A pipe $(k=59\frac{W}{m}K$ with an inner diameter of $3\mathrm{.}75$ cm and wall thickness of $0\mathrm{.}318$ cm is externally heated by saturated vapour of temperature $180C.$ The water flows through the pipe with a velocity of $1\mathrm{.}22\frac{m}{s}.$ Calculate the length of the pipe, required to heat water from $30C$ ta$.90C.$ Assume the heat transfer coefficients are to be $11\mathrm{.}3k\frac{W}{m^2}K.$ and $5\mathrm{.}69k\frac{W}{m^2}K$ on the vapour side and inner side respectively. The overall heat transfer coefficient based on the inner surface is $3529\mathrm{.}4\frac{W}{m^2}K.$ Draw the length Vs$.$ Temperature curve and state the assumptions for the analysis.