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We developed a model for the enhancement of the heat flux by spherical and elongated nanoparticles in sheared laminar flows of nanofluids. Besides the heat flux carried by the nanoparticles, the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect: it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the Maxwell-Garnett limit for the spherical nanoparticles. The road ahead, which should lead toward robust predictive models of heat flux enhancement, is discussed.

Udgivelsesdato: April

In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its three-dimensional (3D) counterpart by having a second quadratic conserved variable in addition to the energy and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity V and energy K as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number Ret instead of being Ret independent in 3D channels.

Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave "clusters" consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finite-dimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wave-kinetic equations that account for interactions with overlapping quasiresonances of finite amplitude waves. The present results are directly applicable to finite-dimensional wave turbulence in any wave system in finite domains with three-mode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.

In this Letter, we suggest a simple and physically transparent analytical model of pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model provides an accurate quantitative description of the profiles of the mean-velocity and Reynolds stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe, for a wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We construct, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by "statistically preserved structures" which are associated with exact conservation laws. The latter can be used, for example, to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.

info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

info:eu-repo/semantics/published

A nuclear capture reaction of a single neutron by ultracold superfluid He3 results in a rapid overheating followed by the expansion and subsequent cooling of the hot subregion, in a certain analogy with the big bang of the early universe. It was shown in a Grenoble experiment that a significant part of the energy released during the nuclear reaction was not converted into heat even after several seconds. It was thought that the missing energy was stored in a tangle of quantized vortex lines. This explanation, however, contradicts the expected lifetime of a bulk vortex tangle, 10-5-10-4 s, which is much shorter than the observed time delay of seconds. In this paper we propose a scenario that resolves the contradiction: the vortex tangle, created by the hot spot, emits isolated vortex loops that take with them a significant part of the tangle's energy. These loops quickly reach the container walls. The dilute ensemble of vortex loops attached to the walls can survive for a long time, while the remaining bulk vortex tangle decays quickly. © 2014 American Physical Society.

A nuclear capture reaction of a single neutron by ultracold superfluid He3 results in a rapid overheating followed by the expansion and subsequent cooling of the hot subregion, in a certain analogy with the big bang of the early universe. It was shown in a Grenoble experiment that a significant part of the energy released during the nuclear reaction was not converted into heat even after several seconds. It was thought that the missing energy was stored in a tangle of quantized vortex lines. This explanation, however, contradicts the expected lifetime of a bulk vortex tangle, 10-5-10-4 s, which is much shorter than the observed time delay of seconds. In this paper we propose a scenario that resolves the contradiction: the vortex tangle, created by the hot spot, emits isolated vortex loops that take with them a significant part of the tangle's energy. These loops quickly reach the container walls. The dilute ensemble of vortex loops attached to the walls can survive for a long time, while the remaining bulk vortex tangle decays quickly. © 2014 American Physical Society.