QUESTION $2$

The control room in a chemical power plant is equipped with a blast proof wall

$m.K$ on the external side, aside from the main concrete wall $(k_B=3\mathrm{.}5\frac{W}{m}.K)$ and an insulator

$(k_C=0\mathrm{.}5\frac{W}{m}.K)$ on the inside. On a particularly hot day of $39C,$ the outer surface of the

external wall temperature is measured at $30C,$ while the internal wall temperature inside the

control room is $23C.$ A plant operator sets the air$-$condition in the control room to $16C,$ but

the actual temperature was determined as $20C.$ The blast proof and concrete wall are $30cm$

thick each, while the insulator is $15cm$ thick, and the wall measures at $7m$ in length and $3m$

in height.

a$)$ Calculate the overall heat transfer coefficient and the total heat flux through the wall

considering conduction and convection, assuming the heat transfer occurs only on one side

of the wall. Please include the schematic diagram.

$[20$ Marks$]$

$[$C$01,$ P$01,$ C$4]$

b$)$ How thick should the insulator be$,$ to ensure the control room temperature can be

maintained at $16C?$

$[5$ Marks$]$

$[$C$01,$ P$01,$ C$4]$