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American Society for Testing and Materials

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Boundary-layer flow of a nanofluid past a stretching sheet

The flow of homogeneous fluids through porous media: analogies with other physical problems

Natural convective boundary-layer flow of a nanofluid past a vertical plate

Thermal Development of Forced Convection in a Channel or Duct Partly Occupied by a Porous Medium

Thermo-Calc software is used to model the composition diagram for alloys based on γ-TiAl of the systems Ti – Al – Mo – (4 – 10) at.% Nb and Ti – Al – Nb – X (X is Cr, Mo, V). The effect of alloying on critical points and sequence of phase transformations is established. Changes in phase composition in relation to alloy TNM-B1 temperature are analyzed using a polythermal section of the Ti – Al – Nb – Mo system.

Thermodynamic Modeling and Experimental Study of Phase Transformations in Alloys Based on γ-TiAl

Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number (Ra) for high values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto- plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.

Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media

Segregation and microporosity formation are two important physicalphenomena that occur during solidification of binary alloys. The aim ofthis study is to investigate the effect of the model of solute diffusionat the local scale (which means at the local scale of the microscopicrepresentative elemental average volume (REV)) on solute transport andthe microporosity formation during this process. The Scheil rule and thelever rule are used to describe the solute diffusion at the local scale.Results indicate that solute diffusion at the local scale is animportant factor in microporosity formation. Also, microporosityformation slightly reduces inverse segregation because it partiallycompensates for shrinkage. The increase of the external pressure at thefree surface or the decrease of the initial hydrogen concentration inthe molten alloy can be effectively utilized to control microporosityformation.

Comparison between Lever and Scheil Rules for Modeling of Microporosity Formation during Solidification

The goal of this paper is to use mathematical modeling to investigate the fate of dense core vesicles (DCVs) captured in en passant boutons located in nerve terminals. One possibility is that all DCVs captured in boutons are destroyed, another possibility is that captured DCVs can escape and reenter the pool of transiting DCVs that move through the boutons, and a third possibility is that some DCVs are destroyed in boutons, while some reenter the transiting pool. We developed a model by applying the conservation of DCVs in various compartments composing the terminal, to predict different scenarios that emerge from the above assumptions about the fate of DCVs captured in boutons. We simulated DCV transport in type Ib and type III terminals. The simulations demonstrate that, if no DCV destruction in boutons is assumed and all captured DCVs reenter the transiting pool, the DCV fluxes evolve to a uniform circulation in a type Ib terminal at steady-state and the DCV flux remains constant from bouton to bouton. Because at steady-state the amount of captured DCVs is equal to the amount of DCVs that reenter the transiting pool, no decay of DCV fluxes occurs. In a type III terminal at steady-state, the anterograde DCV fluxes decay from bouton to bouton, while retrograde fluxes increase. This is explained by a larger capture efficiency of anterogradely moving DCVs than of retrogradely moving DCVs in type III boutons, while the captured DCVs that reenter the transiting pool are assumed to be equally split between anterogradely and retrogradely moving components. At steady-state, the physiologically reasonable assumption of no DCV destruction in boutons results in the same number of DCVs entering and leaving a nerve terminal. Because published experimental results indicate no DCV circulation in type III terminals, modeling results suggest that DCV transport in these type III terminals may not be at steady-state. To better understand the kinetics of DCV capture and release, future experiments in type III terminals at different times after DCV release (molting) may be proposed.

Simulating Reversibility of Dense Core Vesicles Capture in En Passant Boutons: Using Mathematical Modeling to Understand the Fate of Dense Core Vesicles in En Passant Boutons.

Andrey V. Kuznetsov

Papers

Thermal Development of Forced Convection in a Channel or Duct Partly Occupied by a Porous Medium

Thermodynamic Modeling and Experimental Study of Phase Transformations in Alloys Based on γ-TiAl

Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media

Comparison between Lever and Scheil Rules for Modeling of Microporosity Formation during Solidification

Simulating Reversibility of Dense Core Vesicles Capture in En Passant Boutons: Using Mathematical Modeling to Understand the Fate of Dense Core Vesicles in En Passant Boutons.