A. I. Tyrinov

An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe

The paper presents results of an investigation of the response of an incompressible fluid in a circular micropipe and a parallel-plate microchannel to a sudden time-independent pressure drop. Solutions of the problem were obtained analytically using the Laplace transform technique and numerically using the lattice Boltzmann method. The unsteady velocity profiles in the pipe and in the channel were obtained with the help of the infinite series solutions validated against numerical simulations. In line with the expectations, the flow asymptotically tends to the fully developed pattern, which is attained quicker for smaller Knudsen numbers. The solution enabled also obtaining relations to estimate the hydraulic resistance coefficient.

Dean instability of nanofluids with radial temperature and concentration non-uniformity

The paper focuses on an investigation into instability of Dean flows of nanofluids in curved channels restricted by two concentric cylinders. The flow is caused by a constant azimuthal pressure gradient. Critical values of the Dean number, which serves as the instability criterion, were found numerically by the collocation method. Functional dependencies of the critical Dean number on the ratio between the radii of the concave and convex walls (0.1…0.99), as well as dimensionless parameters describing the temperature gradient (−3…6), the relative density of the nanoparticles (0…4), the ratio of the Brownian and thermophoreticdiffusion (0.1…0.9), Prandtl (0.1…10) and Schmidt (10…100) number were revealed. It was shown that an increase in the relative density of the nanoparticles, the ratio of the Brownian and thermophoreticdiffusion, and Schmidt number causes instability under conditions of either positive or negative temperature gradients. An increase in the Prandtl number enforces flow stability for the negative temperature gradient and deteriorates stability for the positive temperature gradient. In light of the complexity of the physical problem in the present paper, only axisymmetric perturbations are considered as the first step to be further developed in future investigations.

Self-similar analysis of fluid flow, heat, and mass transfer at orthogonal nanofluid impingement onto a flat surface

Momentum, heat, and mass transfer in the vicinity of a stagnation point at uniform impingement of a nanofluid onto a flat plate were investigated. The novelty of the work consists in obtaining self-similar forms for the Hiemenz flow of a nanofluid and the self-similar representation of the velocity, thermal, and diffusion boundary layer equations derived on the basis of symmetry analysis using discrete symmetries. Momentum, energy, and concentration equations in the self-similar form were solved numerically. In frames of this analysis, functional dependence of the physical properties of nanofluids (viscosity, thermal conductivity, and diffusion coefficient) on concentration and temperature profiles was included as a part of the mathematical model, whose form enables including different models for the thermophysical properties of the nanofluid. Also novel are numerical results that revealed the influence of the nanoparticle concentration on the velocity, temperature, and concentration profiles, as well as ...

MODELING LEFTWARD FLOW IN THE EMBRYONIC NODE

The establishment of the left-right asymmetry during the development of vertebrates is a fascinating phenomenon that is still not fully understood. Extensive research suggests that in mice a small triangular cavity, called the ventral node, is responsible for breaking the left-right symmetry. A mouse node is ∼ 50 microns across and ∼10 microns deep. The surface of the nodal pit is covered by 200–300 monocilia whose rotation is responsible for the leftward flow in the node. We developed a simplified method of modeling the extraembryonic fluid flow and morphogen transport in a nodal cavity. We simplified the problem as flow in a 2D cavity; the effect of rotating cilia was modeled by specifying a constant vorticity at the edge of the ciliated layer. We also developed approximate solutions for morphogen transport in the nodal pit. The solutions were obtained utilizing the proper generalized decomposition method. We compared our approximate solutions with the results of numerical simulation of flow caused by the rotation of 81 cilia, and obtained reasonable agreement in most of the flow domain. We discuss locations where agreement is less accurate. The obtained semi-analytical solutions enable a quick analysis of flow and morphogen distribution in a nodal pit.Copyright

Mixed Convection in Vertical Flat and Circular Porous Microchannels

The paper outlines results of a study of mixed free and forced convection in vertical flat and circular microchannels occupied with porous medium subject to slip boundary conditions. The problem was solved using analytical and numerical methodology including the lattice Boltzmann method. Effects of the Knudsen and Rayleigh numbers and porosity on velocity and temperature profiles, as well as the normalized Nusselt number and friction factor were elucidated. It was revealed that Knudsen number effects dominate in the vicinity of the wall, whereas the Rayleigh number effects are more significant near the channel axis. For high Rayleigh numbers, velocity profiles exhibit M-shapes having a point of minimum at the channel axis. In the same time, temperature profiles become uniform, so that the fluid temperature across the channel is almost equal to the wall temperature. An increase in porosity causes a decrease in the temperature and velocity jumps on the wall. It has been shown that for low Rayleigh numbers a decrease in the Darcy number causes an increase in heat transfer and hydraulic resistance. However, for high Rayleigh numbers, the trend becomes opposite. Comparisons of the quantitative results for the circular and flat channels revealed that the shape of channel cross section makes a significant influence on heat transfer and fluid flow. Results of the analytical studies were validated via comparisons with numerical simulations using the lattice Boltzmann method, which proved to be an accurate and powerful tool able to simulate mixed convection in microchannels, with the deviation from the analytical solution not exceeding 1%.

Application of renormalization group analysis to two-phase turbulent flows with solid dust particles

Renormalization group methods are used to develop a macroscopic turbulence model for incompressible two phase turbulent flows. The velocity field is divided into slow (large-scale) and fast (small-scale) modes. With the help of the renormalization procedure, momentum equations for the large-scale modes and expressions for effective turbulent viscosity were obtained. These expressions reveal that the presence of the second phase causes decreased turbulent viscosity.Renormalization group methods are used to develop a macroscopic turbulence model for incompressible two phase turbulent flows. The velocity field is divided into slow (large-scale) and fast (small-scale) modes. With the help of the renormalization procedure, momentum equations for the large-scale modes and expressions for effective turbulent viscosity were obtained. These expressions reveal that the presence of the second phase causes decreased turbulent viscosity.