Free Convective Flow in a Two Enclosure Arrangement With a High Aspect Ratio Side Enclosure Joined to a Large Square Enclosure

2000 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Vertical Wall ◽  
Heated Wall ◽  
Free Convective Flow ◽  
Square Enclosure

Abstract A numerical study of free convective flow in a vertical joined two-enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is separated from a larger square enclosure by a vertical dividing wall which is impermeable but offers no resistance to heat transfer. The vertical wall of the main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. All remaining walls in both enclosures are adiabatic. The situation considered is an approximate model of a window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number and the dimensionless width of the side enclosure on the Nusselt number have been investigated. The results show that there is a minimum in the Nusselt number variation with side enclosure width for a fixed Rayleigh number. The effect of Rayleigh number on the conditions under which this minimum occurs and on the value of the minimum Nusselt number has been investigated.

Natural Convective Flow in a Three Enclosure System Involving Two High Aspect Ratio Side Enclosures Joined to a Large Square Enclosure With Interfacial Heat Generation

2003 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Generation ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Square Enclosure ◽  
Number Variation ◽  
Resistance To Heat

A numerical study of free convective flow in a vertical joined three enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is joined to a second high aspect ratio rectangular side enclosure which has the same height as the first side enclosure, the two enclosures being separated by a vertical impermeable dividing wall which offers no resistance to heat transfer. The second side enclosure is joined to a larger square enclosure, the vertical dividing wall between these two enclosures also being impermeable and offering no resistance to heat transfer. The vertical wall of the square main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. There is a uniform rate of heat generation in the dividing wall between the inner side enclosure and the main enclosure. The situation considered is an approximate model of a double-paned window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. In some such cases there can be significant heat generation in the blind due to the absorbtion of solar energy, this being modeled by the heat generation in the one dividing wall. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number, dimensionless width of the side enclosures and dimensionless heat generation rate in the blind on the Nusselt number have been investigated. The results show that for a fixed Rayleigh number and for a given dimensionless first (i.e., outer) side enclosure width, there is a minimum in the Nusselt number variation with the dimensionless width of the second side enclosure. An approximate solution for the Nusselt number variation with the dimensionless width of the second side enclosure for small values of this dimensionless width has also been derived.

Natural Convection in a Cylindrical Porous Enclosure With Internal Heat Generation

1989 ◽  
Vol 111 (4) ◽  
pp. 916-925 ◽  
Author(s):  
V. Prasad ◽  
A. Chui
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Vertical Wall ◽  
Internal Heat ◽  
Heat Removal ◽  
Maximum Temperature ◽  
Wall Boundary Conditions

A numerical study is performed on natural convection inside a cylindrical enclosure filled with a volumetrically heated, saturated porous medium for the case when the vertical wall is isothermal and the horizontal walls are either adiabatic or isothermally cooled. When the horizontal walls are insulated, the flow in the cavity is unicellular and the temperature field in upper layers is highly stratified. However, if the top wall is cooled, there may exist a multicellular flow and an unstable thermal stratification in the upper region of the cylinder. Under the influence of weak convection, the maximum temperature in the cavity can be considerably higher than that predicted for pure conduction. The local heat flux on the bounding walls is generally a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The heat removal on the cold upper surface decreases with the aspect ratio, thereby increasing the Nusselt number on the vertical wall. The effect of Rayleigh number is, however, not straightforward. Several correlations are presented for the maximum cavity temperature and the overall Nusselt number.

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.

Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
G. Lorenzini ◽  
B. S. Machado ◽  
L. A. Isoldi ◽  
E. D. dos Santos ◽  
L. A. O. Rocha
Keyword(s):  
Nusselt Number ◽  
Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Driven Cavity ◽  
Constructal Design ◽  
Mixed Convective Flow ◽  
Forced Convective Flow

The present work shows a numerical study of laminar, steady, and mixed convective flow inside lid-driven square cavity with intruded rectangular fin in its lower surface. The main purpose here is to maximize the heat transfer between the rectangular fin and the surrounding mixed convective flow inside a lid-driven cavity by means of constructal design. The problem is subject to two constraints, the lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (ϕ = 0.05). The investigated geometry has one degree-of-freedom (DOF), the fin aspect ratio (H1/L1), which is varied in the range 0.1 ≤ H1/L1 ≤ 10. The aspect ratio of the cavity is maintained fixed (H/L = 1.0). The effect of the fin geometry over the Nusselt number is investigated for several Rayleigh (RaH = 103, 104, 105 and 106) and Reynolds numbers (ReH = 10, 102, 3.0 × 102, 5.0 × 102, 7.0 × 102 and 103). For all simulations, the Prantdl number is fixed (Pr = 0.71). The conservation equations of mass, momentum, and energy are numerically solved with the finite volume method. Results showed that fin geometry (H1/L1) has strong influence over the Nusselt number in the fin. It was also observed that the effect of H1/L1 over Nusselt number changes considerably for different Rayleigh numbers and for the lowest magnitudes of Reynolds numbers, for example, differences of nearly 770% between RaH = 106 and forced convective flow were observed for the lowest Reynolds number studied (ReH = 10).

scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
pp. 100
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

Numerical Study of Laminar Natural Convection From a Plate to its Cylindrical Enclosure

1991 ◽  
Vol 113 (3) ◽  
pp. 194-199 ◽  
Author(s):  
M. M. Elshamy ◽  
M. N. Ozisik
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Hot Plate ◽  
Cell Pattern ◽  
Laminar Natural Convection

The steady-state laminar natural convection for air bounded by a hot plate and a cold cylindrical enclosure has been studied numerically for the case of cold isothermal cylinder and hot isothermal plate. A correlation is presented for the average Nusselt number over the range of Rayleigh number from 105 to 106 for different values of the width-aspect ratio Sw and thickness aspect-ratio St of the plate. It is found that the average Nusselt number increases with increasing Sw and Rayleigh number. A two-cell pattern is observed for Sw=1.5 and less. The effect of Sw on the average Nusselt number is found to be stronger than that of St.

scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Hayder I. Mohammed ◽  
Donald Giddings
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat And Mass Transfer ◽  
Vertical Wall

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.

Heat Transfer Characteristics of the Phase Change Material Microcapsule Slurry in Solid Phase State

2011 ◽  
Vol 71-78 ◽  
pp. 1187-1190
Author(s):  
Yan Lai Zhang ◽  
Zhong Hao Rao ◽  
Shuang Feng Wang ◽  
Hong Zhang ◽  
Li Jun Li ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Phase State ◽  
Solid Phase ◽  
Heat Transfer Characteristics ◽  
Rectangular Enclosure ◽  
Transfer Characteristics ◽  
Change Material

This experiment is performed to investigate heat transfer characteristics with the PCM microcapsule slurry in a solid phase state at a horizontal rectangular enclosure heating from below and cooling from top. Some important parameters are taken into account such as the mass concentration of the PCM, the temperature difference between heating plate and cooling plate, Nusselt number Nu, Rayleigh number Ra and the aspect ratio (width/height) of the horizontal rectangular enclosure. Experiment is done under the thermal steady condition in the PCM microcapsule slurry. Heat transfer coefficient is measured under various temperature differences in PCM mass concentrations of 10% and 20%. And relationship with Nusselt number Nu and Rayleigh number Ra is summarized to various heights H or the aspect ratio (width/height) Ar of enclosure.

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