Q $3.(8$ pts$)$ A thick slab made of brick material is initially at $400$ K $.$ Large quantity of water at $300$ K is sprayed on top of the slab which makes the surface temperature of the slab to reach the same temperature as the water. Using the data given, answer the followings:

$[$Data: for common brick: $=1920K\frac{g}{m^3}$;$Cp=835\frac{J}{C}hg.$;$k=0\mathrm{.}72\frac{W}{m}.K)$

$($a$)(3$ pts$.)$ Calculate the surface heat flux after an hour

$($b$)(5$ pts$.)$ Calculate the time $($in hours$)$ it will take the temperature, $5$ cm below the slab surface, to reach $380$ K $?$