# Prof. Sarah Mitchell

## Biography

Sarah Mitchell is a Senior Lecturer and Head of the Department of Mathematics and Statistics at the University of Limerick (UL). She obtained her undergraduate degree in 1999 (MMath in Mathematics) and her PhD in 2003, both from the University of Bath, UK. Afterwards she took up two postdoc positions in Canada (University of British Columbia, 2003-2006) and South Africa (University of Cape Town, 2006-2008), before starting a lectureship position in Applied Mathematics at UL in January 2008. In September 2013 she became Deputy Head of Department and then took over as Head in September 2016.Her main research interests are in numerical and mathematical modelling of moving boundary problems relevant to solidification (such as casting of metals) or melting (such as glaciers) and modelling drug diffusion in glassy polymers.## Research Interests

Mathematical Modelling, Numerical Analysis## Peer Reviewed Journals

### On the accurate numerical solution of a two-phase Stefan problem with phase formation and depletion

Mitchell, SL,Vynnycky, M (2016) On the accurate numerical solution of a two-phase Stefan problem with phase formation and depletion. Journal Of Computational And Applied Mathematics :259-274

### The oxygen diffusion problem: Analysis and numerical solution

Mitchell, SL,Vynnycky, M (2015) The oxygen diffusion problem: Analysis and numerical solution. Applied Mathematical Modelling :2763-2776

### On the numerical solution of a Stefan problem with finite extinction time

Vynnycky, M,Mitchell, SL (2015) On the numerical solution of a Stefan problem with finite extinction time. Journal Of Computational And Applied Mathematics :98-109

### Applying the combined integral method to two-phase Stefan problems with delayed onset of phase change

Mitchell, SL (2015) Applying the combined integral method to two-phase Stefan problems with delayed onset of phase change. Journal Of Computational And Applied Mathematics :58-73

### Glacial melt under a porous debris layer

Evatt, GW,Abrahams, ID,Heil, M,Mayer, C,Kingslake, J,Mitchell, SL,Fowler, AC,Clark, CD (2015) Glacial melt under a porous debris layer. Journal Of Glaciology :825-836

### A mathematical model for nanoparticle melting with density change

Font, F,Myers, TG,Mitchell, SL (2015) A mathematical model for nanoparticle melting with density change. Microfluidics And Nanofluidics :233-243

### Mould-taper asymptotics and air gap formation in continuous casting

Florio, BJ,Vynnycky, M,Mitchell, SL,O'Brien, SBG (2015) Mould-taper asymptotics and air gap formation in continuous casting. Applied Mathematics And Computation :1122-1139

### An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue

Mitchell, SL (2014) An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue. Applied Mathematical Modelling :4396-4408

### ASYMPTOTIC AND NUMERICAL SOLUTIONS OF A FREE BOUNDARY PROBLEM FOR THE SORPTION OF A FINITE AMOUNT OF SOLVENT INTO A GLASSY POLYMER

Mitchell, SL,O'Brien, SBG (2014) ASYMPTOTIC AND NUMERICAL SOLUTIONS OF A FREE BOUNDARY PROBLEM FOR THE SORPTION OF A FINITE AMOUNT OF SOLVENT INTO A GLASSY POLYMER. Siam Journal On Applied Mathematics :697-723

### On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions

Mitchell, SL,Vynnycky, M (2014) On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions. Journal Of Computational And Applied Mathematics :49-64

### Reaction front formation in contaminant plumes

Cribbin, LB,Winstanley, HF,Mitchell, SL,Fowler, AC,Sander, GC (2014) Reaction front formation in contaminant plumes. Journal Of Contaminant Hydrology :12-21

### Analysis and simplification of a mathematical model for high-pressure food processes

Smith, NAS,Mitchell, SL,Ramos, AM (2014) Analysis and simplification of a mathematical model for high-pressure food processes. Applied Mathematics And Computation :20-37

### One-dimensional solidification of supercooled melts

Font, F,Mitchell, SL,Myers, TG (2013) One-dimensional solidification of supercooled melts. International Journal Of Heat And Mass Transfer :411-421

### ON THE ACCURACY OF A FINITE-DIFFERENCE METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS

Vynnycky, M,Mitchell, SL (2013) ON THE ACCURACY OF A FINITE-DIFFERENCE METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS. Numerical Heat Transfer Part B-Fundamentals :275-292

### Applying the combined integral method to one-dimensional ablation

Mitchell, SL (2012) Applying the combined integral method to one-dimensional ablation. Applied Mathematical Modelling :127-138

### An accurate finite-difference method for ablation-type Stefan problems

Mitchell, SL,Vynnycky, M (2012) An accurate finite-difference method for ablation-type Stefan problems. Journal Of Computational And Applied Mathematics :4181-4192

### Asymptotic, numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers

Mitchell, SL,O'Brien, SBG (2012) Asymptotic, numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers. Applied Mathematics And Computation :376-388

### Energy conservation in the one-phase supercooled Stefan problem

Myers, TG,Mitchell, SL,Font, F (2012) Energy conservation in the one-phase supercooled Stefan problem. International Communications In Heat And Mass Transfer :1522-1525

### Application of the combined integral method to Stefan problems

Myers, TG; Mitchell, SL (2011) Application of the combined integral method to Stefan problems. Applied Mathematical Modelling :4281-4294

### AN ACCURATE NODAL HEAT BALANCE INTEGRAL METHOD WITH SPATIAL SUBDIVISION

Mitchell, SL (2011) AN ACCURATE NODAL HEAT BALANCE INTEGRAL METHOD WITH SPATIAL SUBDIVISION. Numerical Heat Transfer Part B-Fundamentals :34-56

### An accurate numerical solution for the transient heating of an evaporating spherical droplet

Mitchell, SL; Vynnycky, M; Gusev, IG; Sazhin, SS (2011) An accurate numerical solution for the transient heating of an evaporating spherical droplet. Applied Mathematics And Computation :9219-9233

### Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

Mitchell, SL; Myers, TG (2010) Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions. International Journal Of Heat And Mass Transfer :3540-3551

### Evaporative cooling and the Mpemba effect

Vynnycky, M; Mitchell, SL (2010) Evaporative cooling and the Mpemba effect. Heat And Mass Transfer :881-890

### Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems

Mitchell, SL; Myers, TG (2010) Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems. Siam Review :57-86

### APPLICATION OF THE HEAT-BALANCE AND REFINED INTEGRAL METHODS TO THE KORTEWEG-DE VRIES EQUATION

Myers, TG; Mitchell, SL (2009) APPLICATION OF THE HEAT-BALANCE AND REFINED INTEGRAL METHODS TO THE KORTEWEG-DE VRIES EQUATION. Thermal Science :113-119

### Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems

Mitchell, SL; Vynnycky, M (2009) Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems. Applied Mathematics And Computation :1609-1621

### Unsteady contact melting of a rectangular cross-section material on a flat plate

Myers, TG; Mitchell, SL; Muchatibaya, G (2008) Unsteady contact melting of a rectangular cross-section material on a flat plate. Physics Of Fluids

### Approximate solution methods for one-dimensional solidification from an incoming fluid

Mitchell, SL; Myers, TG (2008) Approximate solution methods for one-dimensional solidification from an incoming fluid. Applied Mathematics And Computation :311-326

### Unsteady contact melting of a rectangular cross-section phase change material

Myers,TG; Mitchell, SL; Muchatibaya, G; Myers, TG; Mitchell, SL; Muchatibaya, G (2008) Unsteady contact melting of a rectangular cross-section phase change material. Physics Of Fluids

### Heat balance integral method for one-dimensional finite ablation

Mitchell, SL; Myers, TG (2008) Heat balance integral method for one-dimensional finite ablation. Journal Of Thermophysics And Heat Transfer :508-514

### An asymptotic framework for the analysis of hydraulic fractures: the impermeable case

Mitchell, SL , Kuske, R , Peirce, AP (2007) An asymptotic framework for the analysis of hydraulic fractures: the impermeable case. Journal Of Applied Mechanics :365-372

### A cubic heat balance integral method for one-dimensional melting of a finite thickness layer

Myers, TG; Mitchell, SL; Muchatibaya, G; Myers, MY (2007) A cubic heat balance integral method for one-dimensional melting of a finite thickness layer. International Journal Of Heat And Mass Transfer :5307-5315

### An asymptotic framework for finite hydraulic fractures including leak-off

Mitchell, SL; Kuske, R; Peirce, AP (2007) An asymptotic framework for finite hydraulic fractures including leak-off. S.I.A.M. Journal Of Applied Mathematics :364-386

### Application of Box Schemes to Groundwater Flow Problems

Mitchell, SL; Morton, KW; Spence, A (2006) Application of Box Schemes to Groundwater Flow Problems. Siam Journal On Scientific Computing :1202-1225

## Books

## Book Chapters

## Edited Books

## Other Journals

## Conference Publications

### NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2

Mitchell, SL; Myers, TG (2009) NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2. :1450-1452

### AIP Conference Proceedings

Mitchell S.L., Myers T.G. (2009) AIP Conference Proceedings. :1450-1452

### ECMI 2008

Mitchell, S.L. and Myers, T.G. (2008) ECMI 2008.

### Hydraulic Fracturing Summit VIII

Mitchell, S.L., Kuske, R., Peirce, A.P. (2008) Hydraulic Fracturing Summit VIII.

### SANUM, 2007

Mitchell, S.L. and Myers, T.G. (2007) SANUM, 2007.

### SIAM Annual Meeting

Mitchell, S.L., Kuske, R., Peirce, A.P. (2006) SIAM Annual Meeting.

### Hydraulic Fracturing Summit V

Mitchell, S.L., Kuske, R., Peirce, A.P. (2005) Hydraulic Fracturing Summit V.

## Conference Contributions

## Published Reports

## Editorials

## Book Reviews

## Other Publications

### Evaporative cooling and the Mpemba effect (vol 46, pg 881, 2010)

Vynnycky, M; Mitchell, SL; Maeno, N (2011) Evaporative cooling and the Mpemba effect (vol 46, pg 881, 2010). Heat And Mass Transfer :863-863

### The laminar-turbulent transition of yield stress fluids in large pipes

Mitchell, SL; Myers, TG (2007) The laminar-turbulent transition of yield stress fluids in large pipes.