# transportCoeffSrc¶

Depending on the value of coeff, the transportCoeffSrc kind of Equation can have different outcomes.

## millikanWhiteParkVibTransRelaxationTime¶

Average relaxtion time for vibration-translation mode of energy of species “l” in a gas mixture

\notag \begin{align} \tau_{l} = \frac{\sum_{m} x_{m}}{\sum_{l,m} x_{m}/\tau_{l,m}} \end{align}
\notag \begin{align} \begin{array}{l} \tau_{l,m}\, \text{is obtained using Millikan-White curvefit as follows}\\ \\ \tau_{l,m} = \frac{1}{P/101325}exp\left[A_{l,m}\left(T^{-1/3}-B_{l,m}\right) - 18.42\right]\\ \text{and}\\ A_{l,m} = 0.00116\mu_{l,m}^{1/2}\theta_{v,l}^{4/3}\\ B_{l,m} = 0.015\mu_{l,m}^{1/4}\\ \mu_{l,m} = \frac{M_{l}M_{m}}{M_{l}+M_{m}}\\ \end{array} \end{align}

### Definitions¶

$$x_{m}$$ mole fraction of species m

$$\tau_{l,m}$$ relaxation time of vibration-translation energy between specis l and m

$$\theta_{v,l}$$ characteristic temperature of vibration of species l (parameter thetaS)

$$M_{m}$$ molecular weight of species m (parameter molecularWeight)

$$T$$ translational temperature

$$P$$ pressure of gas

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
millikanWhiteParkVibTransRelaxationTime (fixed)
numSpecies (int):
number of species
molecularWeight (vector):
molecular weight of species m
thetaS (vector):
characteristic temperature of vibration of species l. This is a material dependent constant that must be user supplied.
function (string):
millikanWhiteParkVibTransRelaxationTime (fixed)

### Parent Updater Data¶

in (string vector, required)

1st In Variable

average temperature of the species $$T$$

2nd In Variable

pressure of gas $$P$$

3rd In Variable

number density of the species $$n$$
out (string vector, required)
the average relaxtion time for vibration-translation mode of energy of species “l” in a gas mixture

### Example¶

<Equation vTrelaxationTime>
kind = transportCoeffSrc
coeff = millikanWhiteParkVibTransRelaxationTime
numSpecies = 7
molecularWeight = [M1 M2 M3 M4 M5 M6 M7]
thetaS = [th1 th2 th3 th4 th5 th6 th7]
function = millikanWhiteParkVibTransRelaxationTime
</Equation>


## mWpAverageVtRelaxationTime¶

Average relaxtion time for vibration-traslation mode of energy of a gas mixture

\notag \begin{align} \tau = \frac{\sum_{l} x_{l}}{\sum_{l} x_{l}/\tau_{l}} \end{align}

### Definitions¶

$$x_{l}$$ mole fraction of species l

$$\tau_{l}$$ relaxtion time for vibration-translation mode of energy of species “l” in a gas mixture as calculated in coeff millikanWhiteParkVibTransRelaxationTime

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
mWpAverageVtRelaxationTime (fixed)
numSpecies (int):
number of species
molecularWeight (vector):
molecular weight of species m
thetaS (vector):
characteristic temperature of vibration of species l. This is a material dependent constant that must be user supplied.
function (string):
mWpAverageVtRelaxationTime (fixed)

### Parent Updater Data¶

in (string vector, required)

1st In Variable

average temperature of the species $$T$$

2nd In Variable

pressure of gas $$P$$

3rd In Variable

number density of the species $$n$$
out (string vector, required)
the average relaxtion time for vibration-traslation mode of energy of a gas mixture

### Example¶

<Equation vTrelaxationTime>
kind = transportCoeffSrc
coeff = mWpAverageVtRelaxationTime
numSpecies = 7
molecularWeight = [M1 M2 M3 M4 M5 M6 M7]
thetaS = [th1 th2 th3 th4 th5 th6 th7]
function = mWpAverageVtRelaxationTime
</Equation>


## binaryDiffusionCoeff¶

Average mass diffusion coefficient of species “l” in a gas mixture

\notag \begin{align} \begin{array}{l} D_{l} = \frac{\sum_{m} x_{m}}{\sum_{l,m} x_{m}/D_{l,m}}\\ D_{l,m}\, \text{is obtained using hard sphere model}\\ D_{l,m} = \frac{2.63\times{-7}}{( P/(101325) \sigma_{l,m})} \left(\frac{T^{3} (M_{l}+M_{m})}{2.0M_{l}M_{m}}\right)^{1/2}\\ \end{array} \end{align}

### Definitions¶

$$x_{m}$$ mole fraction of species m

$$M_{m}$$ molecular weight of species m

$$T$$ translational temperature

$$P$$ pressure of gas

$$\sigma_{l,m}$$ collision diameter between species l and m

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
binaryDiffusionCoeff (fixed)
numSpecies (int):
number of species
molecularWeight (vector):
molecular weight of species m
molecularDia (vector):
molecular diameter of species m
function (string):
binaryDiffusionCoeff (fixed)

### Parent Updater Data¶

in (string vector, required)

1st In Variable

average temperature of the species $$T$$

2nd In Variable

pressure of gas $$P$$

3rd In Variable

number density of the species $$n$$
out (string vector, required)
the average mass diffusion coefficient of species “l” in a gas mixture

### Example¶

<Equation diffusionCoeff>
kind = transportCoeffSrc
coeff = binaryDiffusionCoeff
numSpecies = 7
molecularWeight = [M1 M2 M3 M4 M5 M6 M7]
molecularDia = [d1 d2 d3 d4 d5 d6 d7]
function = binaryDiffusionCoeff
</Equation>


## chemicalEnergy¶

Total energy of formation of a mixture

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
chemicalEnergy (fixed)
numSpecies (int):
number of species
fileName (string):
name of the SpeciesDataFile containing the energy of formation data.

### Parent Updater Data¶

in (string vector, required)

1st In Variable

number densities of the species $$1/m^{3}$$

2nd In Variable

specific heat at constant pressure of the species $$J/(kg K)$$

3rd In Variable

average temperature of the species $$K$$
out (string vector, required)
the energy of formation in $$J/m^3$$

### Example¶

<Updater computeChemEn>
kind = equation2d
onGrid = domain

in = [speciesDens,cpR,temperature]
out = [chemEn]

<Equation cp>
kind = transportCoeffSrc
coeff = chemicalEnergy
numSpecies = NSPECIES
fileName = REACTIONS_ATOMIC_DATA
</Equation>
</Updater>


## tempAvgSpecicHeatCp¶

Specific heat at constant pressure

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
tempAvgSpecicHeatCp (fixed)
numSpecies (int):
number of species
fileName (string):
name of the SpeciesDataFile containing the cp data.
cpType (string):
currently allowed option is kineticTheory, which requires molecular data specified in the SpeciesDataFile. Defaults to Shomate polynomial type specificific heat, whch agian required polynomial data specified in the SpeciesDataFile. In case of using using Shomate polynomial, addition parameters lower, upper and steps should also be specified. These parameters specify the temperature range and the number of intervals to evaluate the specific heats.

### Parent Updater Data¶

in (string vector, required)

1st In Variable

average temperature of the species $$K$$
out (string vector, required)
the specific heat $$J/(kg K)$$

### Example¶

<Updater computeCpR>
kind = equation2d
onGrid = domain

in = [temperature]
out = [cpR]

<Equation cpR>
kind = transportCoeffSrc
coeff = tempAvgSpecicHeatCp
fileName = REACTIONS_ATOMIC_DATA
cpType = kineticTheory
numSpecies = NSPECIES
#lower = 300.0
#upper = 30000.0
#steps = 100
</Equation>
</Updater>


## massFractionAvg¶

Average mass fraction of the species

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
massFractionAvg (fixed)
numSpecies (int):
number of species
fileName (string):
name of the SpeciesDataFile containing the atomic data. Note that, massFractionAvg requires MOLECULARWEIGHT entered in the SpeciesDataFile.

### Parent Updater Data¶

in (string vector, required)

1st In Variable

species number density $$1/m^3$$

2nd In Variable

species property
out (string vector, required)
the average mass fraction

### Example¶

<Updater computeCpAvg>
kind = equation2d
onGrid = domain

in = [speciesDens,cpR]
out = [cpAvg]

<Equation cp>
kind = transportCoeffSrc
coeff = massFractionAvg
numSpecies = NSPECIES
fileName = REACTIONS_ATOMIC_DATA
</Equation>
</Updater>


## moleFractionAvg¶

Average molecular fraction of species

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
moleFractionAvg (fixed)
numSpecies (int):
number of species
fileName (string):
name of the SpeciesDataFile containing the atomic data.

### Parent Updater Data¶

in (string vector, required)

1st In Variable

species number density $$1/m^3$$

2nd In Variable

species property
out (string vector, required)
the average molecular fraction

### Example¶

<Updater computeCpAvg>
kind = equation2d
onGrid = domain

in = [speciesDens,cpR]
out = [cpAvg]

<Equation cp>
kind = transportCoeffSrc
coeff = massFractionAvg
numSpecies = NSPECIES
fileName = REACTIONS_ATOMIC_DATA
</Equation>
</Updater>


## molecularWeightAvg¶

Average molecular weight of species

### Parameters¶

kind (string):
transportCoeffSrc (fixed)
coeff (string):
molecularWeightAvg (fixed)
numSpecies (int):
number of species
fileName (string):
name of the SpeciesDataFile containing the MOLECULARWEIGHT data.

### Parent Updater Data¶

in (string vector, required)

1st In Variable

species number density $$1/m^3$$
out (string vector, required)
the average-molecular-weight

### Example¶

<Updater computeMwAvg>
kind = equation2d
onGrid = domain

in = [speciesDens]
out = [mwAvg]

<Equation mwavg>
kind = transportCoeffSrc
coeff = molecularWeightAvg
numSpecies = NSPECIES
fileName = REACTIONS_ATOMIC_DATA
</Equation>
</Updater>