A Numerical Study of Laminar Natural Convection in Shallow Cavities

1981 ◽  
Vol 103 (2) ◽  
pp. 226-231 ◽  
Author(s):  
G. S. Shiralkar ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Numerical Study ◽  
Aspect Ratios ◽  
Shallow Cavities ◽  
Horizontal Cavity ◽  
Side Walls ◽  
Prandtl Numbers

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

Validation and Development of DNS Database for Low Prandtl Numbers in Rod Bundle

2019 ◽  
Author(s):  
Jonathan K. Lai ◽  
Elia Merzari ◽  
Yassin A. Hassan ◽  
Aleksandr Obabko
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Heat Transfer Characteristics ◽  
Reynolds Analogy ◽  
Transfer Characteristics ◽  
Rod Bundle ◽  
High Thermal Diffusivity ◽  
Prandtl Numbers

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Prt) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Prt. More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above

2000 ◽  
Vol 122 (3) ◽  
pp. 485-491 ◽  
Author(s):  
G. A. Holtzman ◽  
R. W. Hill ◽  
K. S. Ball
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Pitchfork Bifurcation ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Aspect Ratios ◽  
Triangular Enclosure ◽  
Laminar Natural Convection ◽  
Flow Symmetry

A numerical study of natural convection in an isosceles triangular enclosure with a heated horizontal base and cooled upper walls is presented. Nearly every previous study conducted on this subject to date has assumed that the geometric plane of symmetry is also a plane of symmetry for the flow. This problem is re-examined over aspect ratios ranging from 0.2 to 1.0 and Grashof numbers from 103 to 105. It is found that a pitchfork bifurcation occurs at a critical Grashof number for each of the aspect ratios considered, above which the symmetric solutions are unstable to finite perturbations and asymmetric solutions are instead obtained. Results are presented detailing the occurrence of the pitchfork bifurcation in each of the aspect ratios considered, and the resulting flow patterns are described. A flow visualization study is used to validate the numerical observations. Computed local and mean heat transfer coefficients are also presented and compared with results obtained when flow symmetry is assumed. Differences in local values of the Nusselt number between asymmetric and symmetric solutions are found to be more than 500 percent due to the shifting of the buoyancy-driven cells. [S0022-1481(00)02503-2]

Three-Dimensional Steady and Oscillatory Natural Convection in a Rectangular Enclosure With Heat Sources

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Amin Bouraoui ◽  
Rachid Bessaïh
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Three Dimensional ◽  
Air Cooling ◽  
Heat Sources ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Simpler Algorithm ◽  
Strong Relation

In this paper, a numerical study of three-dimensional (3D) natural convection air-cooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region.

A Numerical Study of Natural Convective Heat Transfer From Isothermal High Aspect Ratio Rectangular Cylinders

2013 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Width Ratio ◽  
Heated Cylinder ◽  
Aspect Ratios ◽  
Study Results ◽  
Rectangular Cylinders

Natural convective heat transfer from isothermal rectangular cylinders which have an exposed upper surface has been numerically studied. The cylinders considered have high aspect ratios, i.e., have high width-to-depth ratios, and are relatively short, i.e., have a “height” that is of the same order of magnitude as their width. The cylinders considered are mounted on a plane adiabatic base, the cylinders being normal to the plane base with the cylinders pointing either vertically upwards or vertically downwards. One of the main aims of the present work was to numerically determine how the depth-to-width ratio of the rectangular cylinder influences the mean heat transfer rate from the cylinder when this depth-to-width ratio is large. The flow has also been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations using the commercial CFD solver, ANSYS FLUENT©. The solution is dependent on the Rayleigh number, the ratio of the width to the height of the heated cylinder, the ratio of the width to the depth of the heated cylinder, the Prandtl number, Pr, and on whether the cylinder is pointing vertically upwards or vertically downwards. Because of the applications that motivated this study, results have only been obtained for a Prandtl number of 0.74, i.e., effectively the value for air. A range of the other governing parameters has been considered and the effects of these governing parameters on the Nusselt number variation have been examined.

Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall(s)

2007 ◽  
Author(s):  
E. Natarajan ◽  
Tanmay Basak ◽  
S. Roy
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Vertical Wall ◽  
Side Wall ◽  
Convection Flow ◽  
Left Wall ◽  
Wide Range ◽  
Stream Functions ◽  
Side Walls

The present numerical study deals with natural convection flow in a trapezoidal cavity when the bottom wall is uniformly heated and the vertical wall(s) are linearly heated and cooled whereas the top wall is well insulated. Nonlinear coupled partial differential equations governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Parametric study for the wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 105 and Prandtl number (Pr), 0.07 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For linearly heated side walls symmetry is observed while representing the flow patterns in terms of stream functions whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. Local Nusselt number becomes negative at the side wall for linearly heated side walls and at the left wall for linearly heated left wall and cooled right wall indicating the reversal of heat flow. The effect of Prandtl number in the variation of average Nusselt numbers is more significant for Prandtl numbers in the range 0.07 to 0.7 than 10 to 100.

Study of Natural Convection in Volumetrically Heated Enclosures for Different Aspect Ratios and Prandtl Numbers

2009 ◽  
Author(s):  
Parameshwar Deshmukh ◽  
Sushanta K. Mitra ◽  
U. N. Gaitonde
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Simple Algorithm ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
Fluid Properties ◽  
Inclination Angles ◽  
Parametric Studies ◽  
Horizontal Cavity ◽  
Prandtl Numbers

Natural convection in volumetrically heated rectangular enclosures is studied in this work. The walls of the enclosure are maintained isothermal. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. The code is benchmarked with the results for a lid-driven cavity and a differentially heated cavity. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 106. For a horizontal cavity, the flow becomes periodically oscillating at Ra = 5×104 and chaotic at Ra = 8×105. With a slight increase in the inclination angle, the oscillations die down and for inclination angles greater than 15°, the flow attain a steady state over a range of Ra. The aspect ratio AR, defined as the ratio of the height to the width of the cavity, is varied from 0.25 to 0.75 (AR < 1: wide cavities) and from 2.0 to 6.0 (AR > 1: long cavities). The values of critical Ra at which the convection sets in the cavity are presented for the range of AR studied here. The corresponding flow regimes are also identified.

Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
S. Roy ◽  
Tanmay Basak ◽  
Ch. Thirumalesha ◽  
Ch. Murali Krishna
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Average Nusselt Number ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Triangular Enclosure ◽  
Prandtl Numbers

A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), 103⩽Ra⩽105 and Prandtl numbers (Pr), 0.026⩽Pr⩽1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr=0.026−0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7–1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is 2 times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).

An Experimental Investigation of Natural Convection With a Low Prandtl Number Fluid in a Vertical Channel With Uniform Wall Heat Flux

1974 ◽  
Vol 96 (4) ◽  
pp. 448-454 ◽  
Author(s):  
R. G. Colwell ◽  
J. R. Welty
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Experimental Program ◽  
Convection Flow ◽  
Width Ratio ◽  
Channel Height ◽  
Heated Plate ◽  
Aspect Ratios

An experimental program was conducted to study the heat transfer characteristics of mercury in laminar natural convection flow within a vertical open-ended channel over a range of channel widths. Two sets of boundary conditions were investigated separately: (1) uniform heat flux at one wall with the other insulated, and (2) both walls symmetrically and uniformly heated. A decrease in channel width caused a decrease in channel wall temperature in the developing portion of the flow. This unexpected phenomenon persisted until the channel height-to-width ratio, Ar, reached a value greater than 18. Hence, the buoyancy induced flow of a low Prandtl number fluid in a channel is more thermally efficient than a single heated plate. Temperature data have been correlated into local Nusselt versus modified Grashof number plots, based on streamwise position, for several aspect ratios. The effect of aspect ratio on channel temperature is displayed on NuL versus Ar curves for several GrL*. The infinite spacing limit is compared to previous work with temperature profiles and local heat transfer results. Expressions for local and average heat transfer correlations are presented, with suggested limits on their application. The effect of flow in from the sides of the channel was investigated by affixing plastic side plates to the channel.

scholarly journals Numerical study of flow and heat transfer in differentially heated enclosures

2014 ◽  
Vol 18 (2) ◽  
pp. 451-463 ◽  
Author(s):  
Byong-Hoon Chang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Two Dimensional ◽  
Flow And Heat Transfer ◽  
Aspect Ratios ◽  
Heated Air ◽  
Side Walls ◽  
Laminar Natural Convection

Two-dimensional laminar natural convection is studied numerically for differentially heated air-filled rectangular enclosures with adiabatic side walls and aspect ratios of 1, 2, 4 and 8. The inclination angle of the enclosure was varied from 0? to 180?, and the effect of inclination on flow field and heat transfer was investigated over the range 103 ? Ra ? 106. Correlations of average Nusselt number based on the present results are presented for horizontal and vertical cases. Large discrepancies were found among published results.

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