Question $4-(15$ Points$)$: These are conceptual questions that you should be able to answer without

the need of equations or diagrams $($except when required$).$ However, you are free to use both

equations and diagrams as needed to provide an answer or make your point clear.

a$.(8$ points$)$ A rectangular flat plate is placed onto a free stream flow in two different orientations

as depicted below. If the plate is at a constant surface temperature T$\_($s$)>$ T$\_($oo$),$ and the flow remains

laminar throughout the whole plate in both configurations, which orientation results in a higher

overall heat transfer rate from the plate into the flow and why?

Orientation $1$

Orientation $2$

$7$ points$)$ Sketch the mixed mean temperature Tm as a function of axial location x along a

circular pipe with constant surface temperature Ts for the following two conditions: $($i$)$

thermally fully develop conditions throughout the whole length of pipe L$,$ and $($ii$)$ thermally

developing conditions over a finite but appreciable portion of the pipe length L$.$ Show both

mixed mean temperature $($Tm$)$ progressions for $($i$)$ and $($ii$)$ as a function of x in the same graph

below and explain your reasoning for their behaviors. You can assume that the flow remains

laminar throughout L in both cases and that the mass flow rate and specific heat capacity of

the fluid cp are the same. Also, and as depicted in the graph below, Tm$,$i $$ Ts$.$ For the first case

$($i$),$ how long should the circular pipe be $($i$.$e$.,$ what should be the value of L$)$ in order to ensure

$99\%$ of heat transfer from the pipe to the fluid?