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
Formula: Pr = μCₚ/k = 0.000e+0 × 0 / 0.000
Physical meaning: Ratio of momentum diffusivity to thermal diffusivity
Interpretation Guide
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
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.