15. Flow over Flat Plate

Laminar flow: \[{Nu_x = \frac{h_x x}{k} = 0.332\; \text{Re}_x^{0.5}\; \text{Pr}^{1/3}} \qquad \text{Pr} > 0.6\] Turbulent flow: \[{Nu_x = \frac{h_x x}{k} = 0.03\; \text{Re}_x^{0.8}\; \text{Pr}^{1/3}} \qquad \begin{array}{c} 0.6 \le \text{Pr} \le 60 \\ 5 \times 10^5 \le \text{Re}_x \le 10^7 \end{array}\] Note:

For laminar flow, \(h_x\) is proportional to \(\text{Re}_x^{0.5}\) and thus to \(x^{-0.5}\).

For turbulent flow, \(h_x\) is proportional to \(x^{-0.2}\).