Scaling behavior for the onset of convection in a colloidal suspension

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=delta*/d scales as Ra-ps, where Ras=Rasdelta is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p=0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.     

Universality in crossover function for convection in fluids with a free surface

We show that in the onset of convection in a thin fluid layer with a free surface, the passage from surface tension driven to buoyancy driven convection with changing thickness of the fluid layer follows a universal curve and can be calculated very accurately using a variational method. We have shown that the balance between surface tension traction to buoyancy force determines the crossover length scale of the fluid which is independent of viscosity or thermal diffusivity. We suggest a scenario near critical point of fluids in which this crossover can be observed.     

Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection

We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from 2x10(7) to 3x10(10), all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about 20% over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.     

A fractal model for heat transfer of nanofluids by convection in a pool

Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.     

Combined action of different mechanisms of convective instability in multilayer systems

The nonlinear regimes of convection in a system of three immiscible viscous fluids are investigated by the finite-difference method. We study new phenomena caused by direct and indirect interaction of thermocapillary and buoyancy (Rayleigh and anticonvective) instability mechanisms. Two variants of heating-from below and from above-are considered. The interfaces are assumed to be flat. We focus on nonlinear evolution of steady and oscillatory motions and selection of stable convective structures depending on the parameters of systems. The influence of the lateral boundary conditions is also investigated. A classification of different variants of interaction between Rayleigh and thermocapillary instability mechanisms is presented, and several typical examples are studied. Specifically, we considered six different configurations where the Rayleigh convection arises mainly in a definite layer, and the thermocapillary convection appears mainly near the definite interface. Also, the case where both interfaces are active and alternatively play a dominant role is investigated. Some configurations of interaction between anticonvective and thermocapillary instability mechanisms are considered.     

Free thermal convection in complex plasma with background-gas friction

The onset of free thermal convection in complex fluids with background friction is theoretically investigated. It is shown that in the limit when friction prevails--opposite to the classic Rayleigh-Bénard case--the onset is determined by a renormalized Rayleigh number and also depends on the Prandtl number. Such convection should be observable in experiments with complex plasmas.     

Simulations of complex fluids by mixed lattice Boltzmann—finite difference methods

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier–Stokes equation and a finite difference scheme for the convection–diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.     

Bifurcation analysis and amplitude equations for viscoelastic convective fluids

Summary The possible bifurcations of a convective instability in viscoelastic fluid are studied. The viscoelastic behaviour is modelized by means of the Oldroyd type fluid whose parameters can be adjusted to suit a large class of polymeric fluids. We analyse in some detail bifurcations of codimension one (stationary or oscillatory convection) and codimension two for such kind of fluids. By a weak nonlinear analysis, the coefficients of the amplitude equations corresponding to the different bifurcations are also determined. It has been found that the nature of the convective solution depends crucially on both the viscoelastic parameters and the constitutive equation used to describe the fluid.     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

Dynamics of zero-Prandtl number convection near onset

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Be?nard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.     

Thermal instability in Maxwellian and Oldroydian viscoelastic fluids with suspended particles in porous medium

The effect of suspended particles on thermal instability is considered separately in Maxwellian and Oldroydian viscoelastic fluids in a porous medium. The principle of exchange of stabilities is found to hold well under a condition which is the same for Maxwellian as well as Oldroydian fluid. For stationary convection, both the Maxwellian and Oldroydian fluids behave like Newtonian fluid and the medium permeability and the suspended particles have destabilizing effects on the system. The sufficient conditions for the non-existence of overstability for both Maxwellian and Oldroydian viscoelastic fluids are also obtained.     

Natural Convection with Dissipative Heating

We derive a system of equations which models the motion of linear viscous fluids that undergo isochoric motions in isothermal processes but not necessarily isochoric ones in non-isothermal processes. The main point is that in contrast to the usual Oberbeck–Boussinesq approximation we do not neglect dissipative heating. We study Rayleigh–Bénard convection for our system and investigate existence, uniqueness and regularity of solutions and conditions for the stability of the motionless state. Received: 26 April 1999 / Accepted: 29 March 2000     

Analysis of the convective heat transfer characteristics in a two-dimensional cavity subjected to an external magnetic field

Natural convection heat transfer in the presence of a magnetic field has received considerable attention in the past few decades because of its various applications in industrial installations. In particular, a large number of numerical studies analyzing the effect of the magnetic field on natural convection in a two-dimensional cavity have been performed. In this work, we propose to study the main characteristics of the convective heat transfer of pure fluids and nanofluids in a two-dimensional cavity differentially heated and subjected to an external magnetic field. The scale analysis method is used first to obtain a correlation giving the heat transfer rate, which is then developed to predict the behavior of the heat transfer rate for pure fluids and nanofluids. To verify the reliability of the theoretical predictions, a numerical study is also carried out. The results show that the proposed correlation predicts well the convective heat transfer characteristics obtained numerically.     

Complex spatiotemporal convection patterns

This paper reviews recent efforts to describe complex patterns in isotropic fluids (Rayleigh-Benard convection) as well as in anisotropic liquid crystals (electro-hydrodynamic convection) when driven away from equilibrium. A numerical scheme for solving the full hydrodynamic equations is presented that allows surprisingly well for a detailed comparison with experiments. The approach can also be useful for a systematic construction of models (order parameter equations). (c) 1996 American Institute of Physics.     

The effect of shear flow on the Helfrich interaction in lyotropic lamellar systems

We study the effect of shear flow on the entropic Helfrich interaction in lyotropic surfactant smectic fluids. Arguing that flow induces an effective anisotropic surface tension in bilayers due to a combination of intermonolayer friction, bilayer collisions and convection, we calculate the reduction in fluctuations and hence the renormalised change in effective compression modulus and steady-state layer spacing. We demonstrate that non-permeable or slowly permeating membranes can be susceptible to an undulatory instability of the Helfrich-Hurault type, and speculate that such an instability could be one source of a transition to multilamellar vesicles.     

Mutual Voronoi tessellation in spoke pattern convection

Planar cellular networks are made of polygonal cells usually having an average of six sides and trivalent vertices. We analyze the topological properties of spoke patterns observed in the convection of highly viscous fluids. The competition between ascending and descending columns of fluid generates dual networks where on average cells are four sided and vertices tetravalent. This observation identifies a new class of dual networks satisfying a mutual Voronoi relation. The metric of the pattern is dominated by the distance between nearest neighbors vertices of opposite species.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

Noise, coherent fluctuations, and the onset of order in an oscillated granular fluid

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and increase in power and coherence. The scaling behavior and the shift in the onset of order agrees with the Swift-Hohenberg theory for convection in fluids. However, the noise in the granular system is an order of magnitude larger than the thermal noise in the most sensitive convecting fluid experiments to date; the effect of the granular noise is observable 20% below the onset of order.     

平板热管相变传热特性的实验研究

平板热管具有很好的均热性,能够避免电子器件散热时热点的产生,使热沉具有更好的散热效果.为了研究平板热管的相变传热特性,制作了可视化平板热管,通过实验研究了加热功率、冷却风速、不同工质对平板热管性能的影响.同时,还研究了槽道结构对平板热管内部沸腾换热的强化作用.     

Mode-to-mode energy transfers in convective patterns

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R _c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.