Bear $1$: $(25$pts$)$ To increase the effectiveness of oil to air heat exchanger, you propose to keep the surface wetted with a film of water. The heat exchanger is modelled as a horizontal tube with a diameter $\backslash (\backslash$mathbf$\{$D$\}\_\{\backslash$mathbf$\{0\}\}=\backslash$mathbf$\{10$ m m$\},\backslash$mathbf$\{$D$\}\_\{\backslash$mathbf$\{$i$\}\}=\backslash$mathbf$\{8$ m m$\}\backslash )$ that is exposed to a crossflow of dry air $\backslash (\backslash$left$(\backslash$mathbf$\{$T$\}\_\{\backslash$infty$\}=\backslash$mathbf$\{300$ K$\},\backslash$mathbf$\{$V$\}=\backslash$mathbf$\{10$ m$\}/\backslash$mathbf$\{$s$\}\backslash$right$)\backslash ).$ If the outer surface of the tube is maintained at $\backslash (\backslash$mathbf$\{$T$\}\_\{\backslash$mathrm$\{$s$\}\}=\backslash$mathbf$\{340$ K$\}\backslash ),$ evaluate the effectiveness of the proposed wetting strategy by comparing the rate of heat transfer with and without the wetted surface. $($Steady state, neglect radiation$)$

a$)$ What is the best temperature to pull the air properties? Use the properties given.

b$)$ Calculate the rates of heat transfer with and without the wetted surface. If you need other properties, do not interpolate or scale to save time. $($watch units $-$ you don't know length$)$