Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Brinkman 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 characteristic speed, directly with dynamic viscosity, inversely with thermal conductivity and inversely with the difference between the temperature of the wall and the fluid.

Formula

QuantityVariable["Br", "BrinkmanNumber"] == (Quantity[1, "Kelvins"/"KelvinsDifference"]*QuantityVariable["v", "Speed"]^2*QuantityVariable["η", "DynamicViscosity"])/(QuantityVariable["k", "ThermalConductivity"]*(-QuantityVariable[Subscript["T", "f"], "Temperature"] + QuantityVariable[Subscript["T", "w"], "Temperature"]))

symbol description physical quantity
Br Brinkman number "BrinkmanNumber"
k thermal conductivity "ThermalConductivity"
v characteristic speed "Speed"
η dynamic viscosity "DynamicViscosity"
Tf temperature of fluid "Temperature"
Tw temperature of wall "Temperature"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Brinkman Number"], {QuantityVariable["Br","BrinkmanNumber"] -> 1, QuantityVariable[ \!\(\*SubscriptBox[\("T"\), \("f"\)]\),"Temperature"] -> Quantity[300, "Kelvins"], QuantityVariable["v","Speed"] -> Quantity[1, ("Meters")/("Seconds")], QuantityVariable["k","ThermalConductivity"] -> Quantity[1, ("Watts")/("KelvinsDifference" "Meters")]}]
Out[3]=

Publisher Information