Nusselt Number Calculator
Calculate heat transfer enhancement between convection and conduction
Calculate Nusselt Number
Nusselt Number Results
Formula used: Nu = hc × L / kf
Parameters: hc = 100 W/(m²⋅K), L = 0.1 m, kf = 0.6 W/(m⋅K)
Forced Convection: Strong convective enhancement typical of forced convection
Interpretation
Example Calculation
Heat Exchanger Pipe Example
Application: Natural gas pipe heated by water
Reynolds number (Re): 10140 (turbulent flow)
Prandtl number (Pr): 1.0
Geometry: Pipe heating scenario
Calculation
Nu = 0.023 × Re^0.8 × Pr^0.4
Nu = 0.023 × 10140^0.8 × 1.0^0.4
Nu = 0.023 × 1636.7 × 1.0
Nu = 37.6
Convection enhances heat transfer by 37.6 times compared to pure conduction
Nusselt Number Ranges
Nu = 1
Pure conduction
Nu = 1-10
Natural convection range
Nu > 10
Forced convection
Common Applications
Heat exchanger design in boilers
Cooling system optimization
HVAC system design
Electronic component cooling
Key Correlations
Natural Convection
Vertical plate (laminar): Nu = 0.59 Ra^0.25
Vertical plate (turbulent): Nu = 0.1 Ra^0.33
Forced Convection
Flat plate (laminar): Nu = 0.664 Re^0.5 Pr^0.33
Pipe (turbulent): Nu = 0.023 Re^0.8 Pr^0.4
Understanding the Nusselt Number
What is the Nusselt Number?
The Nusselt number (Nu) is a dimensionless parameter that quantifies the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. It represents the ratio of convective to conductive heat transfer.
Physical Significance
- •Nu = 1: Pure conduction (no convective enhancement)
- •Nu > 1: Convective enhancement of heat transfer
- •Higher Nu indicates more efficient heat transfer
Mathematical Definition
Nu = hc × L / kf
- Nu: Nusselt number (dimensionless)
- hc: Convective heat transfer coefficient (W/m²⋅K)
- L: Characteristic length (m)
- kf: Fluid thermal conductivity (W/m⋅K)
Alternative Definition: Nu = qconv / qcond, where qconv is heat transfer by convection and qcond is heat transfer by conduction alone.
Empirical Correlations
Natural Convection
Nu = C × Ra^n
• Vertical plates: C = 0.59, n = 0.25 (laminar)
• Horizontal cylinders: C = 0.48, n = 0.25 (laminar)
• Ra = Rayleigh number
Forced Convection
Nu = C × Re^m × Pr^n
• Flat plates: C = 0.664, m = 0.5, n = 0.33 (laminar)
• Pipes: C = 0.023, m = 0.8, n = 0.4 (turbulent)
• Re = Reynolds number, Pr = Prandtl number