Numerical Analysis of Plume Structures of Fluids on a Horizontal Heated Plate

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
T. Praphul ◽  
P. J. Joshy ◽  
P. S. Tide
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Cube Root ◽  
Heated Plate ◽  
Steady State Model ◽  
Increasing Trend ◽  
Wall Flow ◽  
Near Wall

Numerical investigations have been carried out to predict the near-wall dynamics in indirect natural convection for air (Pr = 0.7) and water (Pr = 5.2). Near-wall flow structures appear to be line plumes. Three-dimensional laminar, steady-state model was used to model the problem. Density was formulated using the Boussinesq approximation. Flux scaling, plume spacing and plume lengths obtained numerically are found to have the same trend with the results available in the literature. Plume length and Nusselt number, Nu exhibits an increasing trend with an increase in Rayleigh number, RaH for both Pr fluids. The plume spacing is found to have an inverse relationship with RaH. The cube root of Rayleigh number based on plume spacing, Raλ1/3 is found to have a slight dependence on the dimensionless plume spacing, λ/H. Nu scales as Nu∼CRaHn, n = 0.26 for air and n = 0.3 for water. Heat transfer is thus found to be dominated by near-wall phenomenon. Nu shows a nonlinear relationship with LpH/A and is found to be an accurate representation of heat transfer.

Natural Convection in Yield Stress Fluids From a Confined Horizontal Plate

2019 ◽  
Author(s):  
S. A. Patel ◽  
A. H. Raja ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Boussinesq Approximation ◽  
Critical Value ◽  
Heated Plate ◽  
Bingham Number ◽  
Wide Range ◽  
Energy Equations

Abstract The heat transfer characteristics from an isothermal heated plate in a quiescent yield stress fluid in a cavity was investigated over a wide range of parameters (Rayleigh number, 102 ≤ Ra ≤ 105, Prandtl number, 10 ≤ Pr ≤ 100, and Bingham number, Bn ≥ 0) where the flow is known to be laminar and steady. The coupled momentum and energy equations have solved here numerically within the framework of Boussinesq approximation to capture the temperature-dependent fluid density. The results demonstrate that for a given value of the Rayleigh number, there exists a critical value of the Bingham number, above which the fluid is completely unyielded and heat transfer occurs solely by conduction. In order to delineate the effect of domain geometry on the conduction limit, the study was extended over a range of geometrical aspects by varying the aspect ratio (λ = diameter of the cavity/ a length of the plate), 2 ≤ λ ≤ 5. This work shows that the critical value of the Bingham number can be described as a function of geometry of domain, Ra and Pr. The value of critical Bingham number increases with the increasing aspect ratio and Rayleigh number in order to approach the conduction limit. The yield surfaces show that the increasing values of Rayleigh number induce fluid-like behaviour whereas Bingham number opposes this propensity. The average Nusselt number decreases with the increasing Bingham number due to the suppression of the advective component of heat transfer.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

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.

Effect of Edge Conditions on Natural Convective Heat Transfer From a Narrow Vertical Flat Plate With a Uniform Surface Heat Flux

2007 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Surface Heat Flux ◽  
Three Dimensional ◽  
Surface Heat ◽  
Heated Plate ◽  
Two Dimensional ◽  
Adiabatic Surface

Two-dimensional natural convective heat transfer from vertical plates has been extensively studied. However, when the width of the plate is relatively small compared to its height, the heat transfer rate can be greater than that predicted by these two-dimensional flow results. Because situations that can be approximately modelled as narrow vertical plates occur in a number of practical situations, there exists a need to be able to predict heat transfer rates from such narrow plates. Attention has here been given to a plate with a uniform surface heat flux. The magnitude of the edge effects will, in general, depend on the boundary conditions existing near the edge of the plate. To examine this effect, two situations have been considered. In one, the heated plate is imbedded in a large plane adiabatic surface, the surfaces of the heated plane and the adiabatic surface being in the same plane while in the second there are plane adiabatic surfaces above and below the heated plate but the edge of the plate is directly exposed to the surrounding fluid. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in terms of dimensionless variables. Results have only been obtained for a Prandtl number of 0.7. A wide range of the other governing parameters have been considered for both edge situations and the conditions under which three dimensional flow effects can be neglected have been deduced.

A Comparison Between Experimental and Predicted Flow Profiles Beneath a Semi-Confined Axisymmetric Impinging Jet

2003 ◽  
Author(s):  
C. Y. Cheong ◽  
P. T. Ireland ◽  
S. Ashforth-Frost
Keyword(s):  
Viscous Flow ◽  
Flow Model ◽  
Three Dimensional ◽  
Impinging Jet ◽  
Theoretical Models ◽  
Velocity Profiles ◽  
Axisymmetric Case ◽  
Air Jet ◽  
Wall Flow ◽  
Near Wall

Theoretical predictions have been compared with experiment for a single semi-confined impinging jet. The turbulent air jet discharged at Re = 20 000 and impinged at nozzle-to-plate spacings (z/d) of 2 and 6.5. Experimental velocity profiles were obtained using hot-wire anemometry. Theoretical velocity profiles were derived using stagnation three-dimensional flow model and viscous flow model for an axisymmetric case. For z/d = 2, velocity profiles in the inviscid region of the near wall flow can be predicted accurately using the stagnation flow model. As the edge of the jet is approached, the flow becomes complex and, as expected, cannot be predicted using the model. Prediction of boundary layer profiles using the viscous flow solution for an axisymmetric case is also reasonable. For z/d = 6.5, the developing impinging jet is essentially turbulent on impact and consequently predictions of near wall flow field, using both the theoretical models, are inappropriate.

Instability in a viscous flow driven by streamwise vortices

2001 ◽  
Vol 432 ◽  
pp. 127-166 ◽  
Author(s):  
K. W. BRINCKMAN ◽  
J. D. A. WALKER
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wall Layer ◽  
External Flow ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Wall Flow ◽  
Turbulent Wall ◽  
Near Wall

Unsteady separation processes at large finite, Reynolds number, Re, are considered, as well as the possible relation to existing descriptions of boundary-layer separation in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow, believed to be relevant to bursting near the wall in a turbulent boundary layer. Bursting is known to be associated with streamwise vortex motion, but the vortex/wall interactions that drive the near-wall flow toward breakdown have not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices is used to assess the influence of sustained pumping action on the development of a viscous wall layer. The calculated solutions describe a three-dimensional flow at finite Re that is independent of the streamwise coordinate and consists of a crossflow plane motion, with a developing streamwise flow. The unsteady problem is constructed to mimic a typical cycle in turbulent wall layers and numerical solutions are obtained over a range of Re. Recirculating eddies develop rapidly in the near-wall flow, but these eddies are eventually bisected by alleyways which open up from the external flow region to the wall. At sufficiently high Re, an oscillation was found to develop in the streamwise vorticity field near the alleyways with a concurrent evolution of a local spiky behaviour in the wall shear. Above a critical value of Re, the oscillation grows rapidly in amplitude and eventually penetrates the external flow field, suggesting the onset of an unstable wall-layer breakdown. Local zones of severely retarded streamwise velocity are computed which are reminiscent of the low-speed streaks commonly observed in turbulent boundary layers. A number of other features also bear a resemblance to observed coherent structure in the turbulent wall layer.

scholarly journals Numerical Simulation of the Natural Convection with Presence of the Nanofluids in Cubical Cavity

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Mohamed Sannad ◽  
Abourida Btissam ◽  
Belarche Lahoucine
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Flow And Heat Transfer ◽  
Heating Section ◽  
The Right

This article consists of a numerical study of natural convection heat transfer in three-dimensional cavity filled with nanofluids. This configuration is heated by a partition maintained at a hot constant and uniform temperature TH. The right and left vertical walls are kept at a cold temperature TC while the rest is adiabatic. The fluid flow and heat transfer in the cavity are studied for different sets of the governing parameters, namely, the nanofluid type, the Rayleigh number Ra = 103, 104, 105, and 106, and the volume fraction Ф varying between Ф = 0 and 0.1. The obtained results show a positive effect of the volume fraction and the Rayleigh number on the heat transfer improvement. The analysis of the results related to the heat transfer shows that the copper-based nanofluid guarantees the best thermal transfer. In addition, the increase of the heating section size and Ra leads to an increased amount of heat. Similarly, increasing the volume fraction improves the intensification of the flow and increases the heat exchange.

Buoyancy Effect on Developing Turbulent Flow and Heat Transfer in a Helical Pipe With Finite Pitch

2000 ◽  
Author(s):  
B. Zheng ◽  
C. X. Lin ◽  
M. A. Ebadian
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Control Volume ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Buoyancy Effect ◽  
Constant Wall Temperature ◽  
Flow And Heat Transfer ◽  
Helical Pipe ◽  
Volume Method

Abstract Numerical modeling was performed to investigate the buoyancy effect on developing turbulent flow and the heat transfer characteristics of saturated water in a helical pipe with finite pitch. The renormalization group (RNG) κ–ε model was used to account for the turbulent flow and heat transfer in the helical pipe at a constant wall temperature with or without buoyancy force effect. A control volume method with second-order accuracy was used to numerically solve the three-dimensional full elliptic governing equations for this problem. The O-type nonuniform structured grid system was adopted to discretize the computation domain. The Boussinesq approximation was applied to deal with the buoyancy. This study explored the influence of buoyancy on the developing heat transfer along the helical pipe. Based on the results of this research, the velocity, temperature, and Nusselt number are presented graphically and analyzed.

Influence Of Relative Size Of The U-Shaped Silicon Rod On Conjugate Heat Transfer In The Regime Of Gas Buayancy Induced Convection

2015 ◽  
Vol 10 (3) ◽  
pp. 76-88
Author(s):  
Vladimir Berdnikov ◽  
Konstantin Mitin ◽  
Alina Mitina
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Solid Body ◽  
Conjugate Heat Transfer ◽  
Relative Size ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Spatial Form ◽  
Section Size

The influence of relative cross-section size of an electrically heated U-shaped silicon rod which is placed in a gas-filled rectangle container with isothermal cold walls on conjugate heat transfer in the regime of buoyancy induced convection was numerically studied in three-dimensional formulation. The natural convection equations in the Boussinesq approximation in term temperature, velocity vortex and velocity vector potential were solved by the finite element method. The spatial form of convective flow and temperature fields in liquid and solid body were studied. It was show that spatial form and intensity of convective flows is significantly depends on the cross-section size of U-shaped silicon rod. This is has strong influence on the temperature field in a solid body.

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