Onset of Convection in Liquids Subjected to Transient Heating from Below

1959 ◽  
Vol 2 (2) ◽  
pp. 131 ◽  
Author(s):  
Robert K. Soberman
Keyword(s):  
Transient Heating ◽  
Onset Of Convection ◽  
Heating From Below

Onset of Thermal Convection in a Fluid Layer Subjected to Transient Heating From Below

1984 ◽  
Vol 106 (4) ◽  
pp. 817-823 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Fluid Layer ◽  
Sudden Change ◽  
Onset Time ◽  
Lower Surface ◽  
Analytical Prediction ◽  
Rigid Boundary ◽  
Transient Heating ◽  
Onset Of Convection ◽  
Analytical Results ◽  
Heating From Below

The onset of convection in a horizontal layer of fluid subject to time-dependent heating from below is studied both experimentally and analytically. The fluid layer is confined by a rigid boundary at the bottom and a shear-free surface at the top. The fluid, which is initially quiescent, is heated by increasing the temperature of the lower surface at a constant time-rate. The experimental observation of the time of the onset of convection is made through the sudden change in variation of the temperature of the lower surface with respect to time. The onset is also observed through the sudden change in the fringe pattern created by holographic interferometry. Various layer depths are considered in order to observe the influence of this variable on the onset time. The analytical prediction is made by application of the linear amplification theory subject to boundary conditions similar to those of the experiment. Good agreement is found between the experimental and analytical results. Comparisons are also made with the experimental and analytical results available in the literature.

The Onset of Convection in an Internally Heated Nanofluid Layer

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Brownian Motion ◽  
Boundary Conditions ◽  
Microwave Heating ◽  
Chemical Reaction ◽  
Vertical Gradient ◽  
Horizontal Layer ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Brownian Motion And Thermophoresis ◽  
Heating From Below

We analytically studied the onset of convection, induced by internal heating, such as that produced by microwave heating or chemical reaction, in a horizontal layer of a nanofluid subject to Brownian motion and thermophoresis. This is a fundamentally different situation from traditionally studied heating from below. Convection, when it occurs, is now concentrated in the portion of the layer where the upward vertical gradient is negative, which is the upper portion of the layer. The situation of internal heating also allows employing more realistic boundary conditions than those hitherto used.

Onset and Development of Natural Convection Above a Suddenly Heated Horizontal Surface

1995 ◽  
Vol 117 (4) ◽  
pp. 808-821 ◽  
Author(s):  
R. J. Goldstein ◽  
R. J. Volino
Keyword(s):  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Fluid Motion ◽  
Horizontal Layer ◽  
Onset Of Convection ◽  
Surface Convection ◽  
Heating From Below ◽  
Conduction Layer ◽  
Moving Pattern

The onset and development of flow in a thick horizontal layer subject to a near-constant flux heating from below has been studied experimentally. The overall heat-flux-based Rayleigh number, Ra*, ranges from 2 × 108 to 7 × 1010. Flow visualization shows the growth and breakdown of a conduction layer adjacent to the heated surface. Convection is characterized by the release of warm meandering plumes and thermals from a boundary layer. The planform of convection at the heated surface begins with a pattern of small spots suggestive of Be´nard cells. Some of these cells expand, forming a larger cell pattern. This continues until a quasi-steady state is reached in which the former cell boundaries form a slowly moving pattern of warm lines on the heated surface. The lines are believed to be the source of the plumes and thermals. Quantitatively, the onset of convection occurs at a constant (critical) Rayleigh number based on the conduction layer thickness, Raδ. Based on the first observation of fluid motion, this critical Rayleigh number is approximately 1300. Based on the heated surface temperature the critical Rayleigh number is 2700. The nondimensional wavenumber associated with the observed instabilities at the onset of convection is about 2.2.

Convective Heat Transfer in a Liquid Saturated Porous Layer

1976 ◽  
Vol 43 (2) ◽  
pp. 249-253 ◽  
Author(s):  
R. J. Buretta ◽  
A. S. Berman
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Upper Bound ◽  
Heat Sources ◽  
Onset Of Convection ◽  
Saturated Porous Layer ◽  
Rayleigh Numbers ◽  
Heating From Below ◽  
Good Agreement

The convective heat transfer in fluid saturated porous beds either heated from below or heated by distributed sources is investigated for several bed thicknesses and permeabilities. For the case of heating from below Rayleigh numbers range from about 10–10,000. For distributed heat sources Rayleigh numbers range from about 10–1000. Critical Rayleigh numbers for the onset of convection are estimated as 38 for heating from below and 31.8 for distributed heat sources. Heat transfer results for convection induced by heating from below are in good agreement with analytical upper bound estimates obtained by Gupta and Joseph.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

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