Non-isothermal　melting　phenomenon　widely　exists　in　phase　change　process　where　mixtures　are　utilized　as　phase　change　materials.　It　is　in　the　mushy　zone　that　phase　transition　actually　occurs　during　the　melting　process.　Thus,　an　in-depth　understanding　of　flow　and　heat　transfer　in　the　mushy　zone　can　provide　beneficial　ways　to　improve　melting　technologies.　This　article　focuses　on　the　evolution　of　mushy　zone　for　low-Prandtl　material　under　Neumann　boundary　condition.　A　two-dimensional　model　composed　of　liquid　zone,　mushy　zone,　and　solid　zone　is　established　based　on　the　improved　enthalpy-porosity　method.　The　pressure　and　velocity　are　coupled　with　SIMPLER　algorithm　based　on　the　finite　volume　method　with　a　Fortran　code.　The　results　indicate　that　the　temperature　on　the　heating　surface　is　uneven,　which　are　different　from　the　results　under　Dirac　boundary　condition.　The　existence　of　mushy　zone　can　supply　a　buffer　to　the　unsteady　melting　adjacent　to　the　heating　surface　initially.　And　the　mushy　zone　experiences　expanding　stage　and　shrinking　stage.　More　time　is　needed　for　complete　melting　and　the　average　temperature　on　the　heating　surface　gets　lower　under　greater　melting　temperature　range.　Increasing　Ra　can　result　in　augmentation　of　heat　transfer　in　liquid　domain　and　more　inclined　interface,　and　the　heat　transfer　is　dominated　by　heat　conduction　when　liquid　phase　fraction　is　less　than　20%,　and　thereafter,　it　is　dominated　by　natural　convection.　For　the　same　material,　increasing　heat　flux　obviously　shortens　the　total　melting　time.　And　the　mushy　zone　is　reduced　for　that　greater　temperature　gradient　is　produced　in　the　mushy　area.　©　2020,　©　2020　Taylor　&　Francis　Group,　LLC.