Air at \(40^{\circ} \mathrm{C}\) flows over a long, \(25 \mathrm{~mm}\) diameter cylinder with an embedded electrical heater. Measurements of the effect of the free stream velocity, \(v_{\infty}\), on the power per unit length, \(P^{\prime}\), required to maintain the cylinder surface temperature at \(300^{\circ} \mathrm{C}\) yield the following results:

a. Determine the convection coefficient for each of the test conditions in the table. Plot them.

b. For the corresponding Reynolds number range, determine suitable constants \(C\) and \(m\) for use with the empirical correlation:
\[\overline{N u_{d}}=C \operatorname{Re}_{d}^{m} \operatorname{Pr}^{1 / 3}\]

Transcribed Image Text:

v.. (m/s) 1 2 4 8 P' (W/m) 450 658 983 1507 12 1963