Library / Heat Transfer / HTR-07

Heat Transfer

Prandtl number

Ratio of momentum diffusivity to thermal diffusivity of a fluid.

Ref: HTR-07
Rev: v1
Field: Heat Transfer
Result: Pr

\Pr = \frac{ν}{α_{f}}

For Nusselt and Prandtl numbers use fluid properties. Air has Pr near 0.7, water near 7 at room temperature and oils far above 100. ν and α are in the same units (here 10⁻⁶ m²/s).

Prandtl number says whether heat or momentum spreads faster through a fluid.

Calculator

Solve for

PrPrandtl numberComputed

νKinematic viscosity

10⁻⁶ m²/s

0.110,000

α_fThermal diffusivity

10⁻⁶ m²/s

0.011,000

Boundary-layer thickness ratio δ/δ_t ≈ Pr^(1/3)0.8883
α/ν1.427

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Prandtl number () current value 0.7009

α_fThermal diffusivityKey driver

0.01571,570

νKinematic viscosity

0.00446446

Air has Pr ≈ 0.7, so the thermal boundary layer is slightly thicker than the velocity layer.
Liquid metals have very low Pr, oils very high.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing ()	Local step	Change in result
α_f Thermal diffusivity	0.01 to 1,000 10⁻⁶ m²/s	0.0157	1,570	1,570	+10%	−9.09 %
ν Kinematic viscosity	0.1 to 10,000 10⁻⁶ m²/s	0.004464	446.4	446.4	+10%	+10 %

Sweep of Kinematic viscosity

Kinematic viscosity (10⁻⁶ m²/s)	Prandtl number
0.1	0.004464
0.4217	0.01883
1.778	0.07939
7.499	0.3348
31.62	1.412
133.4	5.953
562.3	25.1
2,371	105.9
10,000	446.4

Sweep one variable

Vary

Prandtl number ()Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

Prandtl number

Result ·

What the equation gives you. Everything else feeds it.

Kinematic viscosity

10⁻⁶ m²/s · typical 0.1 to 10,000

Kinematic viscosity (air 15.7, water 1.0). Directly proportional.

α_f

Thermal diffusivity

10⁻⁶ m²/s · typical 0.01 to 1,000

Thermal diffusivity (air 22.4, water 0.14). Inversely proportional.

Worked example with the values above

ν = 15.7×10⁻⁶ m²/s; α_f = 22.4×10⁻⁶ m²/s.
Divide: 15.7 / 22.4.
Pr = 0.7009.

Assumptions and limits

Fluid properties at the film temperature.
Same units for ν and α.

Common mistakes

Mixing m²/s and mm²/s.
Using Pr of a different fluid.

Statistics and uncertainty

Fluid properties vary with temperature, so state the reference temperature.

Where it is used

Selecting heat-transfer correlations.
Comparing coolants.

Maths you need

Kinematic viscosity: ν = μ/ρ
Thermal diffusivity: α = k/ρcp

Related formulas

Practise this formula