Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Thermal properties and thermal shock resistance of γ-Y 2Si2O7

Thermal properties, namely, Debye temperature, thermal expansion coefficient, heat capacity, and thermal conductivity of γ-Y 2Si2O7, a high-temperature polymorph of yttrium disilicate, were investigated. The anisotropic thermal expansions of γ-Y2Si2O7 powders were examined using high-temperature X-ray diffractometer from 300 to 1373 K and the volumetric thermal expansion coefficient is (6.68±0.35) × 10-6 K-1. The linear thermal expansion coefficient of polycrystalline γ-Y2Si2O7 determined by push-rod dilatometer is (3.90±0.4) × 10-6 K-1, being very close to that of silicon nitride and silicon carbide. Besides, γ-Y2Si2O7 displays a low-thermal conductivity, with a κ value measured below 3.0 W·(m·K) -1 at the temperatures above 600 K. The calculated minimum thermal conductivity, κmin, was 1.35 W·(m·K) -1. The unique combination of low thermal expansion coefficient and low-thermal conductivity of γ-Y2Si2O7 renders it a very competitive candidate material for high temperature structural components and environmental/thermal-barrier coatings. The thermal shock resistance of γ-Y2Si2O7 was estimated by quenching dense materials in water from various temperatures and the critical temperature difference, ΔTc, was determined to be 300 K.