scholarly journals Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh-Bénard convection

2015 ◽  
Vol 7 (0) ◽  
Author(s):  
I. C. Ramos ◽  
Carlos B. Briozzo
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Pseudospectral Method ◽  
Dirichlet Boundary Conditions ◽  
Fourier Pseudospectral Method ◽  
Bénard Convection ◽  
Benard Convection ◽  
Fourier Pseudospectral ◽  
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.

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