When is it useful?
Prandtl number compares momentum diffusivity with thermal diffusivity. It helps describe the relative behavior of velocity and thermal boundary layers in a fluid.
Formula and inputs
Enter dynamic viscosity μ in Pa·s, constant-pressure specific heat cₚ in J/(kg·K), and thermal conductivity k in W/(m·K), all evaluated at a consistent state. The equivalent form Pr = ν/α uses kinematic viscosity ν and thermal diffusivity α.
Open this calculatorWorked example
For illustrative properties μ = 0.001 Pa·s, cₚ = 4180 J/(kg·K), and k = 0.6 W/(m·K), Pr = 0.001 × 4180 ÷ 0.6 ≈ 6.97. These sample values do not replace design-property tables.
Interpreting the result
A value above 1 means momentum diffusivity exceeds thermal diffusivity under this definition. Pr by itself does not determine the convective coefficient or heat-transfer rate.
Limits and cautions
All three properties can depend on temperature. Do not mix values taken at different states or substitute kinematic viscosity ν for dynamic viscosity μ.
Formula and concept reference: MIT — Introduction to Engineering Heat Transfer. We created the sample inputs and calculations for this guide.