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.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

2016 ◽  
Vol 831 ◽  
pp. 83-91
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Maximum Temperature ◽  
Cubical Enclosure ◽  
Simplec Algorithm ◽  
Volume Method

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

scholarly journals Natural convection in a Square Enclosure with Partially Active Vertical Wall

2020 ◽  
Vol 330 ◽  
pp. 01004
Author(s):  
Abdennacer Belazizia ◽  
Smail Benissaad ◽  
Said Abboudi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Vertical Wall ◽  
Left Wall ◽  
Convection And Heat Transfer ◽  
Square Enclosure ◽  
Active Location

Steady, laminar, natural convection flow in a square enclosure with partially active vertical wall is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on three parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), and the aspect ratio of the enclosure (A=1). The active location takes two positions in the left wall: top (T) and middle (M). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rate. The results including the streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also by moving the active location from the top to the middle on the left vertical wall, convection and heat transfer rate are more important in case (M). Furthermore for high Rayleigh number (Ra=106), Convection mechanism in (T) case is principally in the top of the enclosure, whereas in the remaining case it covers the entire enclosure.

scholarly journals Simulation of Natural Convection Heat Transfer in a 2-D Trapezoidal Enclosure

2019 ◽  
Vol 16 (4) ◽  
pp. 7375-7390 ◽  
Author(s):  
K. Venkatadri ◽  
S. Abdul Gaffar ◽  
Ramachandra Prasad V. ◽  
B. Md. Hidayathulla Khan ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Practical Applications ◽  
Wide Range ◽  
Trapezoidal Enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energyrelated applications, in case of proper design of enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 103 ≤ Ra ≤ 105 and Prandtl number (Pr = 0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra = 104 ). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported. 

Numerical computation of natural convection inside a curved-shape nanofluid-filled enclosure with nonuniform heating of the bottom wall

2019 ◽  
Vol 30 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Abdellaziz Yahiaoui ◽  
Mahfoud Djezzar ◽  
Hassane Naji
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Pure Water ◽  
Bottom Wall ◽  
Working Fluid ◽  
Nonuniform Heating ◽  
Square Enclosure ◽  
Nusselt Numbers

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H2O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature [Formula: see text], the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 103, 104, 105, the Prandtl number is fixed at 6.2, and the volume fraction [Formula: see text] is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

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.

An Experimental Study of Natural Convection in a Vertical Cavity With Discrete Heat Sources

1988 ◽  
Vol 110 (3) ◽  
pp. 616-624 ◽  
Author(s):  
M. Keyhani ◽  
V. Prasad ◽  
R. Cox
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Flow Visualization ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Cold Wall ◽  
Onset Of Convection ◽  
Flow Cells ◽  
Nusselt Numbers ◽  
Vertical Cavity

Natural convection heat transfer in a tall vertical cavity (aspect ratio = 16.5), with one isothermal vertical cold wall, and eleven alternately unheated and flush-heated sections of equal height on the opposing vertical wall, is experimentally investigated. The flow visualization pictures for the ethylene glycol–filled cavity reveal a flow pattern consisting of primary, secondary, and tertiary flows. The heat transfer data and the flow visualization photographs indicate that the stratification is the primary factor influencing the temperature of the heated sections. This behavior persists for all the runs where the secondary flow cells cover a large vertical extend of the cavity. Based on the analysis of the photographs it is suggested that the turbulent flow should be expected when the local modified Rayleigh number is in the range of 9.3×1011 to 1.9×1012. It is found that discrete flush-mounted heating in the enclosure results in local Nusselt numbers that are nearly the same as those reported for a wide flush-mounted heater on a vertical plate. This is believed to be due to the fact that the present problem is inherently unstable, and the smallest temperature difference between a heated section and the cold wall results in the onset of convection motion.

Heat Transfer in Discretely Heated Side-Vented Compact Enclosures by Combined Conduction, Natural Convection, and Radiation

1999 ◽  
Vol 121 (4) ◽  
pp. 1002-1010 ◽  
Author(s):  
E. Yu ◽  
Y. K. Joshi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Radiative Heating ◽  
Computational Domain ◽  
Flow Recirculation ◽  
Discrete Heat Source ◽  
Rayleigh Numbers

A three-dimensional investigation of combined conduction, natural convection, and radiation in a side-vented compact enclosure is carried out. The focus of the study is on the enhancement of overall heat transfer through the opening, and the roles of the various modes in achieving it. A discrete heat source, flush-mounted centrally on a vertical substrate, is placed in the enclosure with a single rectangular opening on the opposite vertical wall. Steady-state computations are carried out for Rayleigh numbers, Ra, at 2.6 × 106 and 2.0 × 107. The results show that radiation plays a significant role in the overall heat transfer, and the radiative transport is even more pronounced for lower Ra. It is found that natural convection is weakened by radiation, however, contrary to the existing studies on top vented enclosures, the overall heat transfer is enhanced when radiation is included in the computations. Flow recirculation by radiative heating of enclosure walls is predicted, and is also observed experimentally. Heat spreading in the substrate is found to effect both convection and radiation. The numerical solutions on an extended computational domain are found in good agreement with the experimental data, when the conjugate effects are accounted for.

Heat Transfer by Natural Convection From an Array of Short, Wall-Attached Horizontal Cylinders

1982 ◽  
Vol 104 (1) ◽  
pp. 125-131 ◽  
Author(s):  
E. M. Sparrow ◽  
D. S. Cook ◽  
G. M. Chrysler
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Plate ◽  
Diameter Ratio ◽  
Nusselt Numbers ◽  
Cylinder Length ◽  
Horizontal Cylinders ◽  
Length To Diameter Ratio

Per-cylinder natural convection Nusselt numbers were measured for an in-line array of short horizontal cylinders that were affixed to a convectively participating vertical plate. The effect of cylinder length-to-diameter ratio, intercylinder spacing, position at which the cylinder is attached to the vertical plate, and Rayleigh number were investigated. The experiments were performed in air. It was found that the extent to which a given cylinder in the array was affected by cylinders situated below it depended on the Rayleigh number, with enhanced heat transfer coefficients being more likely at higher Rayleigh numbers. Greater enhancement occurred at larger intercylinder spacings. The qualitative characteristics of the Nusselt number results were insensitive to the cylinder length-to-diameter ratio, but the longer cylinders exhibited higher values of the Nusselt number. For the most part, the Nusselt numbers for the wall-attached horizontal cylinders fell below those for the classical horizontal cylinder of infinite length.

Natural Convection Cooling of an Array of Flush Mounted Discrete Heaters Inside a 3D Cavity

2017 ◽  
Vol 9 (3) ◽  
pp. 698-721 ◽  
Author(s):  
V. P. M. Senthil Nayaki ◽  
S. Saravanan ◽  
X. D. Niu ◽  
P. Kandaswamy
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Heat Removal ◽  
Simple Algorithm ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Cold Walls ◽  
Volume Method

AbstractAn investigation of natural convective flow and heat transfer inside a three dimensional rectangular cavity containing an array of discrete heat sources is carried out. The array consists of a row and columnwise regular arrangement of identical square shaped isoflux discrete heaters and is flush mounted on a vertical wall of the cavity. A symmetrical isothermal sink condition is maintained by cooling the cavity uniformly from either the opposite wall or the side walls or the top and bottom walls. The other walls of the cavity are maintained adiabatic. A finite volume method based on the SIMPLE algorithm and the power law scheme is used to solve the conservation equations. The parametric study covers the influence of pertinent parameters such as the Rayleigh number, the Prandtl number, side aspect ratio of the cavity and cavity heater ratio. A detailed fluid flow and heat transfer characteristics for the three cases are reported in terms of isothermal and velocity vector plots and Nusselt numbers. In general it is found that the overall heat transfer rate within the cavity for Ra=107 is maximum when the side aspect ratio of the cavity lies between 1.5 and 2. A more complex and peculiar flow pattern is observed in the presence of top and bottom cold walls which in turn introduces hot spots on the adiabatic walls. Their location and size are highly sensitive to the side aspect ratio of the cavity and hence offers more effective ways for passive heat removal.

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