A $0\mathrm{.}2-$m$-$long and $25-$mm$-$thick vertical plate $)=(15\frac{W}{m}*K$ separates the hot water from the cold water. The plate surface exposed to

the hot water has a temperature of $100C,$ and the temperature of the cold water is $7C.$ Determine the temperature of the plate

surface exposed to the cold water $(T_{s,C}).$ Start the iteration process with an initial guess of $53\mathrm{.}5C$ for the $T_{s,c}.$ Given that $Pr=5\mathrm{.}502.$

Given: The properties of water at $T_{f,C}=30\mathrm{.}25C.$

$k=0\mathrm{.}6033\frac{W}{m}*K,$

$=995\mathrm{.}5k\frac{g}{m^3},$

$=0\mathrm{.}0007935k\frac{g}{m}*s,$

$=0\mathrm{.}0003072K^{-1}$

The thermal conductivity of the plate is given as $k_{\text{p}\text{l}\text{a}\text{t}\text{e}}=15\frac{W}{m}*K.$

The temperature of the plate surface exposed to the cold water is