Example $12\mathrm{.}7$ Many early reactors were built with flat plate aluminum fuel elements. Calculate the film heat transfer coefficient and coefficient of friction for flow across a flat plate $0\mathrm{.}5$ meter in length at a water velocity of $1\mathrm{.}5\frac{m}{s}.$ The bulk water temperature is $350$ K $,$ and the fuel plate surface temperature is $365$ K $.$ Assume a constant heat flux from the plate.

Solution Evaluating the water properties at the mid$-$film temperature $357\mathrm{.}5$ K :

$=973\mathrm{.}7-\frac{357\mathrm{.}5-350}{400-350}(973\mathrm{.}7-937\mathrm{.}2)=973\mathrm{.}7-{0\mathrm{.}15}^{**}36\mathrm{.}5=968\mathrm{.}2k\frac{g}{m^3}$

$C_p=4195\mathrm{.}0+{0\mathrm{.}15}^{**}(4256-4195)=4204\mathrm{.}2\frac{J}{k}\frac{g}{K}$

$=3\mathrm{.}43E-04-{0\mathrm{.}15}^{**}(3\mathrm{.}43-2\mathrm{.}17)E-04=3\mathrm{.}24E-04N**\frac{s}{m^2}$

$k=0\mathrm{.}668+{0\mathrm{.}15}^{**}(0\mathrm{.}688-0\mathrm{.}668)=0\mathrm{.}672\frac{W}{m}\frac{?}{K}$