$\backslash (\backslash$underline$\{\backslash$text $\{$ Given: $\}\}\backslash )$ A flat, horizontal automobile hood $(1$ m long by $1$ m wide$)$ undergoes convection by air at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ on its outer surface, while the automobile is driven at $\backslash (20\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ with zero wind speed. Beneath the hood heat is transferred to it from air at $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ forced with a free stream velocity of $\backslash (5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ along the hood's length. The flows on both sides of the hood can be modeled as parallel flow over a flat plate. Also, the film temperature on either side can be estimated by the particular free$-$stream temperature associated with that flow.

Find:

$($a$)$ Sketch the variation of thermal boundary layer thickness with the hood's length on both the outside of the hood and beneath it with zero wind speed. If$,$ in addition to the automobile's motion, a side wind was blowing at $\backslash (20\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ onto the driver's side of the automobile, at what position would thermal boundary layer thickness be largest?

$($b$)$ Determine the average heat transfer coefficient for outside air $\backslash (\backslash$left$(\backslash$bar$\{$h$\}\_\{$o$\}\backslash$right$)\backslash )$ and engine$-$bay air $\backslash (\backslash$left$(\backslash$bar$\{$h$\}\_\{$e b$\}\backslash$right$)\backslash ).$ Consider zero side$-$wind velocity in this part and hereafter.

$($c$)$ Find the total heat$-$transfer rate to the outside air. Heat transfer due to conduction between the hood and the automobile's body can be neglected.

$($d$)$ The hood is washed, leaving a $1$ mm water film on its outer surface. How long must dry air at $\backslash (20\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ blow along the hood's length to dry it completely? Assume that the hood is also at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$