$($b$)$ Water at $22C$ flows through a steel pipe with a velocity of $0\mathrm{.}30m{s}^{-1}.$ The pipe has an inside diameter of $3\mathrm{.}8cm.$ Determine the heat transfer film coefficient, $h,$ based on the inside surface of the pipe. Take density of the water $()$ as $963\mathrm{.}2kg{m}^{-3},$ viscosity $()=3\mathrm{.}06{10}^{-4}kg{m}^{-1}{s}^{-1},$ its thermal conductivity $(k)=0\mathrm{.}678W{m}^{-1}{C}^{-1}$ and the heat capacity, $(Cp)=4183Jk{g}^{-10}{C}^{-1}.$

Use the relations: $=0\mathrm{.}023(Re{)}^{0\mathrm{.}8}(Pr{)}^{0\mathrm{.}4}$ for turbulent flow, and $=0\mathrm{.}86(Re{)}^{0\mathrm{.}43}(Pr{)}^{0\mathrm{.}3}$ for streamline flow.

$($c$)$ Saturated steam flows in the annulus of a single effect evaporator at a gauge pressure of $125$kPa. The outer evaporator tube is made of carbon steel and I.D$.=120mm,$ O$.$D$.($:$=130(mm)\}.$ It is lagged with a $10mm$ thickness of kapok $)=(0\mathrm{.}0346(W)m^{-1}{C}^{-1}$ and $15mm$ thick layer magnesia $(k_{\text{m}\text{a}\text{g}\text{n}\text{e}\text{s}\text{i}\text{a}}=0\mathrm{.}233W{m}^{-1}{C}^{-1}.$

If the temperature of the lagging in contact with air is $37C,$ determine the heat loss from the lagged evaporator tube.

Refer to the Steam Tables in Appendix $1.$