# M. VynnyckyUniversity of Limerick | UL · Department of Mathematics and Statistics (MACSI)

M. Vynnycky

Doctor of Philosophy

## About

175

Publications

28,645

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2,142

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Citations since 2016

Introduction

**Skills and Expertise**

Additional affiliations

January 2008 - April 2014

## Publications

Publications (175)

The Prandtl–Batchelor theorem states that the vorticity in a steady laminar high Reynolds ( Re) number flow containing closed streamlines should be constant; however, apart from the simple case of circular streamlines, very little is known about how to determine this constant ( ω 0 ). This paper revisits earlier work for flow driven by a surroundin...

This work is concerned with a reaction–diffusion system in cylindrical coordinates that arises from electrochemistry. A Laplace transform solution for the current density is found to have two branch points and is inverted by a suitable Bromwich contour, with the solution taking the form of the sum of two integrals; in a special case, one of the int...

We develop a novel phase-wise sequential numerical approach based on the method of fundamental solutions (MFS) for inverse two-phase nonlinear Stefan and Cauchy-Stefan problems in one dimension (1D). By treating each phase independently, the inverse two-phase nonlinear Stefan problem splits into two single-phase inverse problems: an inverse nonline...

In this paper, we reassess the local solute redistribution equation (LSRE) of macrosegregation which, since it first appeared in 1960s, has served as a cornerstone for understanding the composition variations that occur in the solidification of alloys. We highlight some anomalies in earlier literature, in particular as regards the prediction of rem...

In this work, we revisit a recent transient three-dimensional (3D) model for longitudinal electromagnetic stirring in the continuous casting of rectangular steel blooms. Whereas the earlier work was able to demonstrate accurate approximations to the solutions in two asymptotic limits, both of which gave economical alternatives to time-consuming 3D...

Transient electrochemical experiments are usually described theoretically by systems of reaction–diffusion partial differential equations. Converting them to integral equations is a classical and valuable modelling approach. Unfortunately, if any reaction–diffusion equation contains nonlinear reaction rate terms, up to now such a conversion has onl...

In this paper, we present and analyse a coupled electrochemomechanical model for the cycling of a nanowire composed of amorphous Si coated on Cu15Si4, using large-deformation theory. This study is motivated by a recent novel design for the anode current collector in a lithium-ion battery, and the modelling efforts are linked to half-cell experiment...

In this paper, we consider the steady-state base flow for natural convection in a vertical porous slab with permeable boundaries. Although recent work proposed a one-dimensional solution for this flow, we make a strong case for this flow to be two-dimensional; this centres on an oversight in the use of the Oberbeck–Boussinesq approximation in the e...

In this article, we study a novel computational technique for the efficient numerical solution of the inverse boundary identification problem with uncertain data in two dimensions. The method essentially relies on a posteriori error indicators consisting of the Tikhonov regularized solutions obtained by the method of fundamental solutions (MFS) and...

Understanding drug release from pharmaceutical granules is vital to the development of targeted release profiles. A model describing diffusion and solubility-limited drug dissolution and release from a porous spherical granule of drug and excipient is considered. Radially varying porosity and initial concentration profiles which can arise in pharma...

In this paper, we develop a method to alleviate the loss of accuracy that occurs when parabolic partial differential equations (PDEs), subject to discontinuous boundary conditions, are solved numerically. Employing the Keller box finite-difference method, we consider a benchmark case involving the linear one-dimensional transient heat equation, sub...

A recent asymptotics-based thermomechanical model is adapted and applied to the mould region in the continuous casting of round steel billets, with a view to describing the complex interplay between air-gap formation, mould taper, cooling channel width and cooling water velocity. Although the situation is steady state, the analysis leads to what is...

In this paper, a recent algorithm, based around the method of fundamental solutions (MFS), for reconstructing boundary data in inverse Stefan problems is extended and applied to inverse Cauchy–Stefan problems, wherein initial data must also be reconstructed. A key feature of the algorithm is that it is adaptive and iterates to find the optimal loca...

Accurate mechanistic in-vitro dissolution models can deliver insight into drug release behaviour and guide formulation development. Drug release profiles from drug-excipient granules can be impacted by variation of porosity and drug load within granules, which may arise from inherent variability in granulation processes. Here, we analyse and valida...

This paper uses computational fluid dynamics (CFD), in the form of the OpenFOAM software package, to investigate the forces on the salt core in high-pressure die casting (HPDC) when being exposed to the impact of the inflowing melt in the die filling stage, with particular respect to the moment of first impact—commonly known as slamming. The melt-a...

A recent three-dimensional (3D) model that revisited earlier theoretical work for longitudinal electromagnetic stirring in the continuous casting of steel blooms is analyzed further to explore how the bloom width interacts with the pole pitch of the stirrer to affect the magnetic flux density. Whereas the first work indicated the presence of a boun...

Abstract A recent asymptotic model for solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys is extended for the purposes of understanding the link between solute segregation and centreline shrinkage porosity, a defect that commonly occurs in the continuous casting of steel. In particular, the analysis elucida...

Although two-dimensional (2D) parabolic integro-differential equations (PIDEs) arise in many physical contexts, there is no generally available software that is able to solve them numerically. To remedy this situation, in this article, we provide a compact implementation for solving 2D PIDEs using the finite element method (FEM) on unstructured gri...

A recent asymptotic model for the operation of a vanadium redox flow battery (VRFB) is extended to include the dissociation of sulphuric acid—a bulk chemical reaction that occurs in the battery’s porous flow-through electrodes, but which is often omitted from VRFB models. Using asymptotic methods and time-dependent two-dimensional numerical simulat...

This paper investigates the different possible behaviours of a recent asymptotic model for oscillation-mark formation in the continuous casting of steel, with particular focus on how the results obtained vary when the heat transfer coefficient, the thermal resistance and the dependence of the viscosity of the flux powder as a function of temperatur...

In the one-dimensional solidification of a binary alloy undergoing shrinkage, there is a relative motion between solid and liquid phases in the mushy zone, leading to the possibility of macrosegregation; thus, the problem constitutes an invaluable benchmark for the testing of numerical codes that model these phenomena. Here, we revisit an earlier o...

Recent work highlighting an anomaly in the modelling of rotary electromagnetic stirring (EMS) in the continuous casting of round steel billets is extended to the case of longitudinal stirring for rectangular blooms. An earlier, still often-cited, model forms the basis of the current analysis, which uses asymptotic methods on the three-dimensional (...

This paper investigates the fluid-structure interaction (FSI) that would be expected to occur when a lost core deforms in high-pressure die casting. A two-phase compressible Volume of Fluid approach is used to model the fluid. The turbulence contribution to the Navier-Stokes equations is accounted for by using the Reynolds-averaged Navier Stokes (R...

A perda de peças metálicas por ação da corrosão tem sido objeto de estudo de engenheiros e metalúrgicos que procuram constantemente aperfeiçoar e desenvolver novos métodos de proteção que apresentem resistência à corrosão, uma maneira como isso pode ser alcançado é através do processo laser cladding. Nesse processo é depositado um metal de adição d...

Continuous casting is a process whereby molten metal is solidified into a semi-finished billet, bloom, or slab for subsequent rolling in finishing mills; it is the most frequently used process to cast not only steel, but also aluminum and copper alloys [...]

In this paper, earlier dissolutive wetting models describing the dynamics of an axisymmetric alloy drop spreading on pure metal substrate are extended to describe reactive wetting and subsequent joint formation in brazing processes. A two-dimensional time-dependent problem is formulated, and the model equations are nondimensionalized, revealing the...

The occurrence of macrosegregation in alloys produced by ingot casting can adversely affect the quality of the final product. Macrosegregation can be described as a severe variation on the macroscopic scale of the chemical species that compose the alloy, and the ability of computational simulations to predict such defects remains far from perfect....

While studying a problem in biomedical research a simple diffusion problem arose which admitted a solution by Fourier transforms. It was natural to ask if the same problem could be solved by Laplace transforms. In this note, we provide three solution techniques using Laplace transforms, with the last leading to a number of novel mathematical identi...

With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more gr...

This paper investigates the cooling performance of six different lost core designs for automotive cast houses with regard to their cooling efficiency. For this purpose, the conjugate heat transfer (CHT) solver, chtMultiregion, of the freely available CFD-toolbox OpenFOAM in its implementation of version 2.3.1 is used. The turbulence contribution to...

Joining parts using low-melting temperature alloys has long been used for manufacturing complex components such as heat exchangers made of aluminium alloys. Investigations of the process have shown that core/clad interaction during heating and brazing can lead to a significant decrease in the amount of liquid available for joint formation. This stu...

In this exposition, a simple practical adaptive algorithm is developed for ef- ficient and accurate reconstruction of Neumann boundary data in the inverse Stefan problem, which is a highly nontrivial task. Primarily, this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the in...

The perspective 3-point (P3P) problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis, and robotics. One possibility is to formulate it mathematically in terms of finding the solution to a quartic equation. However, there is yet no...

In the continuous casting of steel, solidification begins at a triple point where solid steel, molten steel and molten flux meet; the motion of this point determines how surface defects known as oscillation marks (OSMs) are formed. Here, under a number of simplifying assumptions, we derive an asymptotic model in 15 dimensionless parameters that des...

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusion coefficient is many orders of magnitude smaller. It has been shown in an earlier paper that a similarity solution exists while the front is passing through the first lay...

Early, yet still often-cited, mathematical models for electromagnetic stirring (EMS) in continuous casting are re-examined and found to contain a surprising anomaly: the solutions obtained were not unique. Analysis for the case of a round billet under rotary EMS shows how to avoid this behavior, whilst still making use of the experimental data that...

Current practice in the use of the method of fundamental solutions (MFS) for inverse Stefan problems typically involves setting the source and collocation points at some distance, h, from the boundaries of the domain in which the solution is required, and then varying their number, (Formula presented.), so that the obtained solution fulfils a desir...

The modelling of macrosegregation in the continuous casting of alloys normally requires resource-intensive computational fluid dynamics (CFD). By contrast, here we develop an asymptotic framework for the case when macrosegregation is driven by solidification shrinkage; as a first step, a binary alloy is considered. Systematic asymptotic analysis of...

Asymptotic methods are employed to revisit an earlier model for oscillation-mark formation in the continuous casting of steel. A systematic non-dimensionalization of the governing equations, which was not carried out previously, leads to a model with 12 dimensionless parameters. Analysis is provided in the same parameter regime as for the earlier m...

In the continuous casting of alloys, it is well-known that the mushy zone is decisive for the final properties of the casting. However, most numerical models for the process use enthalpy-based methods on fixed grids which determine the extent the mushy zone implicitly. Here, on the other hand, we develop a methodology for explicitly resolving the g...

The casting of metals is known to involve the complex interaction of turbulent momentum and heat transfer in the presence of solidification, and it is believed that computational fluid dynamical (CFD) techniques are required to model it correctly. Here, using asymptotic methods, we demonstrate that the key quantities obtained in an earlier CFD mode...

The work presented here examines the surface cracks that can form during the continuous casting of near peritectic steels due to the volume changes during the peritectic reaction/transformation. The investigated samples were collected during plant trials from two different steel grades. The role and mode of the peritectic reaction/transformation ar...

The formation of an air gap in continuous casting systems is detrimental to the process efficiency as it acts to thermally insulate the cast from the water-cooled mould. By tapering the mould wall, the thermal contraction of the cooling cast can be accommodated so that the thickness of the air gap is decreased. We consider a coupled thermomechanica...

A comprehensive experimental study of oscillation mark (OM) formation and its characteristics during the solidification of Incoloy alloy 825 in the continuous casting of blooms is investigated by plant trials and metallographic study. The experiments involved two heats with the same casting and mold conditions and sampling at different locations ac...

The modelling of the continuous casting of metals is known to involve the complex interaction of non-isothermal fluid and solid mechanics. However, using asymptotic methods and an earlier numerical result obtained via computational fluid dynamics, we demonstrate how the motion of the liquid metal can be systematically decoupled from the stresses in...

A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a flat permeable surface representing an efficient drainage layer. A fully saturated zone is shown to occur. It is typically a thin layer, relative to the total soil thickness, and lies at the bottom of the...

A mathematical model is derived to predict the trajectories of pores and inclusions that are nucleated in the interdendritic region during the continuous casting of steel. Using basic fluid mechanics and heat transfer, scaling analysis, and asymptotic methods, the model accounts for the possible lateral drift of the pores as a result of the depende...

This work is concerned with the numerical solution of the K-BKZ integral constitutive equation for two-dimensional time-dependent free surface flows. The numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls. The main characteristics of the methodology em...

In this paper, the Keller box finite-difference scheme is employed in tandem with the so-called boundary immobilization method for the purposes of solving a two-phase Stefan problem that has both phase formation and phase depletion. An important component of the work is the use of variable transformations that must be built into the numerical algor...

Statistical, experimental and numerical studies are carried out to investigate the frequencies of breakouts during solidification phenomenon in steel continuous casting process at Arcellor Mittal-Annaba plant (Algeria). These breakouts frequencies which have an impact on the management quality field in terms of the quality cost (CoQ) are statistica...

We develop a coupled thermomechanical model, that includes mould taper, for the formation of air gaps in the vertical continuous casting of round billets. The system is very sensitive to the small width of the air gap. Mould tapers are used to mitigate the contraction of the solidified shell during cooling. We apply numerical and perturbation metho...

Motivated by convection of planetary mantles, we consider a mathematical model for Rayleigh-Bénard convection in a basally heated layer of a fluid whose viscosity depends strongly on temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and s...

In this paper, we extend a recent one-dimensional isothermal steady-state generalized Darcy model for two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell, so as to include the effect of heat transfer. As for the isothermal case, we arrive at either a fixed- or free-boundary problem, depending on the main prob...

Asymptotic methods are employed to analyse a commonly used one-dimensional transient model for coupled heat and mass transfer in the primary drying stage of freeze-drying (lyophilization) in a vial. Mathematically, the problem constitutes a two-phase moving boundary problem, in which one of the phases is a frozen porous matrix that undergoes sublim...

A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is applied to the classical moving boundary problem that arises from the diffusion of oxygen in absorbing tissue; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. New insights are obtained into three...

The computational cost for all-vanadium redox flow batteries (VRFB) models that seek to capture the transport phenomena usually increases with the number of spatial dimensions considered. In this context, we carry out scale analysis to derive a reduced zero-dimensional model. Two nondimensional numbers and their limits to support the model reductio...

In many phase-change problems of practical interest, it is important to know when a phase is depleted, a quantity referred to as the extinction time; however, there are no numerical schemes that are able to compute this with any degree of rigour or formal accuracy. In this paper, we develop such a scheme for the one-dimensional time-dependent probl...

In general, three-dimensional (3D) non-isothermal models for monolithic channels that seek to capture the local transport phenomena are computationally expensive. In this regard, we present a reduced model for a monolithic channel that reduces the computational cost, whilst preserving the 3D geometry and all of the essential physics – this is accom...

Continuous casting of the phosphor bronzes has been investigated experimentally and analyzed with the help of a thermo-mechanical model. The microscopic investigation shows the spread of the tin rich liquid at the chill surface cause by the formation of flow channels underneath the chill surface. Precipitation of the secondary phases has also been...

The computational cost for all-vanadium redox flow batteries (VRFB) models that seek to capture the transport phenomena usually increases with the number of spatial dimensions considered. In this context, we carry out scale analysis to derive an reduced zero-dimensional model. Two nondimensional numbers and their limits to support the model reducti...

Vertical cylinders of bubble-enriched, chemically evolved volcanic rock are found in many inflated pahoehoe lava flows. We provide a putative theoretical explanation for their formation, based on a description of a crystallising three-phase (liquid, solid, gas) crystal pile in which the water-saturated silicate melt exsolves steam and becomes more...

This article examines the steady flow of a sme ctic A liquid crystal sample that is initially aligned in a classical "bookshelf" geometry confined between parallel plates and is then subjected to a lateral pressure gradient which is perpendicular to the initial local smectic layer arrangement. The nonlinear dynamic equations are derived. These equa...