Consider the following fluids, each with a velocity of \(V=3 \mathrm{~m} / \mathrm{s}\) and a temperature of \(T_{\infty}=20^{\circ} \mathrm{C}\), in cross flow over a \(10-\mathrm{mm}\)-diameter cylinder maintained at \(50^{\circ} \mathrm{C}\) : atmospheric air, saturated water, and engine oil.

(a) Calculate the rate of heat transfer per unit length, \(q^{\prime}\), using the Churchill-Bernstein correlation.

(b) Generate a plot of \(q^{\prime}\) as a function of fluid velocity for \(0.5 \leq V \leq 10 \mathrm{~m} / \mathrm{s}\).