A fluid flows through a square tube with side length s $=5$ cm$,$ length L$,$ and a constant surface temperature Ts $=50$C$.$ The average convection coefficient on the inside of the tube h $=150$ W$/$m$2-$K$.$ The fluid enters the tube with Tm$,$i $=15$C$,=0\mathrm{.}027$ kg$/$s$,$ and has a heat capacity cp $=4000$ J$/$kg$-$K$.$ a$.$ Determine the length of the tube L if the mean fluid outlet temperature must be at least $30$C$.$ b$.$ Determine the total heat transfer into the fluid q using the values from part a$.$ c$.$ Sketch the local heat flux into the fluid $$s $()$ as a function of position in the tube x using values from part a$.$ On your plot, label the values $$s $$ at x $=0$ and x $=$ L