Erratum: “Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below” (Journal of Heat Transfer, 1976, 98, pp. 202–207)

1976 ◽  
Vol 98 (3) ◽  
pp. 519-519 ◽  
Author(s):  
H. Ozoe ◽  
K. Yamamoto ◽  
S. W. Churchill ◽  
H. Sayama
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Three Dimensional ◽  
Confined Fluid ◽  
Laminar Natural Convection

Numerical analysis of laminar natural convection in isosceles triangular enclosures

2009 ◽  
Vol 223 (5) ◽  
pp. 1157-1169 ◽  
Author(s):  
E F Kent
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Rayleigh Number ◽  
Flow Field ◽  
Water Heaters ◽  
Thermal Boundary Conditions ◽  
Laminar Natural Convection ◽  
Solar Water Heaters ◽  
Rayleigh Numbers

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures

1970 ◽  
Vol 92 (1) ◽  
pp. 159-167 ◽  
Author(s):  
M. E. Newell ◽  
F. W. Schmidt
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Grashof Number ◽  
Different Temperatures ◽  
Laminar Natural Convection ◽  
Steady State Solutions

Two-dimensional laminar natural convection in air contained in a long horizontal rectangular enclosure with isothermal walls at different temperatures has been investigated using numerical techniques. The time-dependent governing differential equations were solved using a method based on that of Crank and Nicholson. Steady-state solutions were obtained for height to width ratios of 1, 2.5, 10, and 20, and for values of the Grashof number, GrL′, covering the range 4 × 103 to 1.4 × 105. The bounds on the Grashof number for H/L = 20 is 8 × 103 ≤ GrL′ ≤ 4 × 104. The results were correlated with a three-dimensional power law which, yielded H/L=1Nu¯L′=0.0547(GrL′)0.3972.5≤H/L≤20Nu¯L′=0.155(GrL′)0.315(H/L)−0.265 The results compare favorably with available experimental results.

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.

Sign in / Sign up

Export Citation Format

Share Document