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.

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.

Optimizing Laminar Natural Convection for a Heat Generating Cylinder in a Channel

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Corey E. Clifford ◽  
Mark L. Kimber
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Spent Nuclear Fuel ◽  
Reactor Core ◽  
Horizontal Cylinder ◽  
Cylinder Surface ◽  
Transfer Program ◽  
Wet Storage

Natural convection heat transfer from a horizontal cylinder is of importance in a large number of applications. Although the topic has a rich history for unconfined cylinders, maximizing the free convective cooling through the introduction of sidewalls and creation of a chimney effect is considerably less studied. In this investigation, a numerical model of a heated horizontal cylinder confined between two vertical adiabatic walls is employed to evaluate the natural convective heat transfer. Two different treatments of the cylinder surface are investigated: constant temperature (isothermal) and constant surface heat flux (isoflux). To quantify the effect of wall distance on the effective heat transfer from the cylinder surface, 18 different confinement ratios are selected in varying increments from 1.125 to 18.0. All of these geometrical configurations are evaluated at seven distinct Rayleigh numbers ranging from 102 to 105. Maximum values of the surface-averaged Nusselt number are observed at an optimum confinement ratio for each analyzed Rayleigh number. Relative to the “pseudo-unconfined” cylinder at the largest confinement ratio, a 74.2% improvement in the heat transfer from an isothermal cylinder surface is observed at the optimum wall spacing for the highest analyzed Rayleigh number. An analogous improvement of 60.9% is determined for the same conditions with a constant heat flux surface. Several correlations are proposed to evaluate the optimal confinement ratio and the effective rate of heat transfer at that optimal confinement level for both thermal boundary conditions. One of the main application targets for this work is spent nuclear fuel, which after removal from the reactor core is placed in wet storage and then later transferred to cylindrical dry storage canisters. In light of enhanced safety, many are proposing to decrease the amount of time the fuel spends in wet storage conditions. The current study helps to establish a fundamental understanding of the buoyancy-induced flows around these dry cask storage canisters to address the anticipated needs from an accelerated fuel transfer program.

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.

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.

Computational Analysis of Laminar Natural Convection in Rectangular Enclosures of Different Aspect Ratios With Different Heating Conditions

2012 ◽  
Author(s):  
Mosfequr Rahman ◽  
Charles Walker ◽  
Gustavo Molina ◽  
Valentin Soloiu
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
External Temperature ◽  
Aspect Ratios

Natural convection in rectangular enclosures is found in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. The enclosure phenomena can loosely be organized into two large classes: (1) horizontal enclosures heated from below and (2) vertical enclosures heated from the side. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of heat sources with different strength. Numerical simulations are conducted for free convective flow of air with or without internal heat generation in two-dimensional rectangular enclosures of different aspect ratios. The objective of this numerical study is to investigate the effects of external temperature gradient, internal heat generation and aspect ratio (AR) of enclosure (ratio of the length of the isothermal walls to their separation distance), in free convective laminar flow of a fluid. Two-dimensional rectangular enclosures of different aspect ratio (1, 2, 4, 6, 8, and 10) with two adiabatic side walls and isothermal bottom (hot) and top (cold) walls are considered for the first configuration. Whereas for the second configuration, two adiabatic top and bottom walls, isothermal left side (cold) and right side (hot) walls are considered. Two principal parameters considered for the flow of fluid are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the isothermal walls, and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. The effect of external temperature gradient and aspect ratio on natural convection has been observed by varying the value of external Rayleigh number (RaE) equal to 2×104, 2×105, and 2×106 and keeping the internal Rayleigh number constant (RaI = 2×105). Similarly, the effect of internal heat generation and aspect ratio on natural convection has been observed by varying the value of internal Rayleigh number (RaI) equal to 2×104, 2×105, and 2×106 and keeping the external Rayleigh number constant (RaE = 2×105). Significant changes in flow patterns and isotherms have been observed for all cases. Also the variation of average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot and cold walls, and the convection strength have been calculated for all cases. It is found that the aspect ratio has a significant effect in fluid flow and heat transfer in the enclosures. The average heat flux ratio and the strength of convection increase with aspect ratio as the enclosure shape changes square (AR = 1) to shallow (AR > 1).

Numerical Study on Natural Convection and Radiation From a Square Disk

2005 ◽  
Author(s):  
Arnout Willockx ◽  
Christophe Tjoen ◽  
Hendrik-Jan Steeman ◽  
Michel De Paepe
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Simulations ◽  
Flow Pattern ◽  
Numerical Study ◽  
Constant Heat Flux ◽  
Test Case ◽  
Air Velocity ◽  
Closed Cavity ◽  
Small Vortex

In this paper, a numerical study of natural convection from a disk is presented. The disk is placed vertically in a closed cavity (cylinder) and has a constant heat flux. Different numerical simulations of this test case are executed at various gravity accelerations (=g) inside the cavity. The accelerations are varied from 9.81 m/s2 to 53 m/s2. The Rayleigh number changes with these accelerations. The flow pattern and the temperature distribution inside the cavity are visualized. For natural convection inside a cavity, a vortex is expected in the air flow: a plume of warm rising air at the centre of the cylinder above the heated square disk and descending colder air at the walls of the cavity. The air velocity is higher in the central plume. At w = 9.81 m/s2, the maximum air velocity is 0.05 m/s. This velocity increases with increasing acceleration w till 0.6 m/s at w = 53 m/s2. At low w, the flow pattern exists of a stable vortex and thus a steady-state flow. At w = 15 m/s2, the vortex becomes more unstable and is swirling. At w = 27 m/s2, the vortex is even more swirling and the following periodical phenomenon takes place: first the vortex starts to dissolve in a small vortex at the top of the cylinder and a vortex below this around the square disk. Then, the lower vortex starts to increase again and the upper vortex is fading. So there is again one big vortex with a central, unstable plume that reaches the top of the cylinder. After a few seconds, the plume dissolves again. This phenomenon has no constant period. The higher w, the faster this phenomenon happens and thus the shorter the period. At w = 53m/s2, the vortex seems more turbulent than laminar, however the Rayleigh number is still in the laminar range (Ra<106). The numerical simulations are verified with existing correlations. There was a good agreement between correlations and numerical simulation.

scholarly journals Transient Heat Transfer Between Two Horizontal Pipelines in a Heat Tracing Enclosure

Energies ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1440
Author(s):  
C.J. Ho ◽  
G.N. Sou ◽  
Chi-Ming Lai
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Heat Transfer Coefficient ◽  
Average Heat ◽  
Current Test ◽  
Test Conditions ◽  
The Finite Difference Method

In this study, a numerical simulation of natural convection between two horizontal differentially heated pipelines inside a circular air-filled enclosure is performed using the finite difference method. The relevant parameters of the problem are the inclinations of the two cylinders (positioned vertically in this study, with the cold cylinder above the hot cylinder), the distance between cylinders and the Rayleigh number. The results show that transient irregular fluctuations in the flow field and heat transfer occur when the Rayleigh number increases or the distance between cylinders decreases. Under the current test conditions, increasing the Rayleigh number significantly increases the average heat transfer coefficient between the cold and hot cylinders.

An Experimental Study on Natural Convection Heat Transfer in an Inclined Square Enclosure Containing Internal Energy Sources

1988 ◽  
Vol 110 (2) ◽  
pp. 345-349 ◽  
Author(s):  
Jae-Heon Lee ◽  
R. J. Goldstein
Keyword(s):  
Natural Convection ◽  
Internal Energy ◽  
Extreme Values ◽  
Convection Heat Transfer ◽  
Energy Sources ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Inclination Angles ◽  
The Right ◽  
Rayleigh Numbers

An experiment was carried out to study two-dimensional laminar natural convection within an inclined square enclosure containing fluid with internal energy sources bounded by four rigid planes of constant equal temperature. Inclination angles, from the horizontal, of 0, 15, 30, and 45 deg for Rayleigh numbers from 1.0 × 104 to 1.5 × 105 were studied. At inclined angles of 0 and 15 deg, there are two extreme values of temperature and temperature gradient within the fluid, while there is only one at 30 and 45 deg. Local and average Nusselt numbers are obtained on all four walls. As the inclination angle increases, the average Nusselt number increases on the right (upper) and bottom walls, decreases on the left (lower) wall and stays almost constant on the top wall.

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