Referring to the humidity chart provided at the end of the question, answer the following $-$

$($a$)$ If the heat exchanger achieves $T=20C$ along its total length, what is the allowable

maximum humidity and corresponding percentage humidity of the inlet air such that

these design criteria are satisfied? Assume that the sensible heat capacities $(c_S)$ and

flow rates $(N)$ of the air and the material cooled in the heat exchanger are the same.

$($hints: $1)$ The heat exchanger cannot change humidity; $2)N_{\text{a}\text{i}\text{r}}{c}_{s_{\text{a}\text{i}\text{r}}}{T}_{\text{a}\text{i}\text{r}}=$

$N_{\text{m}\text{a}\text{t}\text{e}\text{r}\text{i}\text{a}\text{l}}{c}_{s_{\text{m}\text{a}\text{t}\text{e}\text{r}\text{i}\text{a}\text{l}}}{T}_{\text{m}\text{a}\text{t}\text{e}\text{r}\text{i}\text{a}\text{l}}-$ what does this tell you about the exit temperature of

the cooling air?$)(5$ points$)$

$($b$)$ In the heat exchanger described above, if the sensible heat capacity of air is $2x$ that of

the material being cooled $($the flow rates are still the same$)($hint: what is the $T$ in this

case?$),$ what is the allowable maximum humidity and corresponding percentage

humidity of the inlet air such that exit humidity is still $80\%?5$ points

$($c$)$ If condensation occurs on the heat exchanger, please list at least one material challenge

that may be encountered over the usable life of the exchanger. $(5$ points$)$

$($d$)$ The plant is designed such that the inlet air stream used in the heat exchanger is the

outlet stream from an adiabatic saturator. The cooling air is first cooled to $50C$ in an

adiabatic saturator $($despite its name, the air exiting an adiabatic saturator need not be

saturated$).$ The Occupational Health and Safety Administration $($OSHA$)$ recommends

that workers may work in environments where they may be exposed to humidity in the

range of $20\%-60\%($minimum and maximum limits$).$ If you were to strictly follow

OSHA guidelines, what is the maximum allowable temperature of the inlet sir stream