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to kt. Substituting, the fraction of heat conducted along the copper layer and the effective thermal conductivity of the plate are determined to be FBtu/h. 56125.0)00375.05575.0()()()( FBtu/h. 00375.0ft) F)(0.15/12Btu/h.ft. 15.0(2)( FBtu/h. 5575.0ft) F)(0.03/12Btu/h.ft. 223()( epoxycoppertotal epoxy copper °=+=+= °=°= °=°= ktktkt kt kt and F.Btu/h.ft 20.4 2 °=+ °= + += ft )]12/15.0(2)12/03.0[( FBtu/h. 56125.0 t )()( epoxycopper epoxycopper t ktkt keff 99.3%==== 993.0 56125.0 5575.0 )( )( total copper copper kt kt f PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 3-102 Review Problems 3-159E Steam is produced in copper tubes by heat transferred from another fluid condensing outside the tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer of limestone is formed on the inner surface of the tube is to be determined. Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the surfaces. Properties The thermal conductivities are given to be k = 223 Btu/h\u22c5ft\u22c5°F for copper tubes and k = 1.7 Btu/h\u22c5ft\u22c5°F for limestone. T\u221e2 Rtotal, new HX T\u221e1 Analysis The total thermal resistance of the new heat exchanger is F/Btuh. 005.0 Btu/h 102 F)250350( 4 new 21 newtotal, newtotal, 21 new °=× °\u2212=\u2212=\u23af\u2192\u23af\u2212= \u221e\u221e\u221e\u221e Q TT R R TT Q & & After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be F/Btuh 00689.000189.0005.0 F/Btuh 00189.0 )ft 1(F)Btu/h.ft. 7.1(2 )49.0/5.0ln( 2 )/ln( ilimestone,newtotal,w/limetotal, 1 ilimestone, °=+=+= °=°== RRR kL rr R i \u3c0\u3c0 Rlimestone T\u221e2 Rtotal, new HX T\u221e1 27%) of decline (a F/Btuh 0.00689 F)250350( w/limetotal, 21 w/lime Btu/h 101.45 4×=° °\u2212=\u2212= \u221e\u221e R TT Q& Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal convection resistance slightly, but this effect should be negligible. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 3-103 3-160E Steam is produced in copper tubes by heat transferred from another fluid condensing outside the tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick layer of limestone is formed on the inner and outer surfaces of the tube is to be determined. Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the surfaces. Properties The thermal conductivities are given to be k = 223 Btu/h\u22c5ft\u22c5°F for copper tubes and k = 1.7 Btu/h\u22c5ft\u22c5°F for limestone. T\u221e2 Rtotal, new HX T\u221e1 Analysis The total thermal resistance of the new heat exchanger is F/Btuh. 005.0 Btu/h 102 F)250350( 4 new 21 newtotal, newtotal, 21 new °=× °\u2212=\u2212=\u23af\u2192\u23af\u2212= \u221e\u221e\u221e\u221e Q TT R R TT Q & & After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be Rlimestone, o T\u221e2 Rtotal, new HX T\u221e1 Rlimestone, i F/Btuh. 00832.000143.000189.0005.0 F/Btuh. 00143.0 )ft 1(F)Btu/h.ft. 7.1(2 )65.0/66.0ln( 2 )/ln( F/Btuh. 00189.0 )ft 1(F)Btu/h.ft. 7.1(2 )49.0/5.0ln( 2 )/ln( olimestone,ilimestone,newtotal,w/limetotal, 2 ilimestone, 1 ilimestone, °=++=++= °=°== °=°== RRRR kL rr R kL rr R o i \u3c0\u3c0 \u3c0\u3c0 40%) of decline (a F/Btuh 0.00832 F)250350( w/limetotal, 21 w/lime Btu/h 101.20 4×=° °\u2212=\u2212= \u221e\u221e R TT Q& Discussion Note that the limestone layer will change the inner surface area of the pipe and thus the internal convection resistance slightly, but this effect should be negligible. PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 3-104 3-161 A cylindrical tank filled with liquid propane at 1 atm is exposed to convection and radiation. The time it will take for the propane to evaporate completely as a result of the heat gain from the surroundings for the cases of no insulation and 5-cm thick glass wool insulation are to be determined. Assumptions 1 Heat transfer is steady. 2 Heat transfer is one-dimensional. 3 The combined heat transfer coefficient is constant and uniform over the entire surface. 4 The temperature of the thin-shelled spherical tank is said to be nearly equal to the temperature of the propane inside, and thus thermal resistance of the tank and the internal convection resistance are negligible. Properties The heat of vaporization and density of liquid propane at 1 atm are given to be 425 kJ/kg and 581 kg/m3, respectively. The thermal conductivity of glass wool insulation is given to be k = 0.038 W/m\u22c5°C. Analysis (a) If the tank is not insulated, the heat transfer rate is determined to be 222tank m 88.244/m) (1.22+m) 6(m) 2.1()4/(2 ==+= \u3c0\u3c0\u3c0\u3c0\u3c0 DDLA W787,44C)]42(30)[m 88.24)(C. W/m25()( 2221tank =°\u2212\u2212°=\u2212= \u221e\u221e TThAQ& The volume of the tank and the mass of the propane are Propane tank, -42°C kg 6.3942)m 786.6)(kg/m 581( m 786.6)m 6()m 6.0( 33 322 === === V V \u3c1 \u3c0\u3c0 m Lr The rate of vaporization of propane is kg/s 1054.0 kJ/kg 425 kJ/s 787.44 ===\u2192= fg fg h QmhmQ & &&& Rins, ends Rsins, sides Rconv, o Ts T\u221eThen the time period for the propane tank to empty becomes hours 10.4====\u394 s 413,37 kg/s 0.1054 kg 6.3942 m mt & (b) We now repeat calculations for the case of insulated tank with 5-cm thick insulation. 222 o m 16.274/m) (1.32+m) 6(m) 3.1()4/(2 ==+= \u3c0\u3c0\u3c0\u3c0\u3c0 DDLA C/W 1444.2 ]4/)m 25.1(C)[ W/m.038.0( m 05.022 C/W 05587.0 )m 6(C) W/m.038.0(2 )60/65ln( 2 )/ln( C/W 001473.0 )m 16.27(C). W/m25( 11 2ends,insulation 12 side,insulation 22oconv, °=° ×== °=°== °=°== \u3c0 \u3c0\u3c0 avg oo kA LR kL rr R Ah R Noting that the insulation on the side surface and the end surfaces are in parallel, the equivalent resistance for the insulation is determined to be C/W 05445.0 C/W 1444.2 1 C/W 05587.0 111 1 1 ends,insulationside,insulation insulation °=\u239f\u23a0 \u239e\u239c\u239d \u239b °+°=\u239f\u239f\u23a0 \u239e \u239c\u239c\u239d \u239b += \u2212\u2212 RR R Then the total thermal resistance and the heat transfer rate become C/W 05592.005445.0001473.0insulationoconv,total °=+=+= RRR W1288 C/W 0.05592 C)]42(30[ total =° °\u2212\u2212=\u2212= \u221e R TT Q s& Then the time period for the propane tank to empty becomes days 15.1==×===\u394 ===\u2192= hours 4.361s 10301.1 kg/s 0.003031 kg 6.3942 kg/s 003031.0 kJ/kg 425 kJ/s 288.1 6 m mt h QmhmQ fg fg & & &&& PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 3-105 3-162 Hot water is flowing through a 15-m section of a cast iron pipe. The pipe is exposed to cold air and surfaces in the basement, and it experiences a 3°C-temperature drop. The combined convection and radiation heat transfer coefficient at the outer surface of the pipe is to be determined. Assumptions 1 Heat transfer is steady since there is no indication of any significant change with time. 2 Heat transfer