Rayleigh-Bénard Convection with Experimental Boundary Conditions

2003 ◽  
pp. 189-195
Author(s):  
Joana Prat ◽  
Isabel Mercader ◽  
Edgar Knobloch
Keyword(s):  
Boundary Conditions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

scholarly journals Mixed insulating and conducting thermal boundary conditions in Rayleigh–Bénard convection

2017 ◽  
Vol 835 ◽  
pp. 491-511 ◽  
Author(s):  
Dennis Bakhuis ◽  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Transport ◽  
Bottom Plate ◽  
Bulk Temperature ◽  
Stripe Pattern ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

A series of direct numerical simulations of Rayleigh–Bénard convection, the flow in a fluid layer heated from below and cooled from above, were conducted to investigate the effect of mixed insulating and conducting boundary conditions on convective flows. Rayleigh numbers between $Ra=10^{7}$ and $Ra=10^{9}$ were considered, for Prandtl numbers $\mathit{Pr}=1$ and $\mathit{Pr}=10$. The bottom plate was divided into patterns of conducting and insulating stripes. The size ratio between these stripes was fixed to unity and the total number of stripes was varied. Global quantities, such as the heat transport and average bulk temperature, and local quantities, such as the temperature just below the insulating boundary wall, were investigated. For the case with the top boundary divided into two halves, one conducting and one insulating, the heat transfer was found to be approximately two-thirds of that for the fully conducting case. Increasing the pattern frequency increased the heat transfer, which asymptotically approached the fully conducting case, even if only half of the surface is conducting. Fourier analysis of the temperature field revealed that the imprinted pattern of the plates is diffused in the thermal boundary layers, and cannot be detected in the bulk. With conducting–insulating patterns on both plates, the trends previously described were similar; however, the half-and-half division led to a heat transfer of about a half of that for the fully conducting case instead of two-thirds. The effect of the ratio of conducting and insulating areas was also analysed, and it was found that, even for systems with a top plate with only 25 % conducting surface, heat transport of 60 % of the fully conducting case can be seen. Changing the one-dimensional stripe pattern to a two-dimensional chequerboard tessellation does not result in a significantly different response of the system.

scholarly journals Mixed thermal conditions in convection: how do continents affect the mantle’s circulation?

2017 ◽  
Vol 822 ◽  
pp. 1-4 ◽  
Author(s):  
R. Ostilla-Mónico
Keyword(s):  
Boundary Conditions ◽  
Plate Tectonics ◽  
Large Scale ◽  
Thermal Conditions ◽  
Experimental Proof ◽  
Bénard Convection ◽  
Benard Convection ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh–Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh–Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic–conducting boundary conditions on turbulent Rayleigh–Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

scholarly journals Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection

1992 ◽  
Vol 241 ◽  
pp. 549-585 ◽  
Author(s):  
Yih-Yuh Chen
Keyword(s):  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
System Size ◽  
Perturbative Approach ◽  
Bénard Convection ◽  
Reaction Diffusion Model ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Finite Cell

The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.

scholarly journals Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli

2019 ◽  
Vol 29 (1) ◽  
pp. 251-279 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Bingham Fluids ◽  
Bingham Model ◽  
Content Type ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Mean ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Purpose This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition. Design/methodology/approach The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions. Originality value Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ ri/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 104 ≤ Ra ≤ 105 for the CWHF configuration.

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