Convective Heat Transfer in a Rectangular Porous Cavity—Effect of Aspect Ratio on Flow Structure and Heat Transfer

1984 ◽  
Vol 106 (1) ◽  
pp. 158-165 ◽  
Author(s):  
V. Prasad ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Aspect Ratios ◽  
Family Of Curves ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Rayleigh Numbers ◽  
Cavity Effect ◽  
Cavity Width

Two-dimensional steady natural convection in a porous rectangular cavity bounded by isothermal vertical walls at different temperatures and adiabatic horizontal walls has been studied numerically for aspect ratios less than unity and Rayleigh numbers up to 104. Results indicate the presence of multicellular flow. Also, the average Nusselt number based on cavity width is observed to be a maximum in a restricted range of aspect ratio, depending on the Rayleigh number. Effects of aspect ratio are summarized by a family of curves for constant Rayleigh number, based on cavity height, for aspect ratios from 0.05 to 100. For a cavity with fixed height, the heat transfer rate always increases as the aspect ratio is increased, except when the flow exhibits boundary layers on the vertical walls. Criteria in terms of aspect ratio and Rayleigh number have been established for the existence of different flow regimes.

scholarly journals Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

2010 ◽  
Vol 655 ◽  
pp. 152-173 ◽  
Author(s):  
J. BAILON-CUBA ◽  
M. S. EMRAN ◽  
J. SCHUMACHER
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Turbulent Convection ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Cylindrical Cell ◽  
Aspect Ratios ◽  
Pod Analysis

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio Γ of a closed cylindrical cell and the Rayleigh number Ra. The Prandtl number is Pr = 0.7 throughout the study. The aspect ratio Γ is varied between 0.5 and 12 for a Rayleigh number range between 107 and 109. The Nusselt number Nu is the dimensionless measure of the global turbulent heat transfer. For small and moderate aspect ratios, the global heat transfer law Nu = A × Raβ shows a power law dependence of both fit coefficients A and β on the aspect ratio. A minimum of Nu(Γ) is found at Γ ≈ 2.5 and Γ ≈ 2.25 for Ra = 107 and Ra = 108, respectively. This is the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations in the convection cell. For larger aspect ratios Γ ≳ 8, our data indicate that the heat transfer becomes independent of the aspect ratio of the cylindrical cell. The aspect ratio dependence of the turbulent heat transfer for small and moderate Γ is in line with a varying amount of energy contained in the LSC, as quantified by the Karhunen–Loève or proper orthogonal decomposition (POD) analysis of the turbulent convection field. The POD analysis is conducted here by the snapshot method for at least 100 independent realizations of the turbulent fields. The primary POD mode, which replicates the time-averaged LSC patterns, transports about 50% of the global heat for Γ ≥ 1. The snapshot analysis enables a systematic disentanglement of the contributions of POD modes to the global turbulent heat transfer. Although the smallest scale – the Kolmogorov scale ηK – and the largest scale – the cell height H – are widely separated in a turbulent flow field, the LSC patterns in fully turbulent fields exhibit strikingly similar texture to those in the weakly nonlinear regime right above the onset of convection. Pentagonal or hexagonal circulation cells are observed preferentially if the aspect ratio is sufficiently large (Γ ≳ 8).

Heat Transfer by Natural Convection Across Vertical and Inclined Air Layers

1982 ◽  
Vol 104 (1) ◽  
pp. 96-102 ◽  
Author(s):  
S. M. ElSherbiny ◽  
G. D. Raithby ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Practical Interest ◽  
Correlation Equations ◽  
Linear Temperature ◽  
Aspect Ratios ◽  
Different Temperatures ◽  
Air Layers ◽  
Rayleigh Numbers

Measurements of the heat transfer by natural convection across vertical and inclined air layers are reported. The air layer is bounded by flat isothermal plates at different temperatures and around the edges by a perfectly conducting boundary (i.e., one that takes on a linear temperature distribution between the two plates). Measurements are reported for six aspect ratios between 5 and 110, covering a portion of the range of practical interest for windows, solar collectors, etc. Rayleigh numbers were in the range 102 to 2 × 107. The present measurements permitted the role of aspect ratio to be clearly defined. In addition, correlation equations are presented which allow the heat trnasfer across a vertical or inclined air layer to be calculated.

scholarly journals Natural Convection in Undivided and Partially Divided Rectangular Enclosures

1981 ◽  
Vol 103 (4) ◽  
pp. 623-629 ◽  
Author(s):  
M. W. Nansteel ◽  
R. Greif
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Two Dimensional ◽  
Injection Flow ◽  
Stabilizing Effect ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Rayleigh Numbers

Heat transfer by natural convection in a two-dimensional rectangular enclosure fitted with partial vertical divisions is investigated experimentally. The horizontal walls of the enclosure are adiabatic while the vertical walls are maintained at different temperatures. The experiments are carried out with water, Pr ≃ 3.5, for Rayleigh numbers in the range, 2.3 × 1010 ⩽ RaL ⩽ 1.1 × 1011, and an aspect ratio, A = H/L = 1/2. The effect of the partial vertical divisions on the fluid flow and temperature fields is investigated by dye-injection flow visualization and by thermocouple probes, respectively. The effect of the partitions on the heat transfer across the enclosure is also studied and correlations for the Nusselt number as a function of RaL and partition length are generated for both conducting and non-conducting partition materials. Partial divisions are found to have a significant effect on the heat transfer; especially when the divisions are adiabatic. The results also indicate that the partial divisions may have a stabilizing effect on the laminar-transitional flow on the heated vertical walls of the enclosure.

Convection in a rotating cylinder. Part 1 Linear theory for moderate Prandtl numbers

1993 ◽  
Vol 248 ◽  
pp. 583-604 ◽  
Author(s):  
H. F. Goldstein ◽  
E. Knobloch ◽  
I. Mercader ◽  
M. Net
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Rotation Rate ◽  
Critical Rayleigh Number ◽  
Onset Of Convection ◽  
Aspect Ratios ◽  
Prandtl Numbers ◽  
Rayleigh Numbers

The onset of convection in a uniformly rotating vertical cylinder of height h and radius d heated from below is studied. For non-zero azimuthal wavenumber the instability is a Hopf bifurcation regardless of the Prandtl number of the fluid, and leads to precessing spiral patterns. The patterns typically precess counter to the rotation direction. Two types of modes are distinguished: the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the centre. For aspect ratios τ ≡ d/h of order one or less the fast modes always set in first as the Rayleigh number increases; for larger aspect ratios the slow modes are preferred provided that the rotation rate is sufficiently slow. The precession velocity of the slow modes vanishes as τ → ∞. Thus it is these modes which provide the connection between the results for a finite-aspect-ratio System and the unbounded layer in which the instability is a steady-state one, except in low Prandtl number fluids.The linear stability problem is solved for several different sets of boundary conditions, and the results compared with recent experiments. Results are presented for Prandtl numbers σ in the range 6.7 ≤ σ ≤ 7.0 as a function of both the rotation rate and the aspect ratio. The results for rigid walls, thermally conducting top and bottom and an insulating sidewall agree well with the measured critical Rayleigh numbers and precession frequencies for water in a τ = 1 cylinder. A conducting sidewall raises the critical Rayleigh number, while free-slip boundary conditions lower it. The difference between the critical Rayleigh numbers with no-slip and free-slip boundaries becomes small for dimensionless rotation rates Ωh2/v ≥ 200, where v is the kinematic viscosity.

Natural Convection Heat Transfer in Moderate Aspect Ratio Enclosures

1979 ◽  
Vol 101 (4) ◽  
pp. 655-659 ◽  
Author(s):  
B. A. Meyer ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Aspect Ratios

Local and average heat transfer coefficients for natural convection between parallel plates separated by slats to create enclosures of moderate aspect ratio have been experimentally determined using an interferometric technique. The effects of Rayleigh number, tilt and slat angle, and aspect ratio on the Nusselt number have been determined. The Rayleigh number range tested was up to 7 × 104, and the aspect ratio (ratio of enclosure length to plate spacing) varied between 0.25 and 4. The angles of tilt of the enclosure with respect to the horizontal were 45, 60 and 90 deg. Slat angles of 45, 60, 90 and 135 deg were studied. The results obtained in a previous investigation [1] for aspect ratios of 9 to 36 are included to show continuity. The results indicate that the convective heat transfer is a strong function of the aspect ratio for aspect ratios less than 4. For aspect ratios in the range of 0.5 to 4, spacers between the plates increase, rather than decrease, natural convection heat transfer compared to that for long enclosures. Slat angles less than 90 deg (i.e., oriented downward) reduce convective heat transfer.

Numerical Study of Natural Convection in a Partitioned Cavity

2008 ◽  
Author(s):  
M. Pirmohammadi ◽  
M. Ghassemi ◽  
G. A. Sheikhzadeh
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Cold Wall ◽  
Governing Equations ◽  
Square Cavity ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Energy Equations

The purpose of this study is to investigate the effect of insulated horizontal baffle placed at the hot wall of a differentially heated square cavity. The vertical walls are at different temperatures while the horizontal walls are adiabatic. In our formulation of governing equations, mass, momentum and the energy equations are applied to the cavity and the baffles. To solve the governing differential equations a finite volume code based on Patankar’s SIMPLER method is utilized [1]. The Results are presented for Rayleigh number from 104 up to 106 and are in form of streamlines, isotherms and Nusselt number. The baffle causes that at low Rayleigh number the horizontal isotherms are replaced by nearly vertical ones, specially around the baffle. Also it is found that thermal boundary layers are thickened, and the temperature gradients at the cold wall are reduced from their values for the case without baffle and this implies that a reduction in the heat transfer through the cavity occurs.

Free Convection Heat Transfer across Rectangular-Celled Diathermanous Honeycombs

1980 ◽  
Vol 102 (1) ◽  
pp. 75-80 ◽  
Author(s):  
D. R. Smart ◽  
K. G. T. Hollands ◽  
G. D. Raithby
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Convection Heat Transfer ◽  
Aspect Ratios ◽  
Cell Dimensions ◽  
Free Convection Heat ◽  
Rayleigh Numbers ◽  
Honeycomb Material

Experimentally obtained Nusselt number-Rayleigh number plots are presented for free convective heat transfer across inclined honeycomb panels filled with air. The honeycomb cells were rectangular in shape with very long cell dimensions across the slope and comparatively short dimensions up the slope. Elevation aspect ratios, AE, investigated were 3, 5 and 10; angles of inclination, θ, measured from the horizontal, were 0, 30, 60, 75 and 90 deg. The effect on the Nusselt number, of the emissivities of the plates bounding the honeycomb, and of the emissivity of honeycomb material, was also investigated. The measurements confirmed that the critical Rayleigh number and the post-critical heat transfer depend on the radiant properties of the honeycomb cells. The critical Rayleigh numbers at θ = 0 were well predicted by the methods of Sun and Edwards. For 0 < θ ≤ 75 deg, the critical Rayleigh numbers and the Nusselt-Rayleigh relations were both found to be essentially the same as their horizontal counterparts provided the Rayleigh number was first scaled by cos θ. For θ = 90 deg, the form of the Nusselt-Rayleigh relation was found to be very different from that for θ ≤ 75 deg and similar to that observed for square-celled honeycombs for θ ≥ 30 deg. The θ = 90 deg data were found to be closely correlated by an equation of the form recently proposed by Bejan and Tien.

Influence of Partition Length on Natural Convection in Partially Divided Square Enclosure

2007 ◽  
Vol 129 (11) ◽  
pp. 1592-1599 ◽  
Author(s):  
C. D. Sankhavara ◽  
H. J. Shukla
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Enclosure ◽  
Thermal Boundary Conditions ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Good Agreement

Numerical investigation is carried out for natural convection in square enclosures consisting of partitions protruding from the end walls with different thermal boundary conditions at the end walls and partitions. The vertical walls were maintained isothermal at different temperatures. The Rayleigh number varies from 104 to 106 and the Prandtl number is 0.71. The thickness of the partition is fixed and is equal to one-tenth of the width of the enclosure. Their nondimensional length (l∕H) varies from 0 (a nonpartitioned enclosure) to 0.5 (two separate enclosures). A good agreement was found between the results in the present study and those published previously. The partitions were found to significantly influence the convective heat transfer. The average Nusselt number is less in the presence of partitions, and it decreases with increasing partition length (l∕H) from 0 to 0.5.

scholarly journals Numerical Analysis of Natural Convection Heat Transfer Inside an Inverted T-Shaped Cavity Filled with Nanofluid

2021 ◽  
pp. 180-188
Author(s):  
Gopal Sen ◽  
Mohammad Ilias Inam
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Natural Convection Heat Transfer ◽  
Average Heat Transfer Coefficient ◽  
Rayleigh Numbers

This assessment is centered on the characteristics of natural convection heat transfer of Aluminium Oxide-Air nanofluid inside an inverted T-shaped enclosure with differentially heated sidewalls. The left edges of the enclosed cavity have been treated as a heated wall and are kept at a constant temperature. The right edges are also maintained at a constant temperature but lower than the heated wall. The top and bottom faces of the cavity have been considered adiabatic. The evaluation has been numerically investigated using ANSYS fluent. The effect of different significant parameters like volume fraction of nanoparticles, the shape of the enclosure, and Rayleigh number on the heat transfer characteristics inside an inverted T shape enclosure have been investigated. In this numerical analysis, a series of DNS simulations have been conducted for different Rayleigh numbers in the range of 103 to 106, the volume fraction of particles in the range 0≤ φ ≤0.1, and for the different aspect ratios for the inverted T shape have been conducted. The outcomes of this CFD analysis indicate a remarkable rise in the average heat transfer coefficient with the rising volume fraction of Al2O3 particles in the air. An increase of the average Nusselt number was also observed with the increase of Rayleigh number, but it drops slightly at a higher volume fraction of nanoparticles due to an increase in conductive heat transfer. For Rayleigh numbers ≥ 104, both the average Nusselt number and average heat transfer coefficient decrease up to a certain shape of the cavity aspect ratio. After that cavity aspect ratio, both the parameters value increase. But in the case of Rayleigh number = 103, both of the values decrease with the increase in the cavity aspect ratio.

Sign in / Sign up

Export Citation Format

Share Document