Prandtl Number Calculator

Calculate the dimensionless Prandtl number for fluid heat transfer analysis

Fluid Properties

Internal resistance to flow (viscosity)

Heat capacity at constant pressure

Ability to conduct heat

Required for diffusivity calculations

Calculation Results

0.000000
Prandtl Number (Pr)
Conduction dominant

Formula: Pr = μCₚ/k = 0.000e+0 × 0 / 0.000

Physical meaning: Ratio of momentum diffusivity to thermal diffusivity

Interpretation Guide

Pr < 1: Heat conduction dominates (metals, liquid metals)
Pr ≈ 1: Balanced heat transfer (gases like air)
Pr > 1: Heat convection dominates (oils, viscous fluids)

Example Calculation

Water at 20°C

Given properties:

• Dynamic viscosity: μ = 1.002 × 10⁻³ Pa·s

• Specific heat: Cₚ = 4184 J/(kg·K)

• Thermal conductivity: k = 0.607 W/(m·K)

Solution

Pr = μCₚ/k = (1.002 × 10⁻³) × 4184 / 0.607

Pr = 4.188 / 0.607 = 6.90

Result: Prandtl number = 6.90

Since Pr > 1, convective heat transfer dominates for water.

Typical Prandtl Numbers

Air (20°C)0.716
Water (20°C)6.90
Engine Oil6280
Mercury0.024
Liquid Sodium0.004

Physical Significance

🌊

Relates momentum transport to heat transport

🔥

Determines dominant heat transfer mechanism

📏

Ratio of velocity boundary layer to thermal boundary layer thickness

⚖️

Dimensionless number for heat transfer correlations

Understanding the Prandtl Number

What is the Prandtl Number?

The Prandtl number is a dimensionless quantity that characterizes the relative importance of momentum diffusion to thermal diffusion in a fluid. It relates the rate of momentum transport to the rate of heat transport in fluids.

Key Applications

  • Heat exchanger design
  • Boundary layer analysis
  • Convective heat transfer correlations
  • Fluid flow characterization

Mathematical Definition

Pr = μCₚ/k

Pr = ν/α

  • μ: Dynamic viscosity (Pa·s)
  • Cₚ: Specific heat at constant pressure (J/(kg·K))
  • k: Thermal conductivity (W/(m·K))
  • ν: Kinematic viscosity (m²/s)
  • α: Thermal diffusivity (m²/s)

Note: The Prandtl number varies with temperature and pressure for most fluids, affecting heat transfer characteristics.