Homework _5 Solutions - Chapter 4

# Homework _5 Solutions - Chapter 4 - PROBLEM 4.9 KNOWN Heat...

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PROBLEM 4.9 K NOWN: Heat generation in a buried spherical container. FIND: (a) Outer surface temperature of the container, (b) Representative isotherms and heat low lines. f SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Soil is a homogeneous medium with onstant properties. c P ROPERTIES: Table A-3 , Soil (300K): k = 0.52 W/m K. ANALYSIS: (a) From an energy balance on the container, and from the first entry in able 4.1, g qE = ± T () 12 2D qk T lD / 4 z T . π =− H ence, q 1 D/4z 500W 1 2m/40m T T 20 C+ 92.7 C W k2D 2 2 m 0.52 mK ππ −− =+ = = DD < (b) The isotherms may be viewed as spherical surfaces whose center moves downward with increasing radius. The surface of the soil is an isotherm for which the center is at z = .

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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 12 tot TT q R = w here the thermal resistance is R tot = R ins + R soil . From Equation 3.28, () ( ) 21 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 ππ == = ×⋅ AA 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 Rm Sk 2 0.52 W/m K L L = = K / W .
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Homework _5 Solutions - Chapter 4 - PROBLEM 4.9 KNOWN Heat...

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