18. Forced Convection - for Turbulent Flow inside Circular Pipe

Dittus-Boelter equation (1930) \[{\boxed{\text{Nu} = 0.023\; \text{Re}^{0.8}\;\text{Pr}^{n} }}\] where \[n = \left\{ \begin{array}{l} \text{0.3 for cooling of the fluid ($T_s < T_\infty$)} \\ \text{0.4 for heating of the fluid ($T_s > T_\infty$)} \end{array} \right.\]

The Dittus-Boelter equation is valid for smooth pipes and for \[0.6 \le \text{Pr} \le 160 \qquad \quad \text{Re} \ge 10,000 \qquad \quad \frac{L}{D} \ge 10\]

The Dittus-Boelter equation is recommended only for rather small temperature differences between the bulk fluid and the pipe wall. A few years later, in 1936, Sieder and Tate proposed the following equation to accommodate larger temperature differences: \[{\boxed{\text{Nu} = 0.023\; \text{Re}^{0.8}\;\text{Pr}^{1/3}\; (\mu/\mu_w)^{0.14} }}\] where

\(\mu\) = viscosity of the fluid at the fluid bulk temperature
\(\mu_w\) = viscosity of the fluid at the pipe wall temperature

Valid for: \[0.7 \le \text{Pr} \le 16,700 \qquad \quad \text{Re} \ge 10,000 \qquad \quad \frac{L}{D} \ge 10\] Both the Dittus-Boelter and Seider-Tate equations are still in widespread use.