Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters.

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.

The effect of temperature dependent viscosity on MHD natural convection flow from an isothermal sphere

Laminar magnetohydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with viscosity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magnetohydrodynamic paramagnet and viscosity-variation parameter.

Advanced numerical study of impact forces on railway sleepers under wheel flat

Wheel-rail interaction is one of the most important research topics in railway engineering. It includes track vibration, track impact response and safety of the track. Track structure failures caused by impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. The wheel-rail impact forces occur because of imperfections on the wheels or rails such as wheel flats, irregular wheel profile, rail corrugation and differences in the height of rails connected at a welded joint. In this paper, a finite element model for the wheel flat study is developed by use of the FEA software package ANSYS. The effect of the wheel flat to impact force on sleepers is investigated. It has found that the wheel flat significantly increases impact forces and maximum Von Mises stress, and also delays the peak position of dynamic variation for impact forces on both rail and sleeper.

Scaling analysis of the thermal boundary layer adjacent to an abruptly heated inclined flat plate

The natural convection thermal boundary layer adjacent to an abruptly heated inclined flat plate is investigated through a scaling analysis and verified by numerical simulations. In general, the development of the thermal flow can be characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady state stage. Major scales including the flow velocity, flow development time, and the thermal and viscous boundary layer thicknesses are established to quantify the flow development at different stages and over a wide range of flow parameters. Details of the scaling analysis and the numerical procedures are described in this paper.

Scaling analysis of unsteady natural convection boundary layer for instantaneous heating

Natural convection thermal boundary layer adjacent to an instantaneous heated inclined flat plate is investigated through a scaling analysis and verified by direct numerical simulations. It is revealed from the analysis that the development of the boundary layer may be characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady state stage. These three stages can be clearly identified from the numerical simulations. Major scales including the flow velocity, flow development time, and the thermal and viscous boundary layer thicknesses are established to quantify the flow development at different stages and over a wide range of flow parameters. Details of the scaling analysis are described in this paper.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.