I. Why Dimensionless Numbers
Flow velocity, pipe diameter, and properties have different units, so direct comparison is meaningless. Combining them into dimensionless numbers makes them universally applicable across scales and media. The two most fundamental in heat exchange:
II. Reynolds Number Re: The Flow Regime Switch
Re = ρ·v·L / μ = v·L / ν
ρ is density, v is flow velocity, L is the characteristic length (e.g., pipe diameter), μ is dynamic viscosity, ν is kinematic viscosity. Small Re → viscosity-dominated → laminar; large Re → inertia-dominated → turbulent. For circular pipes roughly: Re<2300 laminar, >4000 turbulent. It determines the boundary layer thickness and directly ties to h.
III. Prandtl Number Pr: The "Race" Between Heat and Motion
Pr = ν / α = μ·cp / λ
α is the thermal diffusivity (λ/ρcp). Pr describes which is faster, "momentum diffusion" or "heat diffusion":
- Pr<1 (liquid metals): Heat diffuses faster than momentum, the temperature field spreads wider than the velocity field;
- Pr≈0.7 (air, gases): The two are close;
- Pr>>1 (oils): Momentum diffusion far faster than heat, heat is "trapped" in the boundary layer, poor heat transfer.
IV. How They Are Used
Re and Pr together enter the empirical correlation for the Nusselt number Nu (next article), used to predict h. In other words:
Re governs "how chaotic the flow is," Pr governs "how fast heat transfers," and together they determine the strength of convective heat transfer.
For a new medium, first calculate Re to judge flow regime and Pr to judge heat diffusion characteristics, and you can basically predict whether it exchanges heat well.
Related Reading
- The Bernoulli Equation and Pipeline Pressure Drop: The Energy Ledger of Fluid in a Heat Exchanger
- Boundary Layer and Flow Regime: How Laminar and Turbulent Flow Affect Heat Transfer
- Fluid Thermophysical Properties: The Impact of Density, Viscosity, Specific Heat, and Thermal Conductivity on Heat Transfer