A $25$ cm outer diameter saturated steam line at $100C$ runs parallel to a $5$ cm outer diometer cold water line at $25C.$ The pipes axis are $10$ cm apart and buried in a concrete with a thermal conductivity of $1\frac{W}{m}\frac{?}{K}.$

a$.$ What is the heat transfer rate between the two pipes per unit length?

b$.$ What is the decrease rate of the quality of the steam per unit length of the pipe if the mass flow rate of the steam is $0\mathrm{.}5k\frac{g}{s}.$

c$.$ If the steam enters to pipe as soturated vapor, calculate the length of pipe for where at the exit water reaches to the saturated liquid phase.

Sinhulater Maner

$\backslash$table$[[,\backslash$table$[[$Prows$],[($A$.$P$.)]],$Enthalpy, ki$/$ke$,$Entrops, W$/$herk$],[$Sat$,$ Liqualt A$.,\backslash$table$[[$Evap$.],[$tho$]],$Sial. Maper ${}_R,\backslash$table$[[$Sal$.$ Ityuid$],[$if$]],\backslash$table$[[$Fisp$.],["$f$]],$Sal. Vapar $3$