As part of a food-processing operation, a single-pass, countercurrent, shell-and- tube heat exchanger must be designed to warm up a stream of liquid glycerin. The heat exchanger must be constructed of 0.75-inch outer diameter, gage 12 stainless steel tubes (k = 43 W/m2K) with an inner diameter of 0.532 inch and a total length of 5 m. In the present process, liquid glycerin enters the tube side of the heat exchanger at 16C and exits at 60C. The mass flow rate of the liquid glycerin, mG, that must be processed is 5 kg/s and the desired bulk fluid velocity in each tube is 1.80 m/s. The process will use saturated condensing steam at 1 atm pressure (100C, enthalpy of vaporization = 2257 kJ/kg) on the shell side of the heat exchanger to warm up the glycerin. The shell-side convective heat transfer coefficient for condensing steam can be estimated to be 5000 W/m2K. Calculate:

a. The mass flow rate of the steam (kg/s) required on the shell side, assuming all the steam is condensed and exists the exchanger as saturated liquid.

b. The log mean temperature difference c. The overall heat transfer coefficient (U) d. The number of tubes required in the heat exchanger