### 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

### Publications

#### 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

* In Journal Of Computational And Applied Mathematics;*
pp. 259-274

**DOI:** 10.1016/j.cam.2015.12.021

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

* In Microfluidics And Nanofluidics;*
pp. 233-243

**DOI:** 10.1007/s10404-014-1423-x

The oxygen diffusion problem: Analysis and numerical solution

Mitchell, SL,Vynnycky, M

(2015)
The oxygen diffusion problem: Analysis and numerical solution

* In Applied Mathematical Modelling;*
pp. 2763-2776

**DOI:** 10.1016/j.apm.2014.10.068

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

* In Applied Mathematics And Computation;*
pp. 1122-1139

**DOI:** 10.1016/j.amc.2015.07.011

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

* In Journal Of Computational And Applied Mathematics;*
pp. 58-73

**DOI:** 10.1016/j.cam.2014.11.051

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

* In Journal Of Computational And Applied Mathematics;*
pp. 98-109

**DOI:** 10.1016/j.cam.2014.08.023

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

* In Journal Of Glaciology;*
pp. 825-836

**DOI:** 10.3189/2015Jo14J235

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

* In Applied Mathematical Modelling;*
pp. 4396-4408

**DOI:** 10.1016/j.apm.2014.02.021

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

* In Siam Journal On Applied Mathematics;*
pp. 697-723

**DOI:** 10.1137/120899200

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

* In Applied Mathematics And Computation;*
pp. 20-37

**DOI:** 10.1016/j.amc.2013.10.030

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

* In Journal Of Computational And Applied Mathematics;*
pp. 49-64

**DOI:** 10.1016/j.cam.2014.01.003

Reaction front formation in contaminant plumes

Cribbin, LB,Winstanley, HF,Mitchell, SL,Fowler, AC,Sander, GC

(2014)
Reaction front formation in contaminant plumes

* In Journal Of Contaminant Hydrology;*
pp. 12-21

**DOI:** 10.1016/j.jconhyd.2014.10.006

One-dimensional solidification of supercooled melts

Font, F,Mitchell, SL,Myers, TG

(2013)
One-dimensional solidification of supercooled melts

* In International Journal Of Heat And Mass Transfer;*
pp. 411-421

**DOI:** 10.1016/j.ijheatmasstransfer.2013.02.070

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

* In Numerical Heat Transfer Part B-Fundamentals;*
pp. 275-292

**DOI:** 10.1080/10407790.2013.797312

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

* In Applied Mathematics And Computation;*
pp. 376-388

**DOI:** 10.1016/j.amc.2012.06.026

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

* In International Communications In Heat And Mass Transfer;*
pp. 1522-1525

**DOI:** 10.1016/j.icheatmasstransfer.2012.09.005

Applying the combined integral method to one-dimensional ablation

Mitchell, SL

(2012)
Applying the combined integral method to one-dimensional ablation

* In Applied Mathematical Modelling;*
pp. 127-138

**DOI:** 10.1016/j.apm.2011.05.032

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

* In Journal Of Computational And Applied Mathematics;*
pp. 4181-4192

**DOI:** 10.1016/j.cam.2012.05.011

AN ACCURATE NODAL HEAT BALANCE INTEGRAL METHOD WITH SPATIAL SUBDIVISION

Mitchell, SL

(2011)
AN ACCURATE NODAL HEAT BALANCE INTEGRAL METHOD WITH SPATIAL SUBDIVISION

* In Numerical Heat Transfer Part B-Fundamentals;*
pp. 34-56

**DOI:** 10.1080/10407790.2011.588133

Application of the combined integral method to Stefan problems

Myers, TG; Mitchell, SL

(2011)
Application of the combined integral method to Stefan problems

* In Applied Mathematical Modelling;*
pp. 4281-4294

**DOI:** 10.1016/j.apm.2011.02.049

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

* In Applied Mathematics And Computation;*
pp. 9219-9233

**DOI:** 10.1016/j.amc.2011.03.161

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

* In Siam Review;*
pp. 57-86

**DOI:** 10.1137/080733036

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

* In International Journal Of Heat And Mass Transfer;*
pp. 3540-3551

**DOI:** 10.1016/j.ijheatmasstransfer.2010.04.015

Evaporative cooling and the Mpemba effect

Vynnycky, M; Mitchell, SL

(2010)
Evaporative cooling and the Mpemba effect

* In Heat And Mass Transfer;*
pp. 881-890

**DOI:** 10.1007/s00231-010-0637-z

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

* In Applied Mathematics And Computation;*
pp. 1609-1621

**DOI:** 10.1016/j.amc.2009.07.054

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

* In Thermal Science;*
pp. 113-119

**DOI:** 10.2298/TSCI0902113M

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

* In 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

* In Applied Mathematics And Computation;*
pp. 311-326

**DOI:** 10.1016/j.amc.2008.02.031

Heat balance integral method for one-dimensional finite ablation

Mitchell, SL; Myers, TG

(2008)
Heat balance integral method for one-dimensional finite ablation

* In Journal Of Thermophysics And Heat Transfer;*
pp. 508-514

**DOI:** 10.2514/1.31755

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

* In Physics Of Fluids;*

**DOI:** 10.1063/1.2990751

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

* In Journal Of Applied Mechanics;*
pp. 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

* In International Journal Of Heat And Mass Transfer;*
pp. 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

* In S.I.A.M. Journal Of Applied Mathematics;*
pp. 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

* In Siam Journal On Scientific Computing;*
pp. 1202-1225

#### 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

pp. 1450-1452

AIP Conference Proceedings

Mitchell S.L., Myers T.G.

(2009)
AIP Conference Proceedings

pp. 1450-1452

**DOI:** 10.1063/1.3241367

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

#### 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)

* In Heat And Mass Transfer;*
pp. 863-863

**DOI:** 10.1007/s00231-010-0759-3

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

(Ed.)