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Table of Symbols

The symbols used in this document are summarized in the Table of Symbols along with their units. The choice of symbols was made to be consistent with the heat transfer literature and with existing documentation for solar water heating systems. The symbols are listed in alphabetical order. For vector quantities, the units shown are for each component of the vector.

SymbolDescriptionUnits
ACHeating coil surface aream2
ACmaxMaximum surface area of coilm2
AinSurface area over which heat is transferred inm2
AoutSurface area over which heat is transferred outm2
APPhase change material surface aream2
ARAspect ratio
ARmaxMaximum aspect ratio
ARminMinimum aspect ratio
CSpecific heat capacityJkgC
CLSpecific heat capacity of a liquidJkgC
CSSpecific heat capacity of a solidJkgC
CVSpecific heat capacity of a vapourJkgC
CPLSpecific heat capacity of PCM as a liquidJkgC
CPSSpecific heat capacity of PCM as a solidJkgC
CtolRelative tolerance for conservation of energy
CWSpecific heat capacity of waterJkgC
CWmaxMaximum specific heat capacity of waterJkgC
CWminMinimum specific heat capacity of waterJkgC
CPLmaxMaximum specific heat capacity of PCM as a liquidJkgC
CPLminMinimum specific heat capacity of PCM as a liquidJkgC
CPSmaxMaximum specific heat capacity of PCM as a solidJkgC
CPSminMinimum specific heat capacity of PCM as a solidJkgC
DDiameter of tankm
ESensible heatJ
EPChange in heat energy in the PCMJ
EWChange in heat energy in the waterJ
EPmeltinitChange in heat energy in the PCM at the instant when melting beginsJ
gVolumetric heat generation per unit volumeWm3
HfSpecific latent heat of fusionJkg
HfmaxMaximum specific latent heat of fusionJkgC
HfminMinimum specific latent heat of fusionJkgC
hConvective heat transfer coefficientWm2C
hCConvective heat transfer coefficient between coil and waterWm2C
hCmaxMaximum convective heat transfer coefficient between coil and waterWm2C
hCminMinimum convective heat transfer coefficient between coil and waterWm2C
hminMinimum thickness of a sheet of PCMm
hPConvective heat transfer coefficient between PCM and waterWm2C
hPmaxMaximum convective heat transfer coefficient between PCM and waterWm2C
hPminMinimum convective heat transfer coefficient between PCM and waterWm2C
LLength of tankm
LmaxMaximum length of tankm
LminMinimum length of tankm
mMasskg
mPMass of phase change materialkg
mWMass of waterkg
MINFRACTMinimum fraction of the tank volume taken up by the PCM
ˆnUnit outward normal vector for a surface
QLatent heatJ
QPLatent heat energy added to PCMJ
qHeat fluxWm2
qCHeat flux into the water from the coilWm2
qinHeat flux inputWm2
qoutHeat flux outputWm2
qPHeat flux into the PCM from waterWm2
qThermal flux vectorWm2
SSurfacem2
TTemperatureC
ΔTChange in temperatureC
TboilBoiling point temperatureC
TCTemperature of the heating coilC
TenvTemperature of the environmentC
TinitInitial temperatureC
TmeltMelting point temperatureC
TmeltPMelting point temperature for PCMC
TPTemperature of the phase change materialC
TWTemperature of the waterC
tTimes
tfinalFinal times
tfinalmaxMaximum final times
tmeltfinalTime at which melting of PCM endss
tmeltinitTime at which melting of PCM beginss
tstepTime step for simulations
VVolumem3
VPVolume of PCMm3
VtankVolume of the cylindrical tankm3
VWVolume of waterm3
ηODE parameter related to decay rate
πRatio of circumference to diameter for any circle
ρDensitykgm3
ρPDensity of PCMkgm3
ρPmaxMaximum density of PCMkgm3
ρPminMinimum density of PCMkgm3
ρWDensity of waterkgm3
ρWmaxMaximum density of waterkgm3
ρWminMinimum density of waterkgm3
τDummy variable for integration over times
τPLODE parameter for liquid PCMs
τPSODE parameter for solid PCMs
τWODE parameter for water related to decay times
ϕMelt fraction
Gradient

Table of Symbols