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.

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.

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.

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.

Effects of Variable Viscosity and Thermal Conductivity of CuO-Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Eiyad Abu-Nada
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Cylinder Surface ◽  
Transfer Enhancement

Heat transfer enhancement in horizontal annuli using variable thermal conductivity and variable viscosity of CuO-water nanofluid is investigated numerically. The base case of simulation used thermal conductivity and viscosity data that consider temperature property dependence and nanoparticle size. It was observed that for Ra≥104, the average Nusselt number was deteriorated by increasing the volume fraction of nanoparticles. However, for Ra=103, the average Nusselt number enhancement depends on aspect ratio of the annulus as well as volume fraction of nanoparticles. Also, for Ra=103, the average Nusselt number was less sensitive to volume fraction of nanoparticles at high aspect ratio and the average Nusselt number increased by increasing the volume fraction of nanoaprticles for aspect ratios ≤0.4. For Ra≥104, the Nusselt number was deteriorated everywhere around the cylinder surface especially at high aspect ratio. However, this reduction is only restricted to certain regions around the cylinder surface for Ra=103. For Ra≥104, the Maxwell–Garnett and the Chon et al. conductivity models demonstrated similar results. But, there was a deviation in the prediction at Ra=103 and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and the Brinkman model give completely different predictions for Ra≥104, where the difference in prediction of the Nusselt number reached 50%. However, this difference was less than 10% at Ra=103.

MHD natural convection and entropy analysis of a nanofluid inside T-shaped baffled enclosure

2018 ◽  
Vol 28 (12) ◽  
pp. 2916-2941 ◽  
Author(s):  
Taher Armaghani ◽  
A. Kasaeipoor ◽  
Mohsen Izadi ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Content Type ◽  
Thermal Indexes ◽  
The Impact

Purpose The purpose of this paper is to numerically study MHD natural convection and entropy generation of Al2O3-water alumina nanofluid inside of T-shaped baffled cavity which is subjected to a magnetic field. Design/methodology/approach Effect of various geometrical, fluid and flow factors such as aspect ratio of enclosure and baffle length, Rayleigh and Hartmann number of nanofluid have been considered in detail. The hydrodynamics and thermal indexes of nanofluid have been described using streamlines, isotherms and isentropic lines. Findings It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. The interesting finding is an increase in the impact of Hartmann number on heat transfer indexes with augmenting Rayleigh number. However, with augmenting Rayleigh number and, thus, strengthening the buoyant forces, the efficacy of Hartmann number one, an index indicating the simultaneous impact of natural heat transfer to entropy generation increases. It is clearly seen that the efficacy of nanofluid on increased Nusselt number enhances with increasing aspect ratio of the enclosure. Based on the results, the Nusselt number generally enhances with the larger baffle length in the enclosure. Finally, with larger Hartmann number and lesser Nusselt one, entropy production is reduced. Originality/value The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

Study of Natural Convection in Inclined Square Enclosures With Uniform Heat Generation

2007 ◽  
Author(s):  
Manish Kulkarni ◽  
Sushanta K. Mitra ◽  
U. N. Gaitonde
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Generation ◽  
Inclination Angle ◽  
Local Nusselt Number ◽  
Internal Heat ◽  
Square Enclosure ◽  
Inclination Angles ◽  
Inclined Cavity

Two-dimensional laminar natural convection in an inclined square enclosure with uniform internal heat generation is studied here. The steady-state solutions are obtained for inclination angles of 45°, 30° and 15° and at Rayleigh number of 1.5 × 105. For these cases, the two counter-rotating rolls of fluid are present in the cavity. Streamlines, isotherms and heat transfer for these results are compared with the existing experimental results and are found to be in reasonably good agreement. It is found that the location of maximum non-dimensional temperature in the inclined cavity is higher than that for pure conduction case. The maximum non-dimensional temperature in the cavity decreases as the Rayleigh number increases. For Ra > 5 × 104, the maximum non-dimensional temperature in inclined cavity is almost independent of the inclination angle. It is also observed that the local Nusselt number at the top wall is greater than the pure conduction solution, whereas that for bottom wall it is lower than the Nusselt number for pure conduction. The effect of Rayleigh number and inclination angle on the local Nusselt number and modified local Nusselt number are also studied. For horizontal cavity, at Rayleigh number greater than or equal to 5 × 104, periodic solutions are obtained. In this case, two unstable secondary rolls are present near the center of top wall, in addition to the primary rolls. The secondary rolls are dissipated and recreated during one period of oscillation.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
S. M. Dash ◽  
S. Sahoo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lattice Boltzmann Model ◽  
Immersed Boundary ◽  
Heat Sources ◽  
Square Enclosure ◽  
Thermal Lattice Boltzmann

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

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.

Natural Convection in a Nano-Fluid Filled Square Enclosure

2020 ◽  
Vol 847 ◽  
pp. 114-119
Author(s):  
Barbie Leena Barhoi ◽  
Ramesh Chandra Borah ◽  
Sandeep Singh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Control Volume ◽  
Convection Heat Transfer ◽  
Ansys Fluent ◽  
Square Enclosure ◽  
Nano Fluid

The present study relates to numerical investigation of natural convection heat transfer in a nanofluid filled square enclosure. One side of the enclosure is maintained at high temperature and the other side at a low temperature; while the top and bottom sides are adiabatic. The commercial CFD software ANSYS-FLUENT© was used to solve this numerical problem with the governing differential equations discretized by a control volume approach. nanofluids of Cu-water, Al2O3-water and TiO2-water have been simulated for a range of Rayleigh numbers and volume fractions. The results were obtained in the form of streamlines and isotherms. Interpretations of the results are done based on heat transfer rates, volume fraction, Rayleigh number and Nusselt number. It is to be noted that addition of nanoparticles enhances the heat transfer rate. It is also observed that the Nusselt number is highly affected by volume fraction and Rayleigh number.

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