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Nusselt Number for Transitional and Rough Flow in Circular Tube Calculator

Formula

The formula to calculate the Nusselt Number (Nu) is:

$Nu = \frac{\left(\frac{f_{Darcy}}{8}\right) \cdot (Re - 1000) \cdot Pr}{1 + 12.7 \cdot \left(\left(\frac{f_{Darcy}}{8}\right)^{0.5}\right) \cdot \left(Pr^{\frac{2}{3}} - 1\right)}$

Definition

The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion.

Example Calculation

Let's assume the following values:

Darcy Friction Factor (fDarcy) = 0.04
Reynolds Number (Re) = 5000
Prandtl Number (Pr) = 0.7

Using the formula:

$Nu = \frac{\left(\frac{0.04}{8}\right) \cdot (5000 - 1000) \cdot 0.7}{1 + 12.7 \cdot \left(\left(\frac{0.04}{8}\right)^{0.5}\right) \cdot \left(0.7^{\frac{2}{3}} - 1\right)} \approx 17.2849322852078$

The Nusselt Number is approximately 17.2849322852078.

Conversion Chart

Darcy Friction Factor	Nusselt Number
0.03	12.568598604681604
0.032	13.493688345385220
0.034	14.427980704373068
0.036	15.371354888060036
0.038	16.323703814518037
0.04	17.284932285207798
0.042	18.254955484455316
0.044	19.233697735074252
0.046	20.221091456752802
0.048	21.217076286806975