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Rayleigh Number Using Thermal Conductivity

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 specific heat capacity, the characteristic length cubed, the coefficient of thermal expansion, temperature difference and the mass density squared divided by the thermal conductivity and the dynamic viscosity.

Formula

QuantityVariable[Subscript["Ra", "1"], "RayleighNumber1"] == (Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable["c", "SpecificHeatCapacity"]*QuantityVariable["l", "Length"]^3*QuantityVariable["α", "ThermalExpansionCoefficient"]*QuantityVariable["Δ​T", "TemperatureDifference"]*QuantityVariable["ρ", "MassDensity"]^2)/(QuantityVariable["k", "ThermalConductivity"]*QuantityVariable["η", "DynamicViscosity"])

symbol description physical quantity
Ra1 Rayleigh number "RayleighNumber1"
c specific heat capacity "SpecificHeatCapacity"
k thermal conductivity "ThermalConductivity"
l characteristic length "Length"
α coefficient of thermal expansion "ThermalExpansionCoefficient"
Δ​T temperature difference "TemperatureDifference"
η dynamic viscosity "DynamicViscosity"
ρ mass density "MassDensity"

Forms

Examples

Get the resource:

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

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

In[3]:=
FormulaData[ ResourceObject[ "Rayleigh Number Using Thermal Conductivity"], {QuantityVariable[ "k","ThermalConductivity"] -> Quantity[1, ("Watts")/("KelvinsDifference" "Meters")], QuantityVariable["l","Length"] -> Quantity[1, "Meters"]}]
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