Laminar Natural Convection under Nonuniform Gravity

1972 ◽  
Vol 94 (1) ◽  
pp. 80-86 ◽  
Author(s):  
J. Lienhard ◽  
R. Eichhorn ◽  
V. Dhir
Keyword(s):  
Natural Convection ◽  
Solution Method ◽  
Leading Edge ◽  
General Integral ◽  
Special Cases ◽  
Method Of Solution ◽  
Arbitrary Position ◽  
Laminar Natural Convection ◽  
Position Dependence ◽  
Integral Solutions

Laminar natural convection is analyzed for cases in which gravity varies with the distance from the leading edge of an isothermal plate. The study includes situations in which gravity varies by virtue of the varying slope of a surface. A general integral solution method which includes certain known integral solutions as special cases is developed to account for arbitrary position-dependence of gravity. A series method of solution is also developed for the full equations. Although it is more cumbersome it provides verification of the integral method.

A theoretical investigation of disturbance amplification in external laminar natural convection

1968 ◽  
Vol 34 (3) ◽  
pp. 551-564 ◽  
Author(s):  
R. P. Dring ◽  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Amplitude Ratio ◽  
Low Frequency ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Uniform Heat Flux ◽  
Laminar Natural Convection ◽  
Sommerfeld Equation

The nature of instability and disturbance amplification in the laminar natural convection boundary layer over a vertical flat surface with uniform heat flux has been theoretically investigated. The coupled Orr-Sommerfeld equation has been numerically integrated for a Prandtl number of 6·7, with the boundary condition that the disturbance heat flux be zero at the surface. The spatial amplification characteristics of disturbances convected downstream were analyzed, and constant amplification rate contours were determined. The relative amplification has been calculated from these contours and is presented in the form of amplitude ratio contours. An important feature of these results is that the low frequency disturbances, which become unstable first, amplify very slowly and also have wavelengths which are much longer than the distance to the leading edge. The higher frequency, shorter wavelength, disturbances amplify much faster and are, therefore, presumed to be the dominant ones in stability considerations. The nature of the velocity and temperature amplitudes and phase profiles across the boundary layer has also been examined.

Laminar natural convection about corrugated surfaces

1981 ◽  
Vol 122 ◽  
pp. 53-66 ◽  
Author(s):  
H. Abdurrachim ◽  
F. Karouta ◽  
M. Daguenet ◽  
P. Dumargue
Keyword(s):  
Natural Convection ◽  
Corrugated Surfaces ◽  
Laminar Natural Convection

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

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