An Experimental Study of Natural Convection in Trapezoidal Enclosures

1980 ◽  
Vol 102 (4) ◽  
pp. 648-653 ◽  
Author(s):  
L. Iyican ◽  
L. C. Witte ◽  
Y. Bayazitogˇlu
Keyword(s):  
Experimental Data ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Tilt Angle ◽  
Circulation Pattern ◽  
Two Dimensional ◽  
Number Range ◽  
Rectangular Channels ◽  
Trapezoidal Enclosure ◽  
Hot Surface

Experimental data for natural convection of air in an inclined trapezoidal enclosure are reported for a Rayleigh number range of ∼ 2 × 103 to ∼ 5 × 107. The small side of the trapezoid was electrically heated while the opposing large side was cooled to a uniform temperature. The effect of tilt angle from 0 to 90 deg (from horizontal) was investigated at 15 deg increments. Data were also obtained for 180 deg (hot surface facing down). A comparison of the data to an analysis using a two-dimensional circulation pattern showed reasonable agreement in the Rayleigh number-tilt angle range where two-dimensional circulation could be expected. The experimental data are correlated by an equation of the form, Nu = C Ran, over a wide Rayleigh number range. The data exhibit a local minimum in the Nusselt number-tilt angle curve between 90 and 0 deg in a manner similar to that observed in inclined rectangular channels.

Natural Convection Heat Transfer Characteristics of Flat Plate Enclosures

1979 ◽  
Vol 101 (1) ◽  
pp. 120-125 ◽  
Author(s):  
K. R. Randall ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Tilt Angle ◽  
Convection Heat Transfer ◽  
Transfer Coefficients ◽  
Number Range ◽  
Grashof Number ◽  
Average Heat ◽  
Plate Spacing

Heat transfer by natural convection in rectangular enclosures has been experimentally studied using interferometric techniques. The effects of Grashof number, tilt angle, and aspect ratio on both the local and average heat transfer coefficients have been determined. The Grashof number range tested was 4 × 103 to 3.1 × 105, and the aspect ratio (ratio of enclosure length to plate spacing) varied between 9 and 36. The angles of tilt of the enclosure with respect to the horizontal were 45, 60, 75 and 90 deg. Correlations are developed for both local and average Nusselt number over the range of test variables. The effect of tilt angle is found to reduce the average heat transfer by about 18 percent from the value of 45 deg to that at 90 deg. No significant effect of aspect ratio over the range tested was found. A method for characterizing the flow regimes that is based on heat transfer mechanisms is proposed.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

Symbolic Calculation for Free Convection in a Circular Cavity With Periodic Heat Generation

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Free Convection ◽  
Heat Generation ◽  
Circular Cavity ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Periodic Heat

We consider the two-dimensional problem of steady natural convection in a circular cavity with periodic heat generation filled with viscous fluid subject to cosine temperature variation on the boundary. The solution is expanded for low Rayleigh number and extended to 16 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but pade approximation leads our result to be good even for higher value of the similarity parameter.

Natural Convection Heat Transfer From a Plate in a Semicircular Enclosure

1992 ◽  
Vol 114 (1) ◽  
pp. 121-126 ◽  
Author(s):  
G. A. Moore ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Plate Thickness ◽  
Fluid Motion ◽  
Convection Heat Transfer ◽  
Bulk Fluid ◽  
Number Range ◽  
Balance Technique ◽  
Conductive Component

In the subject geometry, a long thin plate at uniform temperature is contained coaxially and symmetrically in a long semicircular trough closed at the top and having a uniform but different temperature. Heat flows across the air-filled region between the two by both natural convection and gaseous conduction. The problem of characterizing the free convective component of this heat transfer—that is, the component caused by bulk fluid motion—is treated experimentally by using a heat balance technique, with the measurements being repeated at different pressures, in order to cover a wide Rayleigh number range, from Ra ≈ 10 to Ra ≈ 108. Nusselt number versus Rayleigh number plots are presented for each of several combinations of plate-to-trough spacing and tilt angle, and the plots are correlated by equations. The problem of characterizing the conductive component is treated by numerically solving the steady diffusion equation in the air-filled region, and the results are correlated as a function of the spacing and the plate thickness.

Numerical Simulations of an Unsteady Confined Natural Convection Flow

2009 ◽  
Author(s):  
Gillian Leplat ◽  
Emmanuel Laroche ◽  
Philippe Reulet ◽  
Pierre Millan
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Large Scale ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
High Amplitude ◽  
Joint Fluid ◽  
Convection Flow ◽  
Two Dimensional ◽  
Natural Convection Flow

A two-dimensional numerical analysis of a laminar natural convection flow within an air-filled enclosure is proposed in this paper from an unstable configuration previously studied experimentally. The flow is driven by a heated square-section cylinder located at the center of a square-section enclosure. Instabilities are observed for an aspect ratio (height of the cylinder over the height of the cavity) of 0.4 and cause the flow to turn into a three-dimensional and unsteady regime characterized by a symmetry breaking and large scale high amplitude flappings around the cylinder. The multi-physic computational software CEDRE, developed at the ONERA, is used to study this unstable behavior and a time-dependent compressible flow solver is used to perform the two-dimensional simulations under the low Mach number approximation, corresponding to the mid-depth cross-section of the enclosure from the experimental configuration. The first results on the investigation of the first unstable modes confirm the onset of the instabilities at the Rayleigh number of the experiment with asymmetrical motions of the fluid around the cylinder. Further analyses highlight the critical Rayleigh number that defines the instability threshold of the first bifurcation which origin and nature could have been identified. Finally, joint fluid-solid simulations are performed to determine more precisely the role of boundary conditions in the onset of instabilities.

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. 

Natural Convection in an Externally Heated Vertical or Inclined Square Box Containing Internal Energy Sources

1985 ◽  
Vol 107 (4) ◽  
pp. 855-866 ◽  
Author(s):  
S. Acharya ◽  
R. J. Goldstein
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Pattern ◽  
Internal Energy ◽  
Flux Ratio ◽  
Energy Sources ◽  
Number Range ◽  
Average Heat ◽  
Square Box

A numerical investigation has been made of two-dimensional natural convection of air in an externally heated vertical or inclined square box containing uniformly distributed internal energy sources. Results have been obtained for Rayleigh numbers (both internal and external) up to 107 and inclination angles of 30, 60, and 90 deg from the horizontal. Two distinct flow pattern systems are observed: one, when the external Rayleigh number is larger than the internal Rayleigh number and the other, when the internal Rayleigh number is considerably greater than the external Rayleigh number. The average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot surface is observed to undergo large variations in the external Rayleigh number range associated with the transition from one flow pattern to another. The average heat flux ratio along the cold plate is found to increase with increasing external Rayleigh number and decreasing internal Rayleigh number. The local heat flux ratio along a surface attains its maximum value in the vicinity of the region where the heated (or cooled) fluid from the opposite wall or from the interior encounters the surface.

Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

2007 ◽  
Vol 586 ◽  
pp. 259-293 ◽  
Author(s):  
F. X. TRIAS ◽  
M. SORIA ◽  
A. OLIVA ◽  
C. D. PÉREZ-SEGARRA
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Turbulent Statistics ◽  
Large Eddies ◽  
Three Dimensional Simulations

A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection

2017 ◽  
Vol 814 ◽  
pp. 165-184 ◽  
Author(s):  
Yang Zhang ◽  
Quan Zhou ◽  
Chao Sun
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Rayleigh Number ◽  
Small Scale ◽  
Two Dimensional ◽  
Number Range ◽  
Dissipation Rates ◽  
Log Normal ◽  
Rayleigh Benard ◽  
Gl Theory

We investigate the statistical properties of the kinetic $\unicode[STIX]{x1D700}_{u}$ and thermal $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}$ energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Bénard (RB) convection. Direct numerical simulations were carried out in a box with unit aspect ratio in the Rayleigh number range $10^{6}\leqslant Ra\leqslant 10^{10}$ for Prandtl numbers $Pr=0.7$ and 5.3. The probability density functions (PDFs) of both dissipation rates are found to deviate significantly from a log-normal distribution. The PDF tails can be well described by a stretched exponential function, and become broader for higher Rayleigh number and lower Prandtl number, indicating an increasing degree of small-scale intermittency with increasing Reynolds number. Our results show that the ensemble averages $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ scale as $Ra^{-0.18\sim -0.20}$, which is in excellent agreement with the scaling estimated from the two global exact relations for the dissipation rates. By separating the bulk and boundary-layer contributions to the total dissipations, our results further reveal that $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ are both dominated by the boundary layers, corresponding to regimes $I_{l}$ and $I_{u}$ in the Grossmann–Lohse (GL) theory (J. Fluid Mech., vol. 407, 2000, pp. 27–56). To include the effects of thermal plumes, the plume–background partition is also considered and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ is found to be plume dominated. Moreover, the boundary-layer/plume contributions scale as those predicted by the GL theory, while the deviations from the GL predictions are observed for the bulk/background contributions. The possible reasons for the deviations are discussed.

Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape

1985 ◽  
Vol 107 (3) ◽  
pp. 624-629 ◽  
Author(s):  
M. J. Chamberlain ◽  
K. G. T. Hollands ◽  
G. D. Raithby
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Complex Shape ◽  
Convection Heat Transfer ◽  
Average Error ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Transient Method ◽  
Number Range

Measurements of the heat transfer by natural convection from isothermal bodies to air are reported and compared to the predictions of the method proposed by Raithby and Hollands [7, 8]. The bodies tested were the cube in various orientations and a body consisting of two touching spheres (a bisphere). The experimental Rayleigh number range extended from 10 to 107. The experimental method incorporated measuring the heat transfer by the transient method and varying the Rayleigh number by varying the pressure. The predictions agreed with the measurements to within an average error of about 3 percent. The results are correlated by single equations, which can be extended to fluids other than air.

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