Why is Pr important for heat transfer?

Pr appears in all forced-convection Nusselt number correlations. It determines the relative effectiveness of convective heat transfer. Nu ∝ Pr^n where n is typically 1/3 to 0.4.

What does Pr = 1 mean?

When Pr = 1, velocity and thermal boundary layers have equal thickness. Heat and momentum diffuse at the same rate. This is nearly true for gases (air: Pr = 0.71).

Why do liquid metals have very low Pr?

Liquid metals have high thermal conductivity (due to free electrons) and low viscosity, giving α >> ν. The thermal boundary layer extends far beyond the velocity boundary layer.

How does temperature affect Pr for water?

Water Pr drops dramatically with temperature: Pr ≈ 13 at 0°C, 7 at 20°C, 3 at 60°C, 1.75 at 100°C. This is mostly because viscosity decreases while k increases.

What is the Prandtl number of air?

Air has Pr ≈ 0.71 at room temperature and this barely changes with temperature (0.70-0.72 from 0 to 400°C). This is because µ, Cp, and k all change similarly with temperature for gases.

How does Pr relate to the Schmidt number?

The Schmidt number (Sc = ν/D) is the mass transfer analog of Pr. Their ratio is the Lewis number: Le = Sc/Pr = α/D. When Le = 1, heat and mass transfer are analogous.

Prandtl Number Calculator

Calculate the Prandtl number from fluid properties. Compare thermal and momentum diffusivities, boundary layer ratios, and regime classification for heat transfer analysis.

Dynamic Viscosity µ (mPa·s / cP)

Specific Heat Cp (J/kg·K)

Thermal Conductivity k (W/m·K)

Density ρ (kg/m³)

Prandtl Number

7.0073

Pr = µCp/k = ν/α

Thermal Diffusivity

1.433e-7 m²/s

α = k/(ρCp)

Kinematic Viscosity

1.004e-6 m²/s

ν = µ/ρ

BL Thickness Ratio

1.91

δ_v / δ_T ≈ Pr^(1/3)

Regime

ν > α

Water-like — momentum diffuses faster than heat

Pr Interpretation

Momentum leads

Water-like

Prandtl Number Scale (log)

Pr = 7.01 (10⁻² to 10⁴)

Liquid metalsGasesWaterOilsGlycerin

Prandtl Numbers of Common Fluids

Fluid	Pr	α (m²/s)	ν (m²/s)	Type
Air (20°C)	0.71	22.1×10⁻⁶	15.1×10⁻⁶	Gas
Water (20°C)	7.01	0.143×10⁻⁶	1.004×10⁻⁶	Liquid
Water (100°C)	1.75	0.169×10⁻⁶	0.294×10⁻⁶	Liquid
Mercury	0.025	4.53×10⁻⁶	0.113×10⁻⁶	Liquid metal
Engine oil	2000	0.084×10⁻⁶	170×10⁻⁶	Viscous liquid
Sodium (liquid)	0.005	6.7×10⁻⁵	3.3×10⁻⁷	Liquid metal
Glycerin	12500	0.095×10⁻⁶	1180×10⁻⁶	Very viscous

Planning notes, formulas, and examples

About the Prandtl Number Calculator

The Prandtl number (Pr = ν/α = µCp/k) is a dimensionless number that compares momentum diffusivity (kinematic viscosity ν) to thermal diffusivity (α). It tells you the relative thickness of the velocity and thermal boundary layers and determines which Nusselt number correlation to use.

For gases (Pr ≈ 0.7), heat and momentum diffuse at similar rates and boundary layers have similar thickness. For water (Pr ≈ 7), momentum diffuses faster — the velocity boundary layer is thicker. For oils (Pr > 100-1000), the thermal boundary layer is much thinner than the velocity boundary layer.

This calculator computes Pr from viscosity, specific heat, and thermal conductivity. It also calculates the thermal diffusivity, kinematic viscosity, and boundary layer thickness ratio (δ_v/δ_T ≈ Pr^(1/3)). Preset buttons load properties for water, air, engine oil, mercury, and ethylene glycol.

A reference table lists Prandtl numbers for seven common fluids from liquid metals (Pr ≈ 0.01) to glycerin (Pr ≈ 12,500), spanning five orders of magnitude.

When This Page Helps

The Prandtl number is the first thing you need to know when selecting a Nusselt correlation for heat transfer analysis. This calculator derives it directly from fluid properties.

The boundary layer regime classification and visual scale help build intuition for how different fluids behave in convective heat transfer, especially when you are comparing air, water, oils, or liquid metals under the same thermal boundary condition.

How to Use the Inputs

Enter the dynamic viscosity in mPa·s (centipoise).
Enter the specific heat capacity Cp in J/(kg·K).
Enter the thermal conductivity k in W/(m·K).
Enter the fluid density.
Read the Prandtl number and boundary layer regime.
Use presets for common fluids at standard temperatures.

Formula used

Pr = µCp/k = ν/α.
Thermal diffusivity: α = k/(ρCp).
Kinematic viscosity: ν = µ/ρ.
BL ratio: δ_v/δ_T ≈ Pr^(1/3).

Example Calculation

Result: Pr = 7.01, α = 1.43×10⁻⁷ m²/s, ν = 1.00×10⁻⁶ m²/s

Pr = 0.001002 × 4182 / 0.598 = 7.01. Water at 20°C: momentum diffuses ~7× faster than heat. BL ratio = 7.01^(1/3) = 1.91.

Tips & Best Practices

For gases, Pr ≈ 0.7 and barely changes with temperature — you can often use a constant value.
For water, Pr is strongly temperature-dependent — always use the value at the correct temperature.
For liquid metals (Na, Pb-Bi), standard Nusselt correlations fail — you need special low-Pr correlations.
The Eckert number (Ec = V²/(Cp·ΔT)) determines when viscous dissipation (frictional heating) matters.
Pr appears in natural convection too: Nu ∝ (Gr·Pr)^n where Gr is the Grashof number.

Interpreting Pr

Prandtl number links momentum transport to heat transport. Low-Pr fluids spread heat quickly relative to momentum, while high-Pr fluids keep the thermal boundary layer thin compared with the velocity layer.

Why It Matters

Most forced-convection correlations include Pr explicitly, so picking the right value changes the predicted heat-transfer coefficient. That is especially important when switching between gases, water, oils, and liquid metals.

Practical Use

Use this calculator to decide whether a correlation fits the fluid regime you are working in, and to compare how temperature changes shift the transport balance. For design work, the value is only useful when paired with the correct fluid properties at the right temperature.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

Pr appears in all forced-convection Nusselt number correlations. It determines the relative effectiveness of convective heat transfer. Nu ∝ Pr^n where n is typically 1/3 to 0.4.