As part of a food-processing operation, a single-pass, counter current, 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-in, outer diameter. gage 12 (relatively thick-walled) stainless steel tubes (k = 43 W/m · K) with inner diameters of 0.532 inch (1.35 cm) and total length of 5 m. In the present process, liquid glycerin enters the tube side of the heat exchanger at 16°C and exits at 60°C. The mass flow rate of liquid glycerin, ṁ_G, 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 (100°C, 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 found in Table 15.1. Glycerin is a fairly viscous fluid. 

a. What is the mass flow rate of steam (ṁ_s, kg/s) required on the shell side, assuming all the steam is condensed and exits in the exchanger as a saturated liquid? What is the log-mean temperature difference of the heat exchanger? 

b. What is the overall heat-transfer coefficient associated with this process? 

c. What is the required area of the heat exchanger? 

d. If the configuration is changed from counter current opera- lion to co-current operation. what will be the required heat transfer area?