Thermodynamics HW Solutions 187

# Thermodynamics HW Solutions 187 - heat transfer rate...

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Chapter 15 Steady Heat Conduction 3-54 A wall is to be constructed of 10-cm thick wood studs or with pairs of 5-cm thick wood studs nailed to each other. The rate of heat transfer through the solid stud and through a stud pair nailed to each other, as well as the effective conductivity of the nailed stud pair are to be determined. Assumptions 1 Heat transfer is steady since there is no indication of change with time. 2 Heat transfer can be approximated as being one-dimensional since it is predominantly in the x direction. 3 Thermal conductivities are constant. 4 The thermal contact resistance between the two layers is negligible. 4 Heat transfer by radiation is disregarded. Properties The thermal conductivities are given to be k = 0.11 W/m °C for wood studs and k = 50 W/m °C for manganese steel nails. Analysis ( a ) The heat transfer area of the stud is A = (0.1 m)(2.5 m) = 0.25 m 2 . The thermal resistance and
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Unformatted text preview: heat transfer rate through the solid stud are T 1 Q & Stud R stud T 1 T 2 L T 2 W 2.2 = ° ° = Δ = ° = ° = = C/W 636 . 3 C 8 C/W 636 . 3 ) m 25 . ( C) W/m. 11 . ( m 1 . 2 stud stud R T Q kA L R & ( b ) The thermal resistances of stud pair and nails are in parallel W 4.7 = ° ° = Δ = ° = ⎯→ ⎯ + = + = ° = − ° = = ° = ° = = = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ π = π = C/W 70 . 1 C 8 C/W 70 . 1 18 . 3 1 65 . 3 1 1 1 1 C/W 65 . 3 ) m 000628 . 25 . ( C) W/m. 11 . ( m 1 . C/W 18 . 3 ) m 000628 . ( C) W/m. 50 ( m 1 . m 000628 . 4 m) 004 . ( 50 4 50 2 2 2 2 2 stud total nails stud total stud nails nails R T Q R R R R kA L R kA L R D A & ( c ) The effective conductivity of the nailed stud pair can be determined from C W/m. 0.235 ° = ° = Δ = ⎯→ ⎯ Δ = ) m C)(0.25 8 ( m) 1 . W)( 7 . 4 ( 2 TA L Q k L T A k Q eff eff & & 3-30...
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