$($Problem $2\mathrm{.}10,$ Thomson text, Chapter $2)($Points: $15)$ Liquid sodium is being used

as a heat transfer fluid and, in one application, the temperature distribution in the

flow direction $($z$-$direction$)$ has been empirically fit to give $T=100-10z^2,$ where

$T$ is in degrees Fahrenheit and $z$ is in feet. If the fluid is moving at a velocity of $0\mathrm{.}1$

$f\frac{t}{s},$ compare the magnitude of the molecular energy flux in the z$-$direction to that

of the convective energy flux in the $z-$direction at a position $z=1ft.$ Assume an

enthalpy reference temperature of $0F.\{$Fluid properties: hat$(c{)}_p=0\mathrm{.}3$kca$\frac{l}{k}g-K$;$=$

$\{$:$0\mathrm{.}8\frac{g}{c}{m}^3,k=85\frac{w}{m}-K)$