# CSU MECH 344 - HW9 - Solutions (9 pages)

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## HW9 - Solutions

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- Pages:
- 9
- School:
- Colorado State University- Fort Collins
- Course:
- Mech 344 - Heat and Mass Transfer

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PROBLEM 11 18 KNOWN Inner tube diameter D 0 02 m and fluid inlet and outlet temperatures corresponding to design conditions for a counterflow concentric tube heat exchanger Overall heat transfer coefficient U 500 W m2 K and desired heat rate q 3000 W Cold fluid outlet temperature after three years of operation FIND a Required heat exchanger length b Heat rate hot fluid outlet temperature overall heat transfer coefficient and fouling factor after three years SCHEMATIC ASSUMPTIONS 1 Negligible heat loss to the surroundings 2 Negligible tube wall conduction resistance 3 Constant properties ANALYSIS a The tube length needed to achieve the prescribed conditions may be obtained from Eqs 11 14 and 11 15 where T1 Th i Tc o 80 C and T2 Th o Tc i 120 C Hence T1m 120 80 C ln 120 80 98 7 C and L q 3000 W 0 968 m D U T1m 0 02 m 500 W m2 K 98 7o C b With q Cc Tc o Tc i the following ratio may be formed in terms of the design and 3 year conditions Cc Tc o Tc i q 60o C q3 1 333 oC Cc Tc o Tc i 45 3 Hence q3 q 1 33 3000 W 1 333 2250 W Having determined the ratio of heat rates it follows that Ch Th i Th o q 20o C q3 1 333 oC T Ch Th i Th o 160 h o 3 3 Hence Th o 3 160o C 20o C 1 333 145o C With Tlm 3 125 95 ln 125 95 109 3o C U3 q3 2250 W 338 W m 2 K o DL T 1m 3 0 02 m 0 968 m 109 3 C Continued PROBLEM 11 18 Cont With U 1 h i 1 h o R f c 1 and U3 1 h i 1 h o R f c 1 1 1 1 1 2 4 2 m K W 9 59 10 m K W U3 U 338 500 COMMENTS Over time fouling will always contribute to a degradation of heat exchanger performance In practice it is desirable to remove fluid contaminants and to implement a regular maintenance cleaning procedure PROBLEM 11 23 KNOWN Counterflow concentric tube heat exchanger FIND a Total heat transfer rate and outlet temperature of the water and b Required length SCHEMATIC ASSUMPTIONS 1 Negligible heat loss to surroundings 2 Negligible thermal resistance due to tube wall thickness PROPERTIES given 3 kg m Water 1000 Oil 800 cp J kg K 4200 1900 2 m s k W m K 7 7 10 0 64 4 7 5 1 10 0 134 140 Pr ANALYSIS a With the outlet temperature Tc o 60 C from an overall energy balance on the hot oil fluid find h ch Th i Th o 0 1 kg s 1900 J kg K 100 60 C 7600 W q m From an energy balance on

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