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10 Pages

### Heat Chap13-111

Course: AET AET432, Spring 2007
School: ASU
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Word Count: 2898

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13 Chap Heat Exchangers Review Problems 13-111 Hot oil is cooled by water in a multi-pass shell-and-tube heat exchanger. The overall heat transfer coefficient based on the inner surface is to be determined. Assumptions 1 Water flow is fully developed. 2 Properties of the water are constant. Properties The properties of water at 300 K 25 C are (Table A-9) k Pr 0.607 W/m. C / 6.14 0.894 10 6 m 2 /s Analysis The...

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13 Chap Heat Exchangers Review Problems 13-111 Hot oil is cooled by water in a multi-pass shell-and-tube heat exchanger. The overall heat transfer coefficient based on the inner surface is to be determined. Assumptions 1 Water flow is fully developed. 2 Properties of the water are constant. Properties The properties of water at 300 K 25 C are (Table A-9) k Pr 0.607 W/m. C / 6.14 0.894 10 6 m 2 /s Analysis The Reynolds number is Re Vm D (3 m/s)(0.013 m) 0.894 10 6 m 2 /s 43,771 Outer surface D0, A0, h0, U0 Inner surface Di, Ai, hi, Ui which is greater than 10,000. Therefore, we assume fully developed turbulent flow, and determine Nusselt number from Nu 0.023 Re 0.8 Pr 0.4 0.023(43,771) 0.8 (6.14) 0.4 245 and hi k Nu D 0.607 W/m. C (245) 11,440 W/m 2 . C 0.013 m The inner and the outer surface areas of the tube are Ai Ao Di L Do L (0.013 m)(1 m) (0.015 m)(1 m) 0.04084 m 2 0.04712 m 2 The total thermal resistance of this heat exchanger per unit length is R 1 hi Ai ln( Do / Di ) 2 kL 1 (11,440 W/m 2 . C)(0.04084 m 2 ) 0.609 C/W 1 ho Ao ln(1.5 / 1.3) 2 (110 W/m. C)(1 m) 1 (35 W/m 2 . C)(0.04712 m 2 ) Then the overall heat transfer coefficient of this heat exchanger based on the inner surface becomes R 1 U i Ai Ui 1 RAi 1 (0.609 C/W )(0.04084 m 2 ) 40.2 W/m2 . C 13-87 Chap 13 Heat Exchangers 13-112 Hot oil is cooled by water in a multi-pass shell-and-tube heat exchanger. The overall heat transfer coefficient based on the inner surface is to be determined. Assumptions 1 Water flow is fully developed. 2 Properties of the water are constant. Properties The properties of water at 300 K 25 C are (Table A-9) k Pr 0.607 W/m. C / 6.14 0.894 10 6 m 2 /s Analysis The Reynolds number is Re Vm D (3 m/s)(0.013 m) 0.894 10 6 m 2 /s 43,771 Outer surface D0, A0, h0, U0 Inner surface Di, Ai, hi, Ui which is greater than 10,000. Therefore, we assume fully developed turbulent flow, and determine Nusselt number from Nu 0.023 Re 0.8 Pr 0.4 0.023(43,771) 0.8 (6.14) 0.4 245 and hi k Nu D 0.607 W/m. C (245) 11,440 W/m 2 . C 0.013 m The inner and the outer surface areas of the tube are Ai Ao Di L Do L (0.013 m)(1 m) (0.015 m)(1 m) 0.04084 m 2 0.04712 m 2 The total thermal resistance of this heat exchanger per unit length of it with a fouling factor is R 1 hi Ai ln( Do / Di ) 2 kL 1 (11,440 W/m . C)(0.04084 m ) 0.0004 m 2 . C/W 0.04712 m 0.617 C/W 2 2 2 2 R f ,o Ao 1 ho Ao ln(15 / 13) 2 (110 W/m. C)(1 m) 1 (35 W/m . C)(0.04712 m 2 ) Then the overall heat transfer coefficient of this heat exchanger based on the inner surface becomes R 1 U i Ai Ui 1 RAi 1 (0.617 C/W )(0.04084 m 2 ) 39.7 W/m 2 . C 13-88 Chap 13 Heat Exchangers 13-113 Water is heated by hot oil in a multi-pass shell-and-tube heat exchanger. The rate of heat transfer and the heat transfer surface area on the outer side of the tube are to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of the water and oil are given to be 4.18 and 2.2 kJ/kg. C, respectively. Analysis (a)The rate of heat transfer in this heat exchanger is Q mh C ph (Th,in Th,out ) (3 kg/s)(2.2 kJ/kg. C)(130 C 60 C) = 462 kW (b) The outlet temperature of the cold water is Q mc C pc (Tc,out Tc,in ) Tc,out Tc,in Q mc C pc 20 C 462 kW (3 kg / s)(4.18 kJ / kg. C) 56.8 C The temperature differences at the two ends are T1 T2 Th,in Tc,out Th,out Tc,in 130 C 56.8 C = 73.2 C 60 C 20 C = 40 C Hot Oil 130 C 3 kg/s The logarithmic mean temperature difference is Tlm,CF T1 T2 ln( T1 / T2 ) 73.2 40 ln( 73.2 / 40) 54.9 C Cold Water 20 C 3 kg/s and P R t 2 t1 T1 t1 T2 T1 t 2 t1 56.8 20 130 20 130 60 56.8 20 0.335 F 1.90 0.96 (20 tube passes) 60 C The heat transfer surface area on the outer side of the tube is then determined from Q UAs F Tlm As Q UF Tlm 462 kW (0.3 kW/m . C)(0.96)(54.9 C) 2 29.2 m2 13-89 Chap 13 Heat Exchangers 13-114E Water is heated by solar-heated hot air in a double-pipe counter-flow heat exchanger. The required length of the tube is to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of the water and air are given to be 1.0 and 0.24 Btu/lbm. F, respectively. Analysis The rate of heat transfer in this heat exchanger is Q mh C ph (Th,in Th,out ) (0.7 lbm/s)(0.24 Btu/lbm. F)(190 F 135 F) = 9.24 Btu/s The outlet temperature of the cold water is Q mc C pc (Tc,out Tc,in ) Tc,out Tc,in Q mc C pc 70 F 9.24 Btu/s (0.35 lbm/s)(1.0 Btu/lbm. F) 96.4 F The temperature differences at the two ends are T1 T2 Th,in Tc,out Th,out Tc,in 190 F 96.4 F = 93.6 F 135 F 70 F = 65 F Hot Air 130 F 0.7 lbm/s 135 F Cold Water 70 F 0.35 lbm/s The logarithmic mean temperature difference is Tlm T1 T2 ln( T1 / T2 ) 93.6 65 ln( 93.6 / 65) 78.43 F The heat transfer surface area on the outer side of the tube is determined from Q UAs Tlm As Q U Tlm 9.24 Btu/s (20 / 3600 Btu/s.ft 2 . F)(78.43 F) 21.21 ft 2 Then the length of the tube required becomes As DL L As D 21.21 ft 2 (0.5 / 12 ft) 162.0 ft 13-115 It is to be shown that when T1 = T2 for a heat exchanger, the Tlm relation reduces to Tlm = T1 = T2. Analysis When T1 = T2, we obtain Tlm T1 T2 ln( T1 / T2 ) 0 0 This case can be handled by applying L'Hospital's rule (taking derivatives of nominator and denominator separately with respect to T1 or T2 ). That is, Tlm d ( T1 T2 ) / d T1 d [ln( T1 / T2 )] / d T1 1 1 / T1 T1 T2 13-90 Chap 13 Heat Exchangers 13-116 Refrigerant-134a is condensed by air in the condenser of a room air conditioner. The heat transfer area on the refrigerant side is to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heat of air is given to be 1.005 kJ/kg. C. Analysis The temperature differences at the two ends are T1 T2 Th,in Th,out Tc,out Tc,in 40 C 35 C = 5 C 40 C 25 C = 15 C R-134a 40 C The logarithmic mean temperature difference is Tlm T1 T2 ln( T1 / T2 ) 5 15 ln(5 / 15) 9.1 C Air 25 C 35 C The heat transfer surface area on the outer side of the tube is determined from Q UAs Tlm As Q U Tlm (15,000 / 3600) kW (0.150 kW/m 2 . C) (9.1 C) 3.05 m2 40 C 13-117 Air is preheated by hot exhaust gases in a cross-flow heat exchanger. The rate of heat transfer is to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of air and combustion gases are given to be 1.005 and 1.1 kJ/kg. C, respectively. Analysis The rate of heat transfer is simply Q [mC p (Tin Tout )]gas. (1.1 kg/s)(1.1kJ/kg. C)(180 C 95 C) = 102.9 kW 13-91 Chap 13 Heat Exchangers 13-118 A water-to-water heat exchanger is proposed to preheat the incoming cold water by the drained hot water in a plant to save energy. The heat transfer rating of the heat exchanger and the amount of money this heat exchanger will save are to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat is exchanger well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. Properties The specific heat of the hot water is given to be 4.18 kJ/kg. C. Analysis The maximum rate of heat transfer is Qmax mh C ph (Th,in Tc,in ) Hot water 60 C 8 kg/s Cold Water 14 C (8 / 60 kg/s)(4.18 kJ/kg. C)(60 C 14 C) 25.6 kW Noting that the heat exchanger will recover 72% of it, the actual heat transfer rate becomes Q Qmax (0.72)(256 kJ / s) = 18.43 kW . which is the heat transfer rating. The operating hours per year are The annual operating hours = (8 h/day)(5 days/week)(52 week/year) = 2080 h/year The energy saved during the entire year will be Energy saved = (heat transfer rate)(operating time) = (18.43 kJ/s)(2080 h/year)(3600 s/h) = 1.38x108 kJ/year Then amount of fuel and money saved will be Fuel saved Energy saved Furnace efficiency 1.38 10 8 kJ/year 1 therm 0.78 105,500 kJ 1677 therms/year Money saved = (fuel saved)(the price of fuel) = (1677 therms/year)(\$ 0.54/therm) = \$906/year 13-92 Chap 13 Heat Exchangers 13-119 A shell-and-tube heat exchanger is used to heat water with geothermal steam condensing. The rate of heat transfer, the rate of condensation of steam, and the overall heat transfer coefficient are to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 Fluid properties are constant. Properties The heat of vaporization of geothermal water at 120 C is given to be hfg = 2203 kJ/kg and specific heat of water is given to be Cp = 4180 J/kg. C. Analysis (a) The outlet temperature of the water is Tc,out Th,out 46 120 C 46 C = 74 C Steam 120 C Then the rate of heat transfer becomes Q [mC p (Tout = 847.7 kW Tin )]water 22 C) (3.9 kg/s)(4.18 kJ/kg. C)(74 C (b) The rate of condensation of steam is determined from Q 847.7 kW (mh fg ) geothermal steam 22 C Water 3.9 kg/s 120 C 14 tubes m(2203 kJ/kg) m 0.385 kg/s (c) The heat transfer area is Ai n Di L 14 (0.024 m)(3.2 m) = 3.378 m 2 The logarithmic mean temperature difference for counter-flow arrangement and the correction factor F are T1 T2 Th,in Tc,out Th,out Tc,in 120 C 74 C = 46 C 120 C 22 C = 98 C 46 98 ln( 46 / 98) 0.53 F 0 1 Tlm,CF t 2 t1 T1 t1 T1 T2 ln( T1 / T2 ) 74 22 120 22 120 120 74 22 68.8 C P R T1 T2 t 2 t1 Then the overall heat transfer coefficient is determined to be Q U i Ai F Tlm,CF Ui Q Ai F Tlm,CF 847,700 W (3.378 m )(1)(68.8 C) 2 3648 W/m 2 . C 13-93 Chap 13 Heat Exchangers 13-120 Water is heated by geothermal water in a double-pipe counter-flow heat exchanger. The mass flow rate of the geothermal water and the outlet temperatures of both fluids are to be determined. Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of the geothermal water and the cold water are given to be 4.25 and 4.18 kJ/kg. C, respectively. Analysis The heat capacity rates of the hot and cold fluids are Ch Cc m h C ph mc C pc m h (4.25 kJ/kg. C) = 4.25m h (1.2 kg/s)(4.18 kJ/kg. C) = 5.016 kW/ C Cold Water 12 C 1.2 kg/s Geothermal water 95 C Cmin and Cc C 5.016 kW/ C Cmin Cmax 5.016 4.25mh 1.1802 mh The NTU of this heat exchanger is NTU UAs C min (0.480 kW/m 2 . C)(25 m 2 ) 5.016 kW/ C 2.392 Using the effectiveness relation, we find the capacity ratio 1 exp NTU(1 C ) 1 C exp NTU(1 C ) 0.823 1 exp 2.392(1 C ) 1 C exp 2.392(1 C ) C 0.494 Then the mass flow rate of geothermal water is determined from C 1.1802 mh 0.494 1.1802 mh mh 2.39 kg/s The maximum heat transfer rate is Q max C min (Th,in Tc,in ) (5.016 kW/ C)(95 C - 12 C) 416.328 kW Then the actual rate of heat transfer rate becomes Q Qmax (0.823)(416.328 kW) 342.64 kW The outlet temperatures of the geothermal and cold waters are determined to be Q Cc (Tc,out Tc,in ) 342.64 kW = (5.016 kW/ C)(Tc,out 12) Tc,out 80.3 C Q m h C ph (Th,in Th,out ) Th,out 61.3 C 342.64 kW = (2.39 kg/s)(4.25 kJ/kg. C)(95 Th,out ) 13-94 Chap 13 Heat Exchangers 13-121 Air is to be heated by hot oil in a cross-flow heat exchanger with both fluids unmixed. The effectiveness of the heat exchanger, the mass flow rate of the cold fluid, and the rate of heat transfer are to be determined. .Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of the air and the oil are given to be 1.006 and 2.15 kJ/kg. C, respectively. Analysis (a) The heat capacity rates of the hot and cold fluids are Ch Cc mh C ph mc C pc 0.5mc (2.15 kJ/kg. C) = 1.075mc mc (1.006 kJ/kg. C) = 1.006mc Cc 1.006mc 0.936 Oil 80 C Therefore, Cmin and C Cmin Cmax 1.006mc c 1.075m Air 18 C The effectiveness of the heat exchanger is determined from Q Qmax C c (Tc,out Tc, in ) 58 18 80 18 0.645 58 C C c (Th,in Tc,in ) (b) The NTU of this heat exchanger is expressed as NTU UAs C min (0.750 kW/ C) 1.006mc 0.7455 mc The NTU of this heat exchanger can also be determined from NTU ln C ln(1 C ) 1 ln 0.936 ln(1 0.645) 1 0.936 3.724 Then the mass flow rate of the air is determined to be NTU UAs C min 3.724 (0.750 kW/ C) 1.006mc mc 0.20 kg/s (c) The rate of heat transfer is determined from Q m c C pc (Tc,out Tc,in ) (0.20 kg/s)(1.006 kJ/kg. C)(58 - 18) C 8.05 kW 13-95 Chap 13 Heat Exchangers 13-122 A water-to-water counter-flow heat exchanger is considered. The outlet temperature of the cold water, the effectiveness of the heat exchanger, the mass flow rate of the cold water, and the heat transfer rate are to be determined. .Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The overall heat transfer coefficient is constant and uniform. Properties The specific heats of both the cold and the hot water are given to be 4.18 kJ/kg. C. Analysis (a) The heat capacity rates of the hot and cold fluids are Cold Water 20 C Hot water 95 C Ch Cc mh C ph mc C pc Cc 1.5mc (4.18 kJ/kg. C) = 6.27mc mc (4.18 kJ/kg. C) = 4.18mc 4.18mc 0.667 Therefore, Cmin and C Cmin Cmax 4.18mc c 6.27m The rate of heat transfer can be expressed as Q Q C c (Tc, out C h (Th,in Tc, in ) Th,out ) (4.18m c )(Tc,out 20) 15) (6.27m c )(80 Tc,out ) (6.27m c ) 95 (Tc,out Setting the above two equations equal to each other we obtain the outlet temperature of the cold water Q 4.18mc (Tc,out 20) 6.27mc (80 Tc,out ) Tc,out 56 C (b) The effectiveness of the heat exchanger is determined from Q Qmax C c (Tc,out Tc,in ) C c (Th,in Tc,in ) 4.18mc (56 20) 4.18mc (95 20) 0.48 (c) The NTU of this heat exchanger is determined from NTU 1 ln C 1 1 C 1 1 0.48 1 ln 0.667 1 0.48 0.667 1 0.805 Then, from the definition of NTU, we obtain the mass flow rate of the cold fluid: NTU UAs C min 0.805 1.400 kW/ C 4.18mc mc 0.416 kg/s (d) The rate of heat transfer is determined from Q mc C pc (Tc,out Tc,in ) (0.416 kg/s)(4.18 kJ/kg. C)(56 20) C 62.6 kW 13-123 . . . 13-129 Design and Essay Problems 13-96
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ASU - AET - AET432
Chapter 7 External Forced ConvectionChapter 7 EXTERNAL FORCED CONVECTIONDrag Force and Heat Transfer in External Flow 7-1C The velocity of the fluid relative to the immersed solid body sufficiently far away from a body is called the free-stream velocity
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Chapter 7 External Forced ConvectionFlow Across Cylinders And Spheres 7-35C For the laminar flow, the heat transfer coefficient will be the highest at the stagnation point which corresponds to 0 . In turbulent flow, on the other hand, it will be highest
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Chapter 7 External Forced Convection 7-52 A steam pipe is exposed to a light winds in the atmosphere. The amount of heat loss from the steam during a certain period and the money the facility will save a year as a result of insulating the steam pipe are t
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Chapter 7 External Forced Convection Special Topic: Thermal Insulation 7-73C Thermal insulation is a material that is used primarily to provide resistance to heat flow. It differs from other kinds of insulators in that the purpose of an electrical insulat
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Chapter 7 External Forced Convection 7-99 Wind is blowing over the roof of a house. The rate of heat transfer through the roof and the cost of this heat loss for 14-h period are to be determined. Assumptions 1 Steady operating conditions exist. 2 The crit
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Chapter 8 Internal Forced ConvectionChapter 8 INTERNAL FORCED CONVECTIONGeneral Flow Analysis 8-1C Liquids are usually transported in circular pipes because pipes with a circular cross-section can withstand large pressure differences between the inside
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Chapter 8 Internal Forced Convection 8-53 Hot air enters a sheet metal duct located in a basement. The exit temperature of hot air and the rate of heat loss are to be determined. Assumptions 1 Steady flow conditions exist. 2 The inner surfaces of the duct
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Chapter 8 Internal Forced ConvectionReview Problems 8-61 Geothermal water is supplied to a city through stainless steel pipes at a specified rate. The electric power consumption and its daily cost are to be determined, and it is to be assessed if the fri
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Chapter 9 Natural ConvectionChapter 9 NATURAL CONVECTIONPhysical Mechanisms of Natural Convection 9-1C Natural convection is the mode of heat transfer that occurs between a solid and a fluid which moves under the influence of natural means. Natural conv
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Chapter 9 Natural Convection 9-32 A fluid flows through a pipe in calm ambient air. The pipe is heated electrically. The thickness of the insulation needed to reduce the losses by 85% and the money saved during 10-h are to be determined. Assumptions 1 Ste
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Chapter 9 Natural ConvectionCombined Natural and Forced Convection 9-72C In combined natural and forced convection, the natural convection is negligible when Gr / Re2 01 . Otherwise it is not. . 9-73C In assisting or transverse flows, natural convection
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Chapter 9 Natural ConvectionReview Problems 9-94E A small cylindrical resistor mounted on the lower part of a vertical circuit board. The approximate surface temperature of the resistor is to be determined. Assumptions 1 Steady operating conditions exist
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Chapter 9 Natural Convection 9-103E The components of an electronic device located in a horizontal duct of rectangular cross section is cooled by forced air. The heat transfer from the outer surfaces of the duct by natural convection and the average tempe
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Chapter 10 Boiling and CondensationChapter 10 BOILING AND CONDENSATIONBoiling Heat Transfer10-1C Boiling is the liquid-to-vapor phase change process that occurs at a solid-liquid interface when the surface is heated above the saturation temperature of
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Chapter 10 Boiling and Condensation 10-21 Water is boiled at 1 atm pressure and thus at a saturation (or boiling) temperature of Tsat = 100 C by a horizontal nickel plated copper heating element. The maximum (critical) heat flux and the temperature jump o
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Chapter 10 Boiling and CondensationCondensation Heat Transfer10-34C Condensation is a vapor-to-liquid phase change process. It occurs when the temperature of a vapor is reduced below its saturation temperature Tsat. This is usually done by bringing the
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Chapter 10 Boiling and Condensation Review Problems 10-72 Steam at a saturation temperature of Tsat = 40 C condenses on the outside of a thin horizontal tube. Heat is transferred to the cooling water that enters the tube at 25 C and exits at 35 C. The rat
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Chapter 11 Fundamentals of Thermal RadiationChapter 11 FUNDAMENTALS OF THERMAL RADIATIONElectromagnetic and Thermal Radiation11-1C Electromagnetic waves are caused by accelerated charges or changing electric currents giving rise to electric and magneti
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Chapter 11 Fundamentals of Thermal RadiationAtmospheric and Solar Radiation11-50C The solar constant represents the rate at which solar energy is incident on a surface normal to sun's rays at the outer edge of the atmosphere when the earth is at its mea
UCLA - ACCOUNTING - 120b
CHAPTER 9Inventories: Additional Valuation IssuesASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)Topics 1. Lower-of-cost-or-market. 2. Inventory accounting changes; relative sales value method; net realizable value. 3. Purchase commitments. 4. Gross profit m