Engine oil at $10C$ flows $(u_{}=0\mathrm{.}5\frac{m}{s})$ across a $15$ cm $-$square plate upon which is imposed a constant heat flux of $10k\frac{W}{m^2}.$ Determine $(a)$ the average temperature difference, $(b)$ the temperature difference at the trailing edge, and $(c)$ the average heat$-$transfer coefficient. Use Churchill relation ${}_x=0\mathrm{.}4637P{r}^{\frac{1}{3}}R\frac{e_x^{\frac{1}{2}}}{(1+(\frac{0\mathrm{.}0207}{P}r{)}^{\frac{2}{3}}{)}^{\frac{1}{4}}}.$ Properties of Oil: $Pr=10400,k=0\mathrm{.}145\frac{W}{m}.K,$

$u=0\mathrm{.}0009\frac{m^2}{s}.$