Cylinder (Dia, \(D=10 \mathrm{~cm}\), Length, \(W=100 \mathrm{~cm}\) ) arrays of a heat exchanger with an inline arrangement are exposed to a uniform velocity of \(U=2 \mathrm{~m} / \mathrm{s}\) and temperature \(T_{0}=30^{\circ} \mathrm{C}\). The Nusselt number for a cylinder in this arrangement is given by

\[
N u_{D}=h D / k=0.25 \operatorname{Re}_{D}^{0.63} \operatorname{Pr}^{0.36}
\]

The drag coefficient for the cylinder at this Reynolds number is equal to 0.5 . The cylinder surface temperature is \(50{ }^{\circ} \mathrm{C}\). The working fluid is air with the following average properties. \(ho=1.1267 \mathrm{~kg} / \mathrm{m}^{3} ; k=0.0271 \mathrm{~W} / \mathrm{m}-\mathrm{K} ; \mu=1.91 \times 10^{-5}\) \(\mathrm{kg} / \mathrm{m}-\mathrm{s}\) and \(\operatorname{Pr}=0.711\).

(a) Calculate the entropy generation per cylinder for this arrangement.

(b) If the diameter of the cylinder is reduced by \(50 \%\), what will be the change in entropy generation, keeping all other parameters the same?