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Brinkman Rheological Number

The Brinkman number is a dimensionless number related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing.

The Brinkman number increases quadratically with the flux velocity, directly with dynamic viscosity, inversely with thermal conductivity and inversely with the reference temperature difference.

Formula

QuantityVariable["Br", "Unitless"] == (QuantityVariable["w", "Speed"]^2*QuantityVariable["η", "DynamicViscosity"])/(QuantityVariable["k", "ThermalConductivity"]*QuantityVariable["Δ​T", "TemperatureDifference"])

symbol description physical quantity
Br Brinkman rheological number "Unitless"
k thermal conductivity "ThermalConductivity"
w flux velocity "Speed"
Δ​T reference temperature difference "TemperatureDifference"
η dynamic viscosity "DynamicViscosity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Brinkman Rheological Number"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Brinkman Rheological Number"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Brinkman Rheological Number"], {QuantityVariable[ "k","ThermalConductivity"] -> Quantity[0.58`, ("Watts")/("KelvinsDifference" "Meters")], QuantityVariable["Br","Unitless"] -> 0.138207`, QuantityVariable[ "\[CapitalDelta]\[InvisibleSpace]T","TemperatureDifference"] -> Quantity[0.5`, "KelvinsDifference"]}]
Out[3]=

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