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# final (problem 6, 12 and 18)

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### final (problem 6, 12 and 18)

1. 1. Optimization in Flow of Heat GroupA6 Bermio, Amelou Domingo, Jean Francisco, Cresta Suaco, Kaylee
2. 2. Problem 6 <ul><li>Determine the optimum economic thickness of insulation that should be used under the following conditions: saturated steam is being passed continuously in a horizontal 1” Sch 40 steel pipe. The temperature of the steam is 180oC, 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. Life of the installation is 10 years with time value of money equal to 15%. 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: </li></ul>
3. 3. <ul><li>Given: </li></ul>
4. 8. Problem 12 A condenser for a distillation unit must be designed to condense 2500 kg/h of vapor. The effective condensation temperature for the vapor is 145oC.The heat of condensation for the vapor is 315000 J/kg. Cooling water is available at 15oC.The cost of cooling water is \$25/1000m3.The optimum Heat Transfer Coefficient is 300 W/m2K.The cost of the installed heat exchanger is \$400/m2 and life of the equipment is 20 years. 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.
5. 10. Problem18 <ul><li>An air cooler consisting of a bundle of 1” Sch 40 steel pipes enclosed in a well baffled shell is being built to cool 250 kg/hr of air from 85oC to 30oC. The air flows under pressure through the tubes of a 1-shell 2-tube pass heat exchanger. Cooling water at 25oC 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/m2K and for the outside fluid, 2100 W/m2K. Cooling water costs PhP 0.55/m3 and the annual fixed charges is 16% with cooler cost at PhP 18,000/m2. Calculate the Optimum exit temperature of cooling water and optimum length of tubes. </li></ul>
6. 11. Working equation: