Heat Chap03-152 - Chapter 3 Steady Heat Conduction Review...

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Chapter 3 Steady Heat Conduction Review Problems 3-152E 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 ft °F for copper tubes and k = 1.7 Btu/h ft °F for limestone. Analysis The total thermal resistance of the new heat exchanger is ( ) . Q T T R R T T Q new total,new total,new new 4 F 2 10 Btu / h h. F / Btu = -  → = - = - ° × = ° 1 2 1 2 350 250 0 005 After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be R r r kL R R R i limestone,i total,w/lime total,new limestone,i Btu / h.ft. F) ft h F / Btu h F / Btu = = ° = ° = + = + = ° ln( / ) ln( . / . ) ( . ( ) . . . . 1 2 05 0 49 2 17 1 0 00189 0 005 0 00189 0 00689 π 27%) of decline (a F/Btu h 0.00689 F ) 250 350 ( w/lime total, 2 1 w/lime Btu/h 10 1.45 4 × = ° ° - = - = R T T 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. 3-105 T 2 R total, new HX T 1 R limestone T 2 R total, new HX T 1
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Chapter 3 Steady Heat Conduction 3-153E 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 ft °F for copper tubes and k = 1.7 Btu/h ft °F for limestone. Analysis The total thermal resistance of the new heat exchanger is ( ) . Q T T R R T T Q new total,new total,new new 4 F 2 10 Btu / h h. F / Btu = -  → = - = - ° × = ° 1 2 1 2 350 250 0 005 After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate are determined to be R r r kL R r r kL R R R R i o limestone,i limestone,i total,w/lime total,new limestone,i limestone,o Btu / h.ft. F) ft h. F / Btu Btu / h.ft. F) ft h. F / Btu h. F / Btu = = ° = ° = = ° = ° = + + = + + = ° ln( / ) ln( . / . ) ( . ( ) .
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Heat Chap03-152 - Chapter 3 Steady Heat Conduction Review...

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