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Library / Heat Transfer / HTR-06

Heat Transfer

Nusselt number

Dimensionless heat transfer coefficient comparing convection with conduction in the fluid.

Ref
HTR-06
Rev
v1
Field
Heat Transfer
Result
Nu

Use the fluid conductivity kf and the characteristic length specified by the correlation (diameter for pipes, length for plates). Correlations give Nu from Re and Pr, from which h follows.

The Nusselt number compares heat carried by fluid motion at the surface with what pure conduction through the same fluid layer would carry.

Calculator

Solve for
W/(m²·K)
25,000
m
0.0012
W/(m·K)
0.011
  • Equivalent conduction layer kf/h1.04 mm
  • Heat flux at ΔT = 10 K250 W/m²

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Nusselt number () current value 48.08
hHeat transfer coefficientKey driver
3.859,620
LcCharacteristic length
0.9621,920
kfFluid conductivity
1.25125
  • Nu of 1 would mean conduction only; larger values show convection is boosting the heat transfer.
  • Correlations such as Dittus–Boelter give Nu from Re and Pr, from which h = Nu kf/Lc.
Chart data as tables

Ranked variables

VariableTypical rangeLowest resultHighest resultSwing ()Local stepChange in result
h Heat transfer coefficient2 to 5,000 W/(m²·K)3.8469,6159,612+10%+10 %
Lc Characteristic length0.001 to 2 m0.96151,9231,922+10%+10 %
kf Fluid conductivity0.01 to 1 W/(m·K)1.25125123.8+10%−9.09 %

Sweep of Heat transfer coefficient

Heat transfer coefficient (W/(m²·K))Nusselt number
23.846
5.31810.23
14.1427.2
37.6172.32
100192.3
265.9511.4
707.11,360
1,8803,616
5,0009,615

Sweep one variable

Nusselt number ()Hover, touch, or use the arrow keys on the chart
0200040006000800010k 101001000 Heat transfer coefficient (W/(m²·K)), log scale now 48.08

Variables and how each one contributes

Nu

Nusselt number

Result ·

What the equation gives you. Everything else feeds it.

h

Heat transfer coefficient

W/(m²·K) · typical 2 to 5,000

Surface convection coefficient. Directly proportional.

Lc

Characteristic length

m · typical 0.001 to 2

Length scale used by the correlation. Directly proportional.

kf

Fluid conductivity

W/(m·K) · typical 0.01 to 1

Fluid thermal conductivity (air 0.026, water 0.6). Inversely proportional.

Worked example with the values above

  1. h Lc = 25 × 0.05 = 1.25 W/K per m.
  2. Divide by kf = 0.026.
  3. Nu = 48.08.

Assumptions and limits

  • Fluid properties at the specified reference temperature.
  • Characteristic length consistent with the correlation.

Common mistakes

  • Using the solid’s conductivity.
  • Using the wrong characteristic length.

Statistics and uncertainty

Correlations are good to ±15–25%, so h from Nu inherits this uncertainty.

Where it is used

  • Applying convection correlations.
  • Scaling model tests to full size.

Maths you need

  • Convection coefficient: h
  • Thermal conductivity: k

Related formulas

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