Question $6[12$ marks$]$

Hot engine oil at $80C$ flows over the upper surface of a $10$ m long flat plate whose temperature is $30C$ with a velocity of $2\mathrm{.}5\frac{m}{s}.$ The width of the plate is $3\mathrm{.}5$ m $.$

The properties of engine oil at the film temperature of $T_f=\frac{80+30}{2}=80C$ are: $=867k\frac{g}{m^3}$; $v=7\mathrm{.}04{10}^{-5}\frac{m^2}{s}$;$k=0\mathrm{.}1414\frac{W}{m}.C$;$Pr=1551.$

Determine:

a$)$ The total drag force $[6]$

b$)$ The rate of heat transfer of the plate $[6]$