hater 0:, 8, 4, 47, 50, 5, 55, 7, 75, 77, 8 and 85. 0- Refrigerant-4a is cooled by water a double-ie heat exchanger. he overall heat transfer coefficient is to be determed. Assumtions he thermal resistance of the ner tube is negligible sce the tube material is highly conductive and its thickness is negligible. Both the water and refrigerant-4a flow are fully develoed. Proerties of the water and refrigerant-4a are constant. Proerties he roerties water at 0 are (able A-9) ρ 998 kg/m old water 6 υ µ / ρ.004 0 m /s D k 0.598 W/m. 0 D Pr 7.0 i Analysis he hydraulic diameter for annular sace is Dh Do Di 0. 05 0. 0 0. 05 m he average velocity of water the tube and the Reynolds number are Hot R-4a m m 0. kg/s Vm 0.79 m/s ρa c (0.05 m) (0.0 m) Do Di ρ π (998 kg/m ) 4 π 4 (0.79 m/s)(0.05 m) Re V m D h 0,890 υ 6.004 0 m / s which is greater than 4000. herefore flow is turbulent. Assumg fully develoed flow, hdh 0.8 0.4 0.8 0.4 Nu 0.0Re Pr 0.0(0,890) (7.0) 85.0 k and k 0.598 W/m. h Nu (85.0) 90 W/m o. Dh 0.05 m hen the overall heat transfer coefficient becomes U 00 W/m. + + h i h o 5000 W/m. 90 W/m.
0-8 Steam is condensed by coolg water the condenser of a ower lant. he mass flow rate of the coolg water and the rate of condensation are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 here is no foulg. 5 Fluid roerties are constant. Proerties he heat of vaorization of water at 50 is given to be h fg 05 kj/kg and secific heat of cold water at the average temerature of.5 is given to be 480 J/kg.. Analysis he temerature differences between the steam and the coolg water at the two ends of the condenser are h, c, 50 7 7 h, c, 50 8 and lm 7. ln( / ) ln( / ) 8 hen the heat transfer rate the condenser becomes Q UA lm ( 400 W / m. )(58 m )( 7. ) 800 kw 50 he mass flow rate of the coolg water and the rate of condensation of steam are determed from Q [ m ( )] coolg water m coolg water ( ) 800 kj / s (4.8 kj / kg. )(7 8 ) 0 kg/s 800 kj / s Q ( mh fg) steam m steam.65 kg/s h 05 kj / kg fg Steam 50
0-4 Durg an exeriment, the let and exit temeratures of water and oil and the mass flow rate of water are measured. he overall heat transfer coefficient based on the ner surface area is to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 Fluid roerties are constant. Proerties he secific heats of water and oil are given to be 480 and 50 J/kg., resectively. Analysis he rate of heat transfer from the oil to the water is [ m ( )] water (5kg / s)(4.8 kj / kg. )(55 0 ) 7.5 kw he heat transfer area on the tube side is Ai nπdil 4π( 0. 0 m)( m).8 m he logarithmic mean temerature difference for counter-flow arrangement and the correction factor F are h, c, 0 55 65 Oil 45 0 5 0 lm, F t P R t h, c, 65 5 49. ln( / ) ln( 65 / 5) 55 0 0.5 0 0 F 0.70 0 45.4 55 0 hen the overall heat transfer coefficient becomes U i Ai Flm, F U i A F i lm, F (4 tubes) 45 7.5 kw.9 kw/m (.8 m )(0.70)(4.9 ) 55 0 5 kg/s.
0-47 Enge oil is heated by condensg steam a condenser. he rate of heat transfer and the length of the tube required are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 here is no foulg. 5 Fluid roerties are constant. 6 he thermal resistance of the ner tube is negligible sce the tube is th-walled and highly conductive. Proerties he secific heat of enge oil is given to be. kj/kg.. he heat of condensation of steam at 0 is given to be 74 kj/kg. Analysis he rate of heat transfer this heat exchanger is [ m ( )] oil ( 0. kg / s)(. kj / kg. )(60 0 ) 5. kw he temerature differences at the two ends of the heat exchanger are h, c, 0 60 70 h, c, 0 0 0 and lm 70 0 88. 5 ln( / ) ln( 70 / 0) he surface area is 5. kw A 044. m U lm (. 065kW / m. ) (88. 5 ) hen the length of the tube required becomes A 044. m A πdl L 7.0 m πd π(. 00 m) Oil 0 0. kg/s Steam 0 60
0-50 Air is reheated by hot exhaust gases a cross-flow heat exchanger. he rate of heat transfer and the let temerature of the air are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 here is no foulg. 5 Fluid roerties are constant. Proerties he secific heats of air and combustion gases are given to be 005 and 00 J/kg., resectively. Analysis he rate of heat transfer is [ m ( )] gas. (. kg/s)(.kj/kg. )(80 95 ) 0 kw he mass flow rate of air is m PV (95 kpa)(0.8 m / s) 0904. kg / s R (. 0 87 kpa.m / kg.k) 9 K hen the let temerature of the air becomes m ( c, c, ) c, c, + m 0 0 W 0 + (0.904 kg/s)(005 J/kg. ) Air 95 kpa 0 0.8 m /s Exhaust gases. kg/s 95
0-5 is heated by hot oil a -shell asses and -tube asses heat exchanger. he heat transfer surface area on the tube side is to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 here is no foulg. 5 Fluid roerties are constant. Proerties he secific heats of water and oil are given to be 4.8 and. kj/kg., resectively. Analysis he rate of heat transfer this heat exchanger is [ m ( )] water ( 45. kg / s)(4.8 kj / kg. )(70 0 ) 940.5 kw he let temerature of the hot water is determed from [ m ( )] oil m 70 940.5 kw 9 (0 kg/s)(. kj/kg. ) he logarithmic mean temerature difference for counter-flow arrangement and the correction factor F are h, c, 70 70 00 9 0 09 h, c, 00 09 05 ln( / ) ln(00 / 09) lm, F t P R t 9 70 0.7 0 70 F.0 0 70. 9 70 hen the heat transfer surface area on the tube side becomes 940.5 kw UAFlm, F A 5 m UF (0.6 kw/m. )(.0)(05 ) lm, F 70 0 4.5 kg/s Oil 70 0 kg/s ( tube asses)
0-55E Steam is condensed by coolg water a condenser. he rate of heat transfer, the rate of condensation of steam, and the mass flow rate of cold water are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 here is no foulg. 5 Fluid roerties are constant. 6 he thermal resistance of the ner tube is negligible sce the tube is th-walled and highly conductive. Proerties We take secific heat of water are given to be.0 Btu/lbm. F. he heat of condensation of steam at 90 F is 04 Btu/lbm. Analysis (a) he log mean temerature difference is determed from h, c, 90 F 7 F7 F 90 F 60 F0 F h, c, 7 0 lm, F. 9 F ln( / ) ln( 7 / 0) he heat transfer surface area is A 8nπDL 8 50 π( / 48 ft)(5 ft) 9. 7 ft and Q UA lm (600 Btu/h.ft. F)(9.7 ft )(.9 F) 5.96 0 (b) he rate of condensation of the steam is 6 5.96 0 Btu/h ( mh fg ) steam m steam 57 lbm/h h fg 04 Btu/lbm (c) hen the mass flow rate of cold water becomes [ m ( )] m cold water ( 4.5 0 5 cold water 5.96 0 Btu/h ) (.0 Btu/lbm. F)(7 F 60 F] lbm/h 5 lbm/s 6 Steam 90 F 0 lbm/s 6 Btu/h.44 90 F lbm/s 7 F 60 F
0-7 Hot oil is to be cooled by water a heat exchanger. he mass flow rates and the let temeratures are given. he rate of heat transfer and the let temeratures are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 he thickness of the tube is negligible sce it is th-walled. 5 he overall heat transfer coefficient is constant and uniform. Proerties he secific heats of the water and oil are given to be 4.8 and. kj/kg., resectively. Analysis he heat caacity rates of the hot and cold fluids are h m hh (0. kg / s)(00 J / kg. ) 440 W/ m (0. kg / s)(480 J / kg. ) 48 W/ c c c herefore, m c 48 W/ and m 48 095. max 440 hen the maximum heat transfer rate becomes Q max m ( h, c, ) (48 W/ )(60-8 ) 59.6 kw he heat transfer surface area is A n( πdl) ()( π)(0.08 m)( m).04 m he NU of this heat exchanger is UA ( 40 W/m. ) (. 04 m ) NU 659. 48 W/ m hen the effectiveness of this heat exchanger corresondg to 0.95 and NU.659 is determed from fig. 0-6d to be ε 0.6 hen the actual rate of heat transfer becomes ε max (0.6)(59.6 kw) 6. kw Fally, the let temeratures of the cold and hot fluid streams are determed to be 6. kw Q c ( c, c, ) c, c, + 8 + 04.6 c 048. kw/ Q 6. kw Q h( h, h, ) h, h, 60 77.7 044. kw/ h 8 0. kg/s Oil 60 0. kg/s ( tube asses) 0-75E Inlet and let temeratures of the hot and cold fluids a double-ie heat exchanger are given. It is to be determed the fluid which has the smaller heat caacity rate and the effectiveness of the heat exchanger. Analysis Hot water has the smaller heat caacity rate sce it exeriences a greater temerature change. he effectiveness of this heat exchanger is determed from h ( h, h, ) h ( h, h, ) 00 F 00 F ε 0.769 ( ) ( ) 00 F 70 F max m h, c, h h, c,
0-77 is heated by hot air a heat exchanger. he mass flow rates and the let temeratures are given. he heat transfer surface area of the heat exchanger on the water side is to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 he overall heat transfer coefficient is constant and uniform. Proerties he secific heats of the water and air are given to be 4.8 and.0kj/kg., resectively. Analysis he heat caacity rates of the hot and cold fluids are h m hh (4 kg / s)(4.8 kj / kg. ) 6.7 kw/ m (9 kg / s)(.0 kj / kg. ) 9.09 kw/ c c c herefore, m c 909. kw/ and m 909. 0544. max 6. 7 hen the NU of this heat exchanger corresondg to 0.544 and ε 0.65 is determed from Fig. 0-6 to be Hot Air NU.5 00 hen the surface area of this heat exchanger becomes 9 kg/s UA NU m (.)( 5 9. 09 kw/ ) NU A 5.4 m U 060. kw / m. m 0, 4 kg/s
0-8 old water is heated by hot water a heat exchanger. he net rate of heat transfer and the heat transfer surface area of the heat exchanger are to be determed. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 he overall heat transfer coefficient is constant and uniform. 5 he thickness of the tube is negligible. Proerties he secific heats of the cold and hot water are given to be 4.8 and 4.9 kj/kg., resectively. Analysis he heat caacity rates of the hot and cold fluids are m (0.5 kg / s)(480 J / kg. ) 045 W/ m ( kg / s)(490 J / kg. ), 570 W/ h h h c c c herefore, m c 045 W/ and m 045 008. max, 570 hen the maximum heat transfer rate becomes Q ( ) (045 W/ )(00-5 ) 88, 85 W max m h, c, he actual rate of heat transfer is Q ( ) ( 045 W/ )( 45 5 ),50 W h h, h, hen the effectiveness of this heat exchanger becomes Q, 50 ε 05. Q max 88, 85 he NU of this heat exchanger is determed usg the relation able 0-5 to be ε 0.5 NU ln ln 0.48 ε 0.08 0.5 0.08 hen the surface area of the heat exchanger is determed from UA NU m (. 0 48)( 045 W/ ) NU A 0.48 m U 950 W/m. m Hot 00 kg/s 45 old 5 0.5 kg/s
0-85 Ethyl alcohol is heated by water a shell-and-tube heat exchanger. he heat transfer surface area of the heat exchanger is to be determed usg both the LMD and NU methods. Assumtions Steady oeratg conditions exist. he heat exchanger is well-sulated so that heat loss to cold fluid. hanges the ketic and otential energies of fluid streams are negligible. 4 he overall heat transfer coefficient is constant and uniform. Proerties he secific heats of the ethyl alcohol and water are given to be.67 and 4.9 kj/kg., resectively. Analysis (a) he temerature differences between the two fluids at the two ends of the heat exchanger are 95 70 5 h, c, h, c, 45 5 0 he logarithmic mean temerature difference and the correction factor are 5 0,.4 70 lm F ln( / ) ln(5/0) Alcohol 5. kg/s t 70 5 P 0.64 95 5 F 0.8 (8 tube asses) 95 45 R. t 70 5 he rate of heat transfer is determed from 45 Q m cc ( c, c, ) (. kg / s)(.67 kj / kg. )(70 5 ) 5. kw he surface area of heat transfer is Q 5. kw Q UAlm A UF lm. kw / m. )(. )(. ) 7.4 m 08 08 4 (b) he rate of heat transfer is Q m cc ( c, c, ) (. kg / s)(.67 kj / kg. )(70 5 ) 5. kw he mass flow rate of the hot fluid is 5. kw m h h ( h, h, ) m h. kg/s h ( h, h, ) (4.9 kj/kg. )(95 45 ) he heat caacity rates of the hot and the cold fluids are h m hh (. kg / s)(4.9 kj / kg. ) 50. kw/ c m cc (. kg / s)(.67 kj / kg. ) 56. kw/ herefore, m h 50. W/ and m 50. 09. max 56. hen the maximum heat transfer rate becomes Q max m ( h, c, ) (5.0 W/ )(95 5 ) 5. kw he effectiveness of this heat exchanger is Q 5. ε 07. Q max 5. he NU of this heat exchanger is determed from Fig. 0-6d to be NU 7. hen the surface area of heat exchanger is determed to be UA NU m ( 7)(5. 0kW/ ) NU A 44.0 m m U 08. kw / m. he small difference between the two results is due to the readg error of the chart. 95