A pipe $600mm$ in diamter carrying steam at a temperature of $180$@$C$ for heating the houses in winter, and another $180mm$ diameter for supplyng drinking water at a temperature of $25$ degrees celsius, are burried under the ground with center to center distance $1,8m.$ The length of each pipe is $90m$ and internal conductivity of soil is $0,45\frac{W}{m}oC.$ Assuming that the pipes run parallel to each other, the earth is infinite and the resistance of the pipe material are negligible, dtermine:

a$)$ the net heat trasfer between the two pipes

b$)$ The rise in water temperature due to heat transfer if the velocity of the water in the pipe is $0,05\frac{m}{s}$

Hint

$Q_{x,y}=SK{T}_{1-2}$

$S$ to be determined from table of shape factor

$Q_{x,y}=m{C}_{p}T=>$ rise in water temperature $T=\frac{Q_{x,y}}{m{C}_p}$