NATURAL CONVECTION IN A MICROPOLAR NANOFLUID FILLED OPEN RECTANGULAR ENCLOSURE EMBEDDED WITH A HEATED OBJECT OF DIFFERENT GEOMETRIES

2020 ◽  
Vol 9 (11) ◽  
pp. 9187-9200
Author(s):  
E.G. Ushachew ◽  
M.K. Sharma
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Source ◽  
Uniform Heat Flux ◽  
Rectangular Enclosure ◽  
Micropolar Nanofluid ◽  
Energy Equations ◽  
Successive Over Relaxation ◽  
Heated Object ◽  
Positive Effect

A numerical investigation has been performed to analyze heat convection through a micropolar nanofluid in an open rectangular enclosure. It embedded the inner heated object of different geometries and finite heat source length on the bottom wall with uniform heat flux. The remaining portion of the wall containing heat source and all the remaining walls are assumed as adiabatic except the top wall. Successive over-relaxation (SOR) method coupled with Gauss-Seidel iteration technique are employed in order to numerically tackled the nonlinear model momentum and energy equations. The effect of the calibrated parameters such as Rayleigh number, length of the wall heat source, the geometry of the inner block, vortex viscosity parameter, the type of nanoparticles, and the concentration of nanoparticles on the flow and thermal performance is studied. The computed results show that increasing in the Rayleigh number and the concentration of nanoparticles have a positive effect on Nusselt number whereas increasing in wall heat source length and vortex viscosity attenuates the Nusselt number. Also, the geometry of the inner block has effect in the flow pattern and the temperature distribution.

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.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel

1989 ◽  
Vol 111 (3) ◽  
pp. 649-656 ◽  
Author(s):  
B. W. Webb ◽  
D. P. Hill
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Channel ◽  
Local Heat Transfer ◽  
Heated Wall ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Heating Rates ◽  
Wide Range

Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.

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.

Effects of cavity and heat source aspect ratios on natural convection of a nanofluid in a C-shaped cavity using Lattice Boltzmann method

2018 ◽  
Vol 28 (8) ◽  
pp. 1930-1955 ◽  
Author(s):  
Mohsen Izadi ◽  
Rasul Mohebbi ◽  
A. Chamkha ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Source ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Average Nusselt Number ◽  
Content Type ◽  
Boltzmann Method

PurposeThe purpose of this paper is to consider natural convection of a nanofluid inside of a C-shaped cavity using Lattice Boltzmann method (LBM).Design/methodology/approachEffects of some geometry and flow parameters consisting of the aspect ratio of the cavity, aspect ratio of the heat source; Rayleigh number (Ra = 103− 106) have been investigated. The validity of the method is checked by comparing the present results with ones from the previously published work.FindingsThe results demonstrate that for Ra = 103, the aspect ratio of the heat source has more influence on the average Nusselt number in contrast to the case of Ra = 106. Contrary to the fact that the average Nusselt number increases non-linearly more than twice because of the increase of the aspect ratio of the enclosure at Ra = 103, the average Nusselt number has a linear relation with the aspect ratio for of Ra = 106. Therefore, upon increasing the Rayleigh number, the efficiency of the aspect ratio of the cavity on the thermal convection, gradually diminishes.Originality/valueThe authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

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.

Subcritical convective instability Part 1. Fluid layers

1966 ◽  
Vol 26 (4) ◽  
pp. 753-768 ◽  
Author(s):  
Daniel D. Joseph ◽  
C. C. Shir
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Source ◽  
Linear Theory ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Heat Sources ◽  
Fluid Layers ◽  
Rayleigh Numbers

This paper elaborates on the assertion that energy methods provide an always mathematically rigorous and a sometimes physically precise theory of sub-critical convective instability. The general theory, without explicit solutions, is used to deduce that the critical Rayleigh number is a monotonically increasing function of the Nusselt number, that this increase is very slow if the Nusselt number is large, and that a fluid layer heated from below and internally is definitely stable when $RA < \widetilde{RA}(N_s) > 1708/(N_s + 1)$ where Ns is a heat source parameter and $\widetilde{RA}$ is a critical Rayleigh number. This last problem is also solved numerically and the result compared with linear theory. The critical Rayleigh numbers given by energy theory are slightly less than those given by linear theory, this difference increasing from zero with the magnitude of the heat-source intensity. To previous results proving the non-existence of subcritical instabilities in the absence of heat sources is appended this result giving a narrow band of Rayleigh numbers as possibilities for subcritical instabilities.

Unsteady natural convection with entropy generation in partially open triangular cavities with a local heat source

2017 ◽  
Vol 27 (12) ◽  
pp. 2696-2716 ◽  
Author(s):  
Hakan F. Öztop ◽  
Nadezhda S. Bondareva ◽  
Mikhail A. Sheremet ◽  
Nidal Abu-Hamdeh
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Entropy Generation ◽  
Average Nusselt Number ◽  
Local Heat ◽  
Dimensionless Time ◽  
Content Type ◽  
Local Heat Source

Purpose The main aim of this work is to perform a numerical analysis on natural convection with entropy generation in a partially open triangular cavity with a local heat source. Design/methodology/approach The unsteady governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The effects of dimensionless time is studied, and other governing parameters are Rayleigh number (Ra = 103 − 105), Prandtl number (Pr = 6.82), heater length (w/L = 0.2, 0.4 and 0.6) and distance of heater ratio (δ/L = 0.3). Findings An increase in the Rayleigh number leads to an increment of the fluid flow and heat transfer rates. Average Bejan number decreases with Ra as opposed to the average Nusselt number and average entropy generation. High values of Ra characterize a formation of long-duration oscillating behavior for the average Nusselt number and entropy generation. Originality/value The originality of this work is to analyze the entropy generation in natural convection in a one side open and partial heater-located cavity. This is a good application for electronical systems or building design.

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