Hydrodynamics and heat transfer in bubbly flow in the turbulent boundary layer

In the work presented is a new approach to modelling the bubbly flow in the boundary layer. The approach is based on summation of dissipation energy coming from the shearing turbulent flow in the absence of bubbles and the dissipation contribution from the presence of bubbles. As a result we obtain the dissipation of equivalent single phase turbulent flow. The model has been solved using the method of asymptotic correction to provide an explicit differential equation describing the velocity profile. That can be solved with the assumption of constant void fraction distribution to yield the analytical velocity profile. Alternatively, author has developed his own model of lateral void migration, which is distinct from other models by virtue of presence of another rotational velocity. Velocity distributions calculated using the new model have been compared against the experimental data of turbulent bubble flows with small void fraction. A good consistency between calculations performed using a new model and available experimental data has been obtained. Additionally, a solution of the temperature field is also given. In the case of a constant void fraction distribution analytical distribution of the Nusselt number is given or the set of differential equations needs to be solved.     

Existence of optimal solutions of two-directionally continuous linear repetitive processes

In the paper, an existence theorem for a Lagrange optimal control problem connected with a two-directionally continuous variant of a linear autonomous repetitive process is derived. As a corollary, existence of an optimal solution in the case of cost functional depending on a fixed ??end-function?? is obtained.     

New insights into the mechanism of H2 generation through NaBH4 hydrolysis on Co-based nanocatalysts studied by differential reaction calorimetry

To our knowledge, the present study is the first investigation by liquid-phase calorimetry of the mechanism of hydrogen generation by hydrolysis of sodium borohydride catalyzed by Co₂B nanoparticles generated in situ. The differential reaction calorimeter was coupled with a volumetric hydrogen measurement, allowing a simultaneous thermodynamic and kinetic study of the reaction. At the end of the reaction, the catalyst was characterized ex situ by TEM, XRD, magnetism, N₂ adsorption, TGA–DTA, and the liquid hydrolysis products were analyzed by Wet-STEM and ¹¹B-NMR. The in situ preparation method made it possible to form nanoparticles (<12 nm) of Co₂B which are the active phase for the hydrolysis reaction. In semi-batch conditions, the Co₂B catalyst formed in situ is subsequently reduced by each borohydride addition and oxidized at the end of the hydrolysis reaction by OH⁻ in the presence of metaborate. A coating of the nanoparticles has been observed by calorimetry and physico-chemical characterization, corresponding to the formation of a 2–3 nm layer of cobalt oxide or hydroxide species.