scholarly journals Horizontal convection in a rectangular enclosure driven by a linear temperature profile

2021 ◽  
Author(s):  
Tianyong Yang ◽  
Bofu Wang ◽  
Jianzhao Wu ◽  
Zhiming Lu ◽  
Quan Zhou
Keyword(s):  
Rayleigh Number ◽  
Temperature Profile ◽  
Scaling Law ◽  
Thermal Plume ◽  
Steady Regime ◽  
Linear Temperature ◽  
Square Enclosure ◽  
Horizontal Convection ◽  
Kinetic Boundary Layer ◽  
The Mean

AbstractThe horizontal convection in a square enclosure driven by a linear temperature profile along the bottom boundary is investigated numerically by using a finite difference method. The Prandtl number is fixed at 4.38, and the Rayleigh number Ra ranges from 107 to 1011. The convective flow is steady at a relatively low Rayleigh number, and no thermal plume is observed, whereas it transits to be unsteady when the Rayleigh number increases beyond the critical value. The scaling law for the Nusselt number Nu changes from Rossby’s scaling Nu ∼ Ra1/5 in a steady regime to Nu ∼ Ra1/4 in an unsteady regime, which agrees well with the theoretically predicted results. Accordingly, the Reynolds number Re scaling varies from Re ∼ Ra3/11 to Re ∼ Ra2/5. The investigation on the mean flows shows that the thermal and kinetic boundary layer thickness and the mean temperature in the bulk zone decrease with the increasing Ra. The intensity of fluctuating velocity increases with the increasing Ra.

scholarly journals Very viscous horizontal convection

2008 ◽  
Vol 611 ◽  
pp. 395-426 ◽  
Author(s):  
S. CHIU-WEBSTER ◽  
E. J. HINCH ◽  
J. R. LISTER
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Initial Conditions ◽  
Analytic Solutions ◽  
Rectangular Domain ◽  
Return Flow ◽  
Linear Temperature ◽  
Linear Temperature Gradient ◽  
Horizontal Convection

‘Horizontal convection’ arises when a temperature variation is imposed along a horizontal boundary of a finite fluid volume. Here we study the infinite-Prandtl-number limit relevant to very viscous fluids, motivated by the study of convection in glass furnaces. We consider a rectangular domain with insulating conditions on the sides and bottom, and a linear temperature gradient on the top. We describe steady states for a large range of aspect ratio A and Rayleigh number Ra, and find universal scalings for the transition from small to large Rayleigh numbers. At large Rayleigh number, the top boundary-layer thickness scales as Ra−1/5, with the circulation and heat flux scaling as Ra1/5. These scalings hold for both rigid and shear-free boundary conditions on the top or on the other boundaries, which is initially surprising, but is because the return flow is dominated by a horizontal intrusion immediately beneath the top boundary layer. A downwelling plume also forms on one side, but because of strong stratification in the interior, the volume flux it carries is much smaller than that of the horizontal intrusion, decaying as the inverse of the depth below the top boundary. The fluid in the plume detrains into the interior and then returns to the top boundary, thus forming a ‘filling box’. We find analytic solutions for the interior temperature and streamfunction and match them to a similarity solution for the plume. At depths comparable to the length of the top boundary the streamfunction has O(1) values and the temperature variations scale as 1/Ra. Transient calculations with a large, but finite, Prandtl number, show how the steady state is reached from hot and cold initial conditions.

Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile

1964 ◽  
Vol 18 (4) ◽  
pp. 513-528 ◽  
Author(s):  
E. M. Sparrow ◽  
R. J. Goldstein ◽  
V. K. Jonsson
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
Fluid Layer ◽  
Bounding Surface ◽  
Fixed Temperature ◽  
Linear Temperature ◽  
Lower Bounding ◽  
Horizontal Fluid Layer

An investigation is carried out to determine the conditions marking the onset of convective motion in a horizontal fluid layer in which a negative temperature gradient occurs somewhere within the layer. In such cases, fluid of greater density is situated above fluid of lesser density. Consideration is given to a variety of thermal and hydrodynamic boundary conditions at the surfaces which bound the fluid layer. The thermal conditions include fixed temperature and fixed heat flux at the lower bounding surface, and a general convective-radiative exchange at the upper surface which includes fixed temperature and fixed heat flux as special cases. The hydrodynamic boundary conditions include both rigid and free upper surfaces with a rigid lower bounding surface. It is found that the Rayleigh number marking the onset of motion is greatest for the boundary condition of fixed temperature and decreases monotonically as the condition of fixed heat flux is approached. Non-linear temperature distributions in the fluid layer may result from internal heat generation. With increasing departures from the linear temperature profile, it is found that the fluid layer becomes more prone to instability, that is, the critical Rayleigh number decreases.

Effect of obstacle height on the nanofluid convection patterns inside a hollow square enclosure

2021 ◽  
pp. 2250026
Author(s):  
Rasul Mohebbi ◽  
Mohsen Babamir ◽  
Mohammad Mahdi Amooei ◽  
Yuan Ma
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Volume Fraction ◽  
Critical Rayleigh Number ◽  
Hybrid Nanofluid ◽  
Thermal Plume ◽  
Square Enclosure ◽  
Secondary Vortices ◽  
Obstacle Height

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large ([Formula: see text] or 0.4), at low Rayleigh number (103), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (106). However, at [Formula: see text], these secondary vortices occur again in the middle two vortices at [Formula: see text], which is similar to that at [Formula: see text]. At [Formula: see text], the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 104. However, the critical Rayleigh number becomes 105 at [Formula: see text] or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at [Formula: see text], for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio.

scholarly journals Lattice Boltzmann Simulation of Natural Convection in an Annulus between a Hexagonal Cylinder and a Square Enclosure

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
L. El Moutaouakil ◽  
Z. Zrikem ◽  
A. Abdelbaki
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Square Enclosure ◽  
Lattice Boltzmann Simulation ◽  
Laminar Natural Convection ◽  
Heat Transfers ◽  
Boltzmann Method ◽  
Vertical Case

Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

scholarly journals Effect of Rayleigh Number on Internal Eccentricity in a Heated Horizontal Elliptical Cylinder to its Coaxial Square Enclosure

2020 ◽  
Vol 25 (3) ◽  
pp. 17-29
Author(s):  
Abdelkrim Bouras ◽  
Djedid Taloub ◽  
Zied Driss
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Commercial Code ◽  
Volume Method ◽  
Rayleigh Numbers

AbstractThis paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure’s sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

scholarly journals Bounds for convection between rough boundaries

2016 ◽  
Vol 804 ◽  
pp. 370-386 ◽  
Author(s):  
David Goluskin ◽  
Charles R. Doering
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Temperature Difference ◽  
Upper Bound ◽  
Bottom Boundary ◽  
Leading Term ◽  
The Mean ◽  
Rough Boundaries ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We consider Rayleigh–Bénard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background method to derive an upper bound on the mean heat flux across the layer for all admissible boundary geometries. This flux, normalized by the temperature difference between the boundaries, can grow with the Rayleigh number ($Ra$) no faster than $O(Ra^{1/2})$ as $Ra\rightarrow \infty$. Our analysis yields a family of similar bounds, depending on how various estimates are tuned, but every version depends explicitly on the boundary geometry. In one version the coefficient of the $O(Ra^{1/2})$ leading term is $0.242+2.925\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$, where $\Vert \unicode[STIX]{x1D735}h\Vert ^{2}$ is the mean squared magnitude of the boundary height gradients. Application to a particular geometry is illustrated for sinusoidal boundaries.

scholarly journals The Formation of Drainage Wind on a Snow-Dome

1965 ◽  
Vol 5 (42) ◽  
pp. 833-841 ◽  
Author(s):  
J.A. Businger ◽  
K. Ramana Rao
Keyword(s):  
Heat Flux ◽  
Temperature Profile ◽  
Energy Budget ◽  
Air Flow ◽  
Sensible Heat Flux ◽  
Wind Component ◽  
Sensible Heat ◽  
Snow Surface ◽  
Direct Measurements ◽  
The Mean

Abstract Direct measurements of the horizontal divergence of the air flow close to the snow surface have been made. The mean vertical wind component has been derived from these observations. The temperature profile has been analyzed near the center of the snow-dome and a method to determine the sensible heat flux independent from the energy budget has been developed.

scholarly journals Thermal Consequences of the Pressure Fluctuations in Intra- and Subglacial Water Drainage Channels

1976 ◽  
Vol 16 (74) ◽  
pp. 309-310 ◽  
Author(s):  
H. Röthlisberger
Keyword(s):  
Stress Field ◽  
Water Content ◽  
Temperature Profile ◽  
Interstitial Water ◽  
Water Pressure ◽  
Pressure Fluctuations ◽  
Water Film ◽  
Ice Flow ◽  
Drainage Channels ◽  
The Mean

Abstract Recent measurements of the water level (pressure head) in drill holes and natural moulins on two glacier tongues in Switzerland (Oberaletschgletscher and Gornergletscher) have confirmed that in those holes which link up to a well developed subglacial drainage system the daily piezometric fluctuations are in the order of 100 m (10 bar) and more. From the fact that it is relatively easy to establish such links (in our experiments at ice depths between 150 and 300 m), it is implied that an extended network of subglacial channels and cavities will be subjected to equally large pressure fluctuations with a mean water pressure considerably below the mean ice pressure at the bed. The scope of the present paper is to discuss some of the thermal effects of the low water pressure and its fluctuations. The effect in the ice—assuming temperate ice with a certain water content—is a positive temperature anomaly around the channel, in accordance with the stress field. The radial temperature profile in the ice around a conduit with a circular cross-section follow's directly from the solution for the stress field, and the heat flux can be deduced, allowing for the ice flow towards the conduit. Pressure changes in the conduit cause a rapid change of temperature (with an associated change in water content) and a related change in heat and ice flow. In the case of a channel or cavity at the glacier bed, the temperature fluctuation produced in the channel and the surrounding ice propagates into the substratum. With rising water pressure, i.e. falling temperature, the substratum becomes a heat source and some melting will occur at the ice/rock interface in a fringe zone around channels and cavities. It is this process which may help to explain the increased sliding component of glacier motion at the time of high melt-water run-off. Another intriguing question is what happens in a highly permeable substratum (shattered rock, moraine) at some distance away from a channel. The temperature profile is determined by the pressure melting point within the glacier down to the bed, and the positive geothermal gradient with increasing depth in the substratum below. The water pressure in the substratum is approximately equal to that in the channel, that is to say well below the mean pressure at the glacier bed. There is therefore an uppermost layer of the substratum at a temperature below the freezing temperature of the interstitial water, implying that the water must be frozen in this layer. This is one way to look at the problem. Starting out from the impermeable frozen layer it may be argued that the water film at the glacier bed is at a high pressure and the interstitial ice should melt until the water breaks through at the lower freezing boundary. This could only happen where and as long as there is no appreciable drainage of the water film and interstitial water. As soon as the water breaks through, the pressure will drop and presumably just enough leakage will be sustained to lead to a pressure drop across the frozen layer in accordance with the temperature profile. A generally impermeable glacier bed results as a most likely model, with permeable bands along subglacial drainage channels and eventual leakage holes in between. Taking the pressure fluctuations into account, one finds that temperature fluctuations have to be expected originating at the lower boundary of the frozen substratum, involving frost cycles. The erosive effectiveness of these will however be limited to the equivalent of the pressure cycles. (A double pressure amplitude of 130 m of water head corresponds roughly to a double temperature amplitude of 0.1 deg.)

scholarly journals 2.5D retrieval of atmospheric properties from exoplanet phase curves: application to WASP-43b observations

2020 ◽  
Vol 493 (1) ◽  
pp. 106-125 ◽  
Author(s):  
Patrick G J Irwin ◽  
Vivien Parmentier ◽  
Jake Taylor ◽  
Jo Barstow ◽  
Suzanne Aigrain ◽  
...  
Keyword(s):  
Temperature Profile ◽  
Water Vapour ◽  
Mole Fraction ◽  
Phase Curve ◽  
Vertical Temperature ◽  
Vertical Temperature Profile ◽  
Retrieval Technique ◽  
The Mean ◽  
Synthetic Phase ◽  
Model Phase

ABSTRACT We present a novel retrieval technique that attempts to model phase curve observations of exoplanets more realistically and reliably, which we call the 2.5-dimensional (2.5D) approach. In our 2.5D approach we retrieve the vertical temperature profile and mean gaseous abundance of a planet at all longitudes and latitudes simultaneously, assuming that the temperature or composition, x, at a particular longitude and latitude (Λ, Φ) is given by $x(\Lambda ,\Phi) = \bar{x} + (x(\Lambda ,0) - \bar{x})\cos ^n\Phi$, where $\bar{x}$ is the mean of the morning and evening terminator values of x(Λ, 0), and n is an assumed coefficient. We compare our new 2.5D scheme with the more traditional 1D approach, which assumes the same temperature profile and gaseous abundances at all points on the visible disc of a planet for each individual phase observation, using a set of synthetic phase curves generated from a GCM-based simulation. We find that our 2.5D model fits these data more realistically than the 1D approach, confining the hotter regions of the planet more closely to the dayside. We then apply both models to WASP-43b phase curve observations of HST/WFC3 and Spitzer/IRAC. We find that the dayside of WASP-43b is apparently much hotter than the nightside and show that this could be explained by the presence of a thick cloud on the nightside with a cloud top at pressure <0.2 bar. We further show that while the mole fraction of water vapour is reasonably well constrained to (1–10) × 10−4, the abundance of CO is very difficult to constrain with these data since it is degenerate with temperature and prone to possible systematic radiometric differences between the HST/WFC3 and Spitzer/IRAC observations. Hence, it is difficult to reliably constrain C/O.

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