Problem $4\mathrm{.}16$ An organic fluid that is initially at a temperature of $10\backslash$deg C is heated to an exit

mean temperature of $50\backslash$deg C by passing it through a uniformly heated pipe with

$12$ mm diameter and length of $2$ m $.$ The flow is hydrodynamically fully

developed before it enters the heated segment. The mass flow rate of the fluid is

$0\mathrm{.}1$k$($g$)/($s$).$ The properties of the fluid are as follows:

Pr$=10,\backslash$rho $=800$k$($g$)/($m$^(3)),$k$=0\mathrm{.}12($W$)/($m$)*$K$,\backslash$mu $=0\mathrm{.}008$k$($g$)/($m$)*$s$.$

a$.$ Calculate the local Nusselt number and heat transfer coefficient at $1$ cm and $10$ cm

downstream from the location where heating is initiated.

b$.$ Assuming thermally developed flow everywhere, calculate and plot the mean fluid

temperature with distance along the pipe.