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Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01 kg/s$ and a temperature of $20^ \circ C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$:

If W ${q_{w}}'' = 2500x$, where $x$ is in $m$ and in the direction of flow ($x = 0$ at the inlet), the bulk mean temperature of the water leaving the pipe in $^\circ \textrm{C}$ is

  1. $42$
  2. $62$
  3. $74$
  4. $104$
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