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Rayleigh Number Using Thermal Diffusivity

The Rayleigh number for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection.

The Rayleigh number equals the product of accceleration due to gravity, the characteristic length cubed, the coefficient of thermal expansion and the temperature difference divided by the thermal diffusivity and the kinematic viscosity.

Formula

QuantityVariable[Subscript["Ra", "1"], "RayleighNumber1"] == (Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable["l", "Length"]^3*QuantityVariable["α", "ThermalExpansionCoefficient"]*QuantityVariable["Δ​T", "TemperatureDifference"])/(QuantityVariable["ν", "KinematicViscosity"]*QuantityVariable[Subscript["α", "td"], "ThermalDiffusivity"])

symbol description physical quantity
Ra1 Rayleigh number "RayleighNumber1"
l characteristic length "Length"
α coefficient of thermal expansion "ThermalExpansionCoefficient"
Δ​T temperature difference "TemperatureDifference"
ν kinematic viscosity "KinematicViscosity"
αtd thermal diffusivity "ThermalDiffusivity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Rayleigh Number Using Thermal Diffusivity"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject["Rayleigh Number Using Thermal Diffusivity"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Rayleigh Number Using Thermal Diffusivity"], {QuantityVariable[ "\[Nu]","KinematicViscosity"] -> Quantity[1, ("Meters")^2/("Seconds")], QuantityVariable["\[Alpha]","ThermalExpansionCoefficient"] -> Quantity[1, 1/("KelvinsDifference")], QuantityVariable["l","Length"] -> Quantity[1, "Meters"], QuantityVariable[ \!\(\*SubscriptBox[\("Ra"\), \("1"\)]\),"RayleighNumber1"] -> 1}]
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