The Prandtl number compares momentum diffusivity to thermal diffusivity: Pr = ν / α. It can also be computed using measurable properties: Pr = (μ · cp) / k.
- μ is dynamic viscosity in Pa·s.
- ν is kinematic viscosity in m²/s.
- α is thermal diffusivity in m²/s.
- cp is specific heat in J/(kg·K).
- k is thermal conductivity in W/(m·K).
- Select what you want to solve for from the dropdown.
- Enter known properties and choose units where offered.
- Leave unknown fields empty to avoid conflicts.
- Use density only when converting μ ↔ ν or computing α.
- Press Calculate to show results above the form.
Approximate reference values for quick testing.
| Fluid | Temp | μ (cP) | cp (kJ/kg·K) | k (W/m·K) | Pr |
|---|---|---|---|---|---|
| Air | 25°C | 0.018 | 1.01 | 0.026 | 0.71 |
| Water | 20°C | 1.00 | 4.18 | 0.60 | 6.9 |
| Ethylene glycol | 20°C | 16.1 | 2.42 | 0.25 | 156 |
| Light oil | 25°C | 50 | 2.0 | 0.13 | 770 |
1) What the Prandtl number represents
The Prandtl number, Pr, is a dimensionless ratio that compares how quickly momentum spreads through a fluid versus how quickly heat spreads. In symbols, Pr = ν/α. When Pr is high, velocity gradients smooth out faster than temperature gradients, so thermal boundary layers tend to be thinner than velocity boundary layers.
2) Why engineers track Pr in heat transfer
Most convection correlations include Pr because it controls the coupling between fluid motion and thermal diffusion. For internal flows, it helps predict the Nusselt number and thus the heat transfer coefficient. For external flows, it influences boundary layer thickness and surface temperature response. Using Pr reduces reliance on trial-and-error testing.
3) Property-based form used in practice
In property tables you often have dynamic viscosity μ, specific heat cp, and thermal conductivity k. Then Pr = (μ·cp)/k, which is convenient because it avoids computing α directly. If density is available, you can also link ν = μ/ρ and α = k/(ρ·cp).
4) Typical Pr ranges with reference data
Many gases cluster near unity: dry air at about 25 °C is near Pr ≈ 0.71. Water at 20 °C is much higher, about Pr ≈ 6.9. Glycols and oils can be very large; light oils commonly fall between Pr ≈ 100 and Pr ≈ 1000. Liquid metals are small, often Pr ≈ 0.01–0.1.
5) Temperature effects and why results shift
Pr can change strongly with temperature because viscosity is temperature-sensitive. For liquids, μ usually decreases as temperature rises, so Pr often drops quickly. For gases, μ increases with temperature while k and cp also change, so Pr tends to vary modestly. Always evaluate properties at the film temperature for convection work.
6) How Pr enters common convection correlations
Widely used correlations apply Pr as a power term. For example, the Dittus–Boelter form for turbulent internal flow uses a factor like Pr0.4 (heating) or Pr0.3 (cooling). Natural convection correlations also combine Grashof and Pr into the Rayleigh number, Ra = Gr·Pr.
7) Practical interpretation for design decisions
High-Pr fluids (oils) develop steep temperature gradients near surfaces, which can raise wall temperatures and increase fouling risk. Low-Pr fluids (liquid metals) spread heat rapidly, often requiring different fin and channel strategies. In compact heat exchangers, selecting a fluid with suitable Pr can improve performance per unit pressure drop.
8) Data quality tips for reliable calculations
Keep units consistent: μ in Pa·s, cp in J/(kg·K), and k in W/(m·K). When using ν and α, ensure both are in the same area-per-time units before forming ν/α. If you supply density, use it only to convert between μ and ν or to compute α from k and cp.
1) Is Prandtl number dimensionless?
Yes. Pr is a pure ratio of diffusivities, so units cancel. This makes it useful for comparing different fluids and scaling heat transfer behavior across systems.
2) Which inputs should I use for best accuracy?
Use μ, cp, and k when you have reliable property data at the same temperature. If you only have ν and α, ensure both values are reported for identical conditions.
3) What is a typical Pr value for air and water?
Air near room temperature is usually around 0.7. Water around 20 °C is about 7, though it varies with temperature and dissolved content.
4) Why do oils have very high Pr values?
Oils often have large viscosity and relatively modest thermal conductivity. That combination increases μ·cp and reduces heat diffusion, pushing Pr into the hundreds or higher.
5) Can I compute Pr from ν and α directly?
Yes. If you know kinematic viscosity ν and thermal diffusivity α for the same temperature, Pr = ν/α. Make sure both are converted to matching units first.
6) When should I include density in the calculator?
Provide density when you want to convert μ to ν (or ν to μ) or when you want α computed from k and cp using α = k/(ρ·cp). Otherwise it can be left blank.
7) Does a higher Pr always mean better heat transfer?
Not necessarily. Higher Pr often increases the Pr term in correlations, but viscosity also affects Reynolds number and pumping power. Evaluate the full design, not Pr alone.