A chemical engineer is to design a shell and tube heat exchanger in a restricted area in a room of a length of $1\mathrm{.}75m\mathrm{.}4k\frac{g}{sec}$ of water at an average velocity of $0\mathrm{.}375\frac{m}{sec}$ is to be heated in the tube side from $45C$ to $60C$ using $1\mathrm{.}875cm($inside diameter$)$ tubes. The overall heat transfer coefficient $($based on inside tube area$)$ is $1390\frac{W}{m^{2}C}.$ The fluid used for heating $($shell side$)$ is water $($entering temperature of $90C)$ with a mass flow rate of $2\mathrm{.}0k\frac{g}{sec}.$

Starting with a single shell pass heat exchanger: find the number of tube passes, the number tubes per pass, and tube length. $($using the LMTD method$).$

Solution by steps all equations and calculations:

Discussion: