and Forced Convection in a Horizontal Isothermal Tube

1981 ◽  
Vol 103 (2) ◽  
pp. 249-256 ◽  
Author(s):  
W. W. Yousef ◽  
J. D. Tarasuk
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Forced Convection ◽  
Average Nusselt Number ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Reynolds Numbers ◽  
Nusselt Numbers ◽  
Free And Forced Convection

A Mach-Zehnder interferometer was employed to determine the three-dimensional temperature field, and the circumferential and average Nusselt numbers for laminar flow of air in the entrance region of an isothermal horizontal tube where the velocity and the temperature profiles were developing simultaneously. The influence of free convection due to buoyancy on forced convection heat transfer was investigated. The Reynolds numbers ranged from 120 to 1200, the Grashof numbers ranged from 0.8 × 104 to 8.7 × 104, and the ratio L/D was varied from 6 to 46. The free convection increases, substantially, the average Nusselt number, by up to a factor of 2.0 from the analytical predictions, which account for forced convection only, near the tube inlet. Far from the tube inlet the free convection tends to decrease the average Nusselt number below the analytical predictions.

An Experimental Study on the Effect of Partition Angle on Free Convection Heat Transfer in a Partition Cavity by Laser Interferometry Method

2010 ◽  
Author(s):  
Tooraj Yousefi ◽  
Sajjad Mahmoodi Nezhad ◽  
Masood Bigharaz ◽  
Saeed Ebrahimi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Free Convection ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Laser Interferometry ◽  
Heated Wall ◽  
Convection Heat ◽  
Free Convection Heat

Steady state two-dimensional free convection heat transfer in a partitioned cavity with adiabatic horizontal and isothermally vertical walls and an adiabatic partition has been investigated experimentally. The experiments have been carried out using a Mach-Zehnder interferometer. The effects of the angel of the adiabatic partition and Rayleigh number on the heat transfer from the heated wall are investigated. Experiments are performed for the values of Rayleigh number based on the cavity side length in the range between 1.5×105 to 4.5×105 and various angle of the partition with respect to horizon from 0° to 90°. The results indicate that at each angle of the adiabatic partition, by increasing the Rayleigh number, the average Nusselt number and heat transfer increase and at each Rayleigh number, the maximum and the minimum heat transfer occur at θ=45° and θ=90°, respectively. A correlation based on the experimental data for the average Nusselt number of the heated wall as a function of Rayleigh number and the angel of the adiabatic partition is presented in the aforementioned ranges.

Computational Study of the Heat Transfer of the Buoyancy-Driven Rotating Cavity With Axial Throughflow of Cooling Air

2009 ◽  
Author(s):  
Zain Dweik ◽  
Roger Briley ◽  
Timothy Swafford ◽  
Barry Hunt
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Free Convection ◽  
Flat Plate ◽  
Computational Study ◽  
Operating Conditions ◽  
Temperature Gradients ◽  
Wide Range ◽  
Complete Set ◽  
The Impact

Buoyancy driven flows that occur in the inter-disk space of an axial compressor spool play a major role in projecting gas turbine engine life and performance. The Rayleigh-Benard-like flow structure developed under the influence of centrifugal buoyancy creates sharp temperature gradients at the rotating walls of the compressor hardware. These sharp temperature gradients greatly influence the running stresses inside the machine and therefore affecting its life. The objective of this work is to generate a complete set of computationally-derived Nusselt number correlations that will be used in conducting the conjugate heat transfer analyses. The impact of engine power condition (Idle, Highpower, and Shutdown) on the heat transfer of these rotating cavities is studied under the wide range of operating conditions encountered by realistic turbomachines. A computational analysis is performed using commercially available computational tools for grid generation (ICEM-CFD) and turbulent-flow simulation (CFX). A total of fifty steady CFD cases for two different cavity configurations were analyzed. The CFD computed results of these cases were used to generate a complete set of Nusselt number correlations for different cavity geometry (gap ratios), flow regimes (forced and free convection dominated regimes), and operating conditions (Rossby Number Ro, Rotational Rayleigh Number RaΩ, and axial Reynolds Number Rez). The CFD computed heat-transfer results revealed that, despite the complicated flow patterns inside these cavities, and despite the large variation in their geometry, the simple Nusselt number correlations for free convection from a vertical flat plate with constant temperature can be used to predict the global Nusselt number values for the buoyancy-dominated regime of all such cavities. Furthermore, the Nusselt number correlations for the laminar and turbulent forced convection over a flat plate can be used to predict the global Nusselt number values for the central-jet dominated regime.

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