The document discusses optimization problems related to heat transfer in pipes and condensers. It provides conditions for four problems involving determining optimum insulation thickness, steam temperature, cooling water flow rate and exit temperature, and optimum tube length and exit cooling water temperature. Solutions are provided for each problem, calculating key parameters needed for optimal economic performance of the heat transfer systems.

1. PROBLEM SET IN OPTIMIZATION IN FLOW OF HEAT Princess Joyce R. Antonio Sherly B. Samson Rochelle Anne B. Saturno Kimberly Kaye B. Valerio Group 4 – 5 Che A

2. NO. 4 Determine the optimum economic thickness of insulation that should be used under the following conditions: saturated steam is being passed continuously in a horizontal 2” Sch 40 steel pipe. The temperature of the steam is 220oC, and the steam is valued at $0.0035/kg. The pipe is to be insulated with a material that has a thermal conductivity of 0.06 W/mK. The cost of the installed insulation per m of pipe length is $ 200x, where x is the thickness of the insulation in meters. Annual fixed charges including maintenance amount to 15% of the initial installed cost. The total length of the pipe is 250 m, and the average temperature of the surroundings is 27oC. Heat transfer resistances due to steam film, scale, pipe wall are negligible. The air film coefficient at the outside of the insulation may be assumed constant for all insulation thicknesses and given by the equation:

3. SOL’N – NO. 4

4. SOL’N – NO. 4 Assume Tw

5. NO. 10 A condenser for a distillation unit must be designed to condense 2000 kg/h of vapor. The effective condensation temperature for the vapor is 132 o C.The heat of condensation for the vapor is 350000 J/kg. Cooling water is available at 25 o C.The cost of cooling water is $22/1000m 3 .The optimum Heat Transfer Coefficient is 300 W/m 2 K.The cost of the installed heat exchanger is $400/m 2 and annual fixed charges including maintenance are 20% of the initial investment. The heat capacity of water is 4184 J/kgK. If the condenser is to operate 7200 hrs/yr, determine the cooling water flow rate in kg/hr and exit temperature for optimum economic conditions.

6. SOL’N – NO. 10 t 2opt = 360.06 K = 87.06 o C w = 2,696 kg/hr

7. NO. 16 An air cooler consisting of a bundle of 1/2” Sch 40 steel pipes enclosed in a well baffled shell is being built to cool 250 kg/hr of air from 82 o C to 27 o C. The air flows under pressure through the tubes of a 1-shell 2-tube pass heat exchanger. Cooling water at 21 o C is under sufficient pressure to force it through at any desired rate, flows through the shell. The heat transfer coefficient based on the inside fluid is 50 W/m 2 K and for the outside fluid, 2100 W/m 2 K. Cooling water costs PhP 0.57/m 3 and the annual fixed charges is 18% with cooler cost at PhP 21,000/m 2 . Calculate the Optimum exit temperature of cooling water and optimum length of tubes.

8. SOL’N – NO. 16

12. THANK YOU.