scholarly journals Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions

2009 ◽  
Vol 21 (8) ◽  
pp. 083603 ◽  
Author(s):  
Gregory P. Chini ◽  
Stephen M. Cox
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Thermal Convection ◽  
Convection Heat ◽  
Strongly Nonlinear ◽  
Nonlinear Solutions ◽  
Large Rayleigh Number

Boundary-layer solutions of single-mode convection equations

1981 ◽  
Vol 102 ◽  
pp. 211-219 ◽  
Author(s):  
N. Riahi
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Single Mode ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Inertial Terms ◽  
Large Rayleigh Number

Nonlinear thermal convection between two stress-free horizontal boundaries is studied using the modal equations for cellular convection. Assuming a large Rayleigh number R the boundary-layer method is used for different ranges of the Prandtl number σ. The heat flux F is determined for the values of the horizontal wavenumber a which maximizes F. For a large Prandtl number, σ [Gt ] R⅙(log R)−1, inertial terms are insignificant, a is either of order one (for $\sigma \geqslant R^{\frac{2}{3}}$) or proportional to $R^{\frac{1}{3}}\sigma^{-\frac{1}{2}}$ (for $\sigma \ll R^{\frac{2}{3}}$) and F is proportional to $R^{\frac{1}{3}}$. For a moderate Prandtl number, \[ (R^{-1}\log R)^{\frac{1}{9}} \ll \sigma \ll R^{\frac{1}{6}}(\log R)^{-1}, \] inertial terms first become significant in an inertial layer adjacent to the viscous buoyancy-dominated interior, and a and F are proportional to R¼ and \[ R^{\frac{3}{10}}\sigma^{\frac{1}{5}} (\log\sigma R^{\frac{1}{4}})^{\frac{1}{10}}, \] respectively. For a small Prandtl number, $R^{-1} \ll \sigma \ll (R^{-1} \log R)^{\frac{1}{9}}$, inertial terms are significant both in the interior and the boundary layers, and a and F are proportional to ($R \sigma)^{\frac{9}{32}} (\log R\sigma)^{-\frac{1}{32}}$ and ($R \sigma)^{\frac{5}{16}} (\log R \sigma)^{\frac{3}{16}}$, respectively.

Natural Convection Heat Transfer of Concentric/Eccentric Annulus Subjected to Inner Tube of Constant Heat Flux

2011 ◽  
Author(s):  
R. Hosseini ◽  
M. Alipour ◽  
A. Gholaminejad
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Surface Temperature ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Eccentric Annulus

This paper describes the experimental results of natural convection heat transfer from vertical, electrically heated cylinder in a concentric/eccentric annulus and develops correlations for the dependence of the average annulus Nusselt number upon the Rayleigh number. Wall surface temperature have been recorded for diameter ratio of d/D = 0.4, with the apparatus immersed in stagnant air with uniform temperature. Measurements have been carried out for eccentric ratios of E = 0, 0.19, 0.34, 0.62 and 0.89 in the range of heat flux of 45 to 430 W/m2. The surface temperature of the heater was found to increase upwards and reach a maximum at some position, beyond which it decreases again. It is observed, that this maximum temperature occurs near h/l = 0.8 for 0 ≤ E ≤ 0.62 at almost all power levels, but shifts downwards for E = 0.89. Moreover, empirical correlations between the average Nusselt number and the Rayleigh number are derived for concentric and eccentric annuli.

scholarly journals Free Convection Heat Transfer from Horizontal Cylinders

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 559
Author(s):  
Janusz T. Cieśliński ◽  
Slawomir Smolen ◽  
Dorota Sawicka
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Correlation Equations ◽  
Convection Heat ◽  
Number Range ◽  
Heated Cylinder ◽  
Free Convection Heat

The results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations that jointly describe the dependence of the average Nusselt number on Rayleigh number and confinement ratios were examined. As a heat source served electrically heated horizontal tube immersed in an ambient fluid. Experiments were performed with pure ethylene glycol (EG), distilled water (W), and a mixture of EG and water at 50%/50% by volume. A set of empirical correlation equations for the prediction of Nu numbers for Rayleigh number range 3.6 × 104 < Ra < 9.2 × 105 or 3.6 × 105 < Raq < 14.8 × 106 and Pr number range 4.5 ≤ Pr ≤ 160 has been developed. The proposed correlation equations are based on two characteristic lengths, i.e., cylinder diameter and boundary layer length.

Linear stability of rotating convection in an imposed shear flow

1997 ◽  
Vol 350 ◽  
pp. 271-293 ◽  
Author(s):  
PAUL MATTHEWS ◽  
STEPHEN COX
Keyword(s):  
Rayleigh Number ◽  
Shear Flow ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Thermal Convection ◽  
Critical Rayleigh Number ◽  
Rotation Vector ◽  
Linear Stability Theory ◽  
Fixed Temperature ◽  
Differential Motion

In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.

Numerical Study of Deteriorated Convection Heat Transfer of Supercritical Fluid Flowing Through Vertical Mini Tube at Relatively Low Reynolds Numbers

2018 ◽  
Author(s):  
Chen-Ru Zhao ◽  
Zhen Zhang ◽  
Qian-Feng Liu ◽  
Han-Liang Bo ◽  
Pei-Xue Jiang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Convection Heat Transfer ◽  
Turbulence Models ◽  
Convection Heat ◽  
Flow Acceleration ◽  
Heat Transfer Deterioration ◽  
Low Reynolds

Numerical investigations are performed on the convection heat transfer of supercritical pressure fluid flowing through vertical mini tube with inner diameter of 0.27 mm and inlet Reynolds number of 1900 under various heat fluxes conditions using low Reynolds number k-ε turbulence models due to LB (Lam and Bremhorst), LS (Launder and Sharma) and V2F (v2-f). The predictions are compared with the corresponding experimentally measured values. The prediction ability of various low Reynolds number k-ε turbulence models under deteriorated heat transfer conditions induced by combinations of buoyancy and flow acceleration effects are evaluated. Results show that all the three models give fairly good predictions of local wall temperature variations in conditions with relatively high inlet Reynolds number. For cases with relatively low inlet Reynolds number, V2F model is able to capture the general trends of deteriorated heat transfer when the heat flux is relatively low. However, the LS and V2F models exaggerate the flow acceleration effect when the heat flux increases, while the LB model produces qualitative predictions, but further improvements are still needed for quantitative prediction. Based on the detailed flow and heat transfer information generated by simulation, a better understanding of the mechanism of heat transfer deterioration is obtained. Results show that the redistribution of flow field induced by the buoyancy and flow acceleration effects are main factors leading to the heat transfer deterioration.

Heat flux enhancement by regular surface roughness in turbulent thermal convection

2014 ◽  
Vol 763 ◽  
pp. 109-135 ◽  
Author(s):  
Sebastian Wagner ◽  
Olga Shishkina
Keyword(s):  
Heat Flux ◽  
Surface Roughness ◽  
Thermal Convection ◽  
Large Scale ◽  
Secondary Flows ◽  
Scaling Exponent ◽  
Wall Roughness ◽  
Regular Surface ◽  
Large Scale Circulation ◽  
Flux Enhancement

AbstractDirect numerical simulations (DNS) of turbulent thermal convection in a box-shaped domain with regular surface roughness at the heated bottom and cooled top surfaces are conducted for Prandtl number $\mathit{Pr}=0.786$ and Rayleigh numbers $\mathit{Ra}$ between $10^{6}$ and $10^{8}$. The surface roughness is introduced by four parallelepiped equidistantly distributed obstacles attached to the bottom plate, and four obstacles located symmetrically at the top plate. By varying $\mathit{Ra}$ and the height and width of the obstacles, we investigate the influence of the regular wall roughness on the turbulent heat transport, measured by the Nusselt number $\mathit{Nu}$. For fixed $\mathit{Ra}$, the change in the value of $\mathit{Nu}$ is determined not only by the covering area of the surface, i.e. the obstacle height, but also by the distance between the obstacles. The heat flux enhancement is found to be largest for wide cavities between the obstacles which can be ‘washed out’ by the flow. This is also manifested in an empirical relation, which is based on the DNS data. We further discuss theoretical limiting cases for very wide and very narrow obstacles and combine them into a simple model for the heat flux enhancement due to the wall roughness, without introducing any free parameters. This model predicts well the general trends and the order of magnitude of the heat flux enhancement obtained in the DNS. In the $\mathit{Nu}$ versus $\mathit{Ra}$ scaling, the obstacles work in two ways: for smaller $\mathit{Ra}$ an increase of the scaling exponent compared to the smooth case is found, which is connected to the heat flux entering the cavities from below. For larger $\mathit{Ra}$ the scaling exponent saturates to the one for smooth plates, which can be understood as a full washing-out of the cavities. The latter is also investigated by considering the strength of the mean secondary flow in the cavities and its relation to the wind (i.e. the large-scale circulation), that develops in the core part of the domain. Generally, an increase in the roughness height leads to stronger flows both in the cavities and in the bulk region, while an increase in the width of the obstacles strengthens only the large-scale circulation of the fluid and weakens the secondary flows. An increase of the Rayleigh number always leads to stronger flows, both in the cavities and in the bulk.

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