problem4-10 - PROBLEM 4.10 KNOWN Temperature diameter and...

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PROBLEM 4.10 K NOWN: Temperature, diameter and burial depth of an insulated pipe. F IND: Heat loss per unit length of pipe. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction through insulation, two-dimensional through soil, (3) Constant properties, (4) Negligible oil onvection and pipe wall conduction resistances. c PROPERTIES: Table A-3 , Soil (300K): k = 0.52 W/m K; Table A-3 , Cellular glass (365K): = 0.069 W/m K. k A NALYSIS: The heat rate can be expressed as 1 2 tot T T q R = w here the thermal resistance is R tot = R ins + R soil . From Equation 3.28, ( ) ( ) 2 1 ins ins n D / D n 0.7m/0.5m 0.776m K/W R . 2 Lk 2 L 0.069 W/m K L π π = = = × A A F rom Equation 4.21 and Table 4.1, ( ) ( ) ( ) -1 -1 2 soil soil soil cosh 2z/D cosh 3/ 0.7 1 0.653 R m Sk 2 Lk 2 0.52 W/m K L L = = = = × π π K/W. H ence, ( ) ( )
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