Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below

1976 ◽  
Vol 98 (2) ◽  
pp. 202-207 ◽  
Author(s):  
H. Ozoe ◽  
K. Yamamoto ◽  
S. W. Churchill ◽  
H. Sayama
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Good Method ◽  
Three Dimensional Model ◽  
Flat Plates ◽  
Dimensional Solution ◽  
Confined Fluid ◽  
Laminar Natural Convection ◽  
Improved Model

An improved model and algorithm were developed for the numerical solution of three-dimensional, laminar natural convection in enclosures. Illustrative calculations were carried out for heating from below in a cubical box, a long channel with a square cross section and in the region between infinite, horizontal plates. The results are in good agreement with prior experimental and theoretical results. For the infinite flat plates the three-dimensional model correctly produces a two-dimensional solution. For the cube the solution produces different stable solutions depending on the initial conditions. A fluid-particle path is shown to be a good method of illustrating the three-dimensional motion. In the cube and in each cubical cell in the channel this streak-line was found to consist of a pair of double helices.

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.

Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core

1990 ◽  
Vol 112 (1) ◽  
pp. 130-136 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
M. Faghri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Wall Boundary Conditions ◽  
Laminar Natural Convection

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical air slot with a thin hexagonal honeycomb core. The air slot is assumed to be of such dimensions that the velocity and temperature fields repeat themselves in successive enclosures. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for fully elliptic three-dimensional flows. The calculations are performed for the Rayleigh number in the range of 103 to 105, for a Prandtl number of 0.7, and for five values of the aspect ratio of the honeycomb enclosure. The average Nusselt number results for the case of a thin honeycomb core are compared with the previously obtained results for a thick honeycomb core with conduction and adiabatic side wall boundary conditions.

Optimum Plate Spacings for Laminar Natural Convection Heat Transfer From Parallel Vertical Isothermal Flat Plates

1971 ◽  
Vol 93 (4) ◽  
pp. 463-465 ◽  
Author(s):  
E. K. Levy
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Difference ◽  
Maximum Rate ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Flat Plates ◽  
Plate Spacing ◽  
Laminar Natural Convection

The problem of determining the optimum spacings between parallel vertical isothermal flat plates which are dissipating heat by natural convection to the environment is discussed. One optimum, first suggested by experimental data of Elenbaas with air and later derived theoretically by Bodoia, corresponds to the spacing between parallel vertical plates attached to a surface which will permit the maximum rate of heat transfer from that surface. A different optimum is derived in this paper which for a given heat flux gives the minimum plate spacing required to minimize the temperature difference between the plates and the fluid. The minimum temperature difference is shown to occur when the plate spacing is made sufficiently large that the wall boundary layers do not merge. It is shown that Elenbaas’ optimum, although requiring a plate spacing only 54 percent of that for minimum ΔT, produces a temperature difference which is 38 percent higher than the minimum.

The Effects of Side-Wall Conduction on Natural Convection in a Slot

1987 ◽  
Vol 109 (2) ◽  
pp. 419-426 ◽  
Author(s):  
G. D. Mallinson
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Radiation Effects ◽  
Three Dimensional ◽  
Side Wall ◽  
Thermal Coupling ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
High Prandtl Number ◽  
Side Walls

A numerical model for the interaction between natural convection in a slot and conduction in the side walls that are parallel to the plane of the slot is described. Two-dimensional equations containing source terms which account for the viscous and thermal coupling between the fluid and the walls are solved by a finite difference method. The model neglects radiation effects. Solutions for a slot of square cross section filled with a high Prandtl number fluid and heated from below are compared with the results of a Galerkin analysis made by Frick [8] and with solutions obtained by a fully three-dimensional model. Solutions for a slot filled with air and heated from the side are also validated by comparison with three-dimensional solutions. The data produced by the model predict that the more conventional Hele Shaw analysis overestimates heat transfer when the slot aspect ratio is greater than 0.05. Perfectly conducting walls are shown to reduce the rate of heat transfer by the fluid but to increase the strength of the flow. Some effects of walls that are neither adiabatic nor perfectly conducting are assessed.

Sign in / Sign up

Export Citation Format

Share Document