Effect of an Insulated Baffle on Pseudosteady-State Natural Convection Inside Spherical Containers

2007 ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Bulk Temperature ◽  
Transfer Path ◽  
Extended Surface ◽  
Parametric Studies ◽  
Energy Equations ◽  
Rayleigh Numbers

The effect of an insulated thin baffle on pseudosteady-state natural convection within spherical containers is studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent, two-dimensional axisymmetric form of the governing continuity, momentum and energy equations are solved. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106 and 107, baffles with 3 lengths positioned at 5 different locations were investigated. In effect, a parametric study involving 60 cases were performed. The computational results were benchmarked against previous data available in the literature by comparing the heat transfer correlations, temperature distribution and streamline patterns for cases with no baffle. In general, regardless of the presence of an insulated baffle, fluid that is heated adjacent to the surface of the sphere rises replacing the colder fluid which sinks downward. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid. This behavior can lead to onset of oscillations in the temperature and flow fields. Due to blockage effect of an insulated thin baffle, multi-cell recirculating vortex structures are observed. The number and strength of these vortices depend on the position and length of the baffle. In the absence of heat transfer path through the insulated baffle, flow obstruction is the major feature of this problem. For the majority of the length and location combinations investigated, less heat is brought into the fluid thus lowering the time rate of rise of the bulk temperature. The extent of heat transfer modification depends on the Rayleigh number, length and location of the extended surface.

Effect of an Isothermal Baffle on Pseudosteady-State Natural Convection Inside Spherical Containers

2007 ◽  
Author(s):  
S. F. Hosseinizadeh ◽  
Yuping Duan ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Bulk Temperature ◽  
Dependent Variables ◽  
Parametric Studies ◽  
Energy Equations ◽  
Rayleigh Numbers ◽  
Temperature And Flow Fields

The influence of an isothermal thin baffle on pseudosteady-state natural convection within spherical containers is studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent, two-dimensional axisymmetric form of the governing continuity, momentum and energy equations are solved. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106 and 107, baffles with 3 lengths positioned at 5 different locations were investigated. In effect, a parametric study involving 60 cases were performed. The computational results were benchmarked against previous data available in the literature by comparing the heat transfer correlations, temperature distribution and streamline patterns for cases with no baffle. In general, regardless of the presence of an isothermal baffle, fluid that is heated adjacent to the surface of the sphere rises replacing the colder fluid which sinks downward. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid. This behavior can lead to onset of oscillations in the temperature and flow fields. Partly due to the blockage effect of an isothermal thin baffle and also the extra heating afforded by the baffle, multi-cell recirculating vortex structures are observed. The number and strength of these vortices depend on the position and length of the baffle. The additional heat that is brought into the baffle through the isothermal baffle is directly linked to creation of a counter clockwise rotating vortex next to the baffle. This baffle, in turn, directs hot fluid into the center of the sphere and disrupts thermal stratified layers. For the majority of the length and location combinations investigated, the Nusselt number is lower than the case with no baffle, however the time rate of rise of the bulk temperature can be greater for some combinations. The extent of heat transfer modifications depends on the Rayleigh number, length and location of the baffle.

Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Extended Surface ◽  
Parametric Studies ◽  
Thermal Layer

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106, and 107, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

Numerical Investigation of Variable Property Effects on Laminar Natural Convection of Gases Between Two Horizontal Isothermal Concentric Cylinders

1986 ◽  
Vol 108 (4) ◽  
pp. 783-789 ◽  
Author(s):  
D. N. Mahony ◽  
R. Kumar ◽  
E. H. Bishop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boussinesq Approximation ◽  
Variable Properties ◽  
Transfer Rates ◽  
Concentric Cylinders ◽  
Weighted Mean Temperature ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Gap Width

A numerical finite difference investigation has been conducted to determine the effects of variable properties on the laminar natural convection of gases between horizontal isothermal concentric cylinders. Velocity profiles, temperature profiles, and heat transfer rates have been computed for diameter ratios of 1.5, 2.28, 2.6, and 5.0 and Rayleigh numbers based on gap width up to 1.8 × 105. The temperature difference ratio θo was varied from 0.2 to 3.0, and the range of validity of the Boussinesq approximation was determined to be θo = 0.2. A volume-weighted mean temperature was shown to be the most effective reference temperature to reduce the heat transfer data for each diameter ratio to a single curve of the form keq = C RaLn, for 0.2 ≤ θo ≤ 3.0 and RaL = 2.0 × 105.

Experimental and Computational Analysis of Natural Convection Over Flat Plate

2008 ◽  
Author(s):  
Farhana Afroz ◽  
Chowdhury Md. Feroz
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Flat Plate ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Heat Fluxes ◽  
Navier Stokes ◽  
Heated Plate ◽  
Wide Range ◽  
Energy Equations

Natural convection heat transfer over a flat plate with a heat source at bottom side of plate is studied experimentally and numerically. We consider the two-dimensional problem of both steady and unsteady natural convection over the flat plate at vertical, horizontal and inclined position. Experimental analysis is done for three different constant heat fluxes for each angle position. The Navier-Stokes and Energy equations with the Boussinesq approximation are written in Cartesian coordinate system. The problem is solved in the physical variables on the basis of a completely implicit Finite element Method order to examine the heat transfer characteristics. To see the effects of different angle position phenomena of natural convection over flat plate, the computational results presented in the form of streamlines for a wide range of Grashof number at different heat fluxes. The average Nusselt number of heated plate for different angle position has been observed.

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.

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

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.

Free-convection effects in the boundary layer along a vertically stretching flat surface

1992 ◽  
Vol 70 (12) ◽  
pp. 1253-1260 ◽  
Author(s):  
John E. Daskalakis
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Flat Surface ◽  
Relaxation Method ◽  
Boussinesq Approximation ◽  
Axial Coordinate ◽  
Prandtl Numbers ◽  
Energy Equations

We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.

Natural Convection in a Horizontal Cavity Partially Occupied by a Porous Media Saturated by a Coolant Liquid

2006 ◽  
Author(s):  
Fakhreddine S. Oueslati ◽  
Rachid Bennacer ◽  
Habib Sammouda ◽  
Ali Belghith
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Flow Structure ◽  
Boussinesq Approximation ◽  
Density Variation ◽  
Heat Fluxes ◽  
Complex Flow ◽  
Coupled Equations ◽  
Complex Flow Structure

The natural convection is studied in a cavity witch the lower half is filled with a porous media that is saturated with a first fluid (liquid), and the upper is filled with a second fluid (gas). The horizontal borders are heated and cooled by uniform heat fluxes and vertical ones are adiabatic. The formulation of the problem is based on the Darcy-Brinkman model. The density variation is taken into account by the Boussinesq approximation. The system of the coupled equations is resolved by the classic finite volume method. The numerical results show that the variation of the conductivity of the porous media influences strongly the flow structure and the heat transfer as well as in upper that in the lower zones. The effect of conductivity is conditioned by the porosity which plays a very significant roll on the heat transfer. The structures of this flow show that this kind of problem with specific boundary conditions generates a complex flow structure of several contra-rotating two to two cells, in the upper half of the cavity.

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