Thermodynamics HW Solutions 280

# Thermodynamics HW Solutions 280 - W 666 C/W 02253 C 8 23...

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Chapter 3 Steady Heat Conduction 3-169 An insulation is to be added to a wall to decrease the heat loss by 85%. The thickness of insulation and the outer surface temperature of the wall are to be determined for two different insulating materials. Assumptions 1 Heat transfer is steady. 2 Heat transfer is one-dimensional. 3 Thermal conductivities are constant. 4 Heat transfer by radiation is accounted for in the heat transfer coefficient. Properties The thermal conductivities of the plaster, brick, covering, polyurethane foam, and glass fiber are given to be 0.72 W/m °C, 0.36 W/m °C, 1.40 W/m °C, 0.025 W/m °C, 0.036 W/m °C, respectively. Analysis The surface area of the wall and the individual resistances are 2 m 8 . 16 m) 8 . 2 ( m) 6 ( = × = A C/W 02253 . 0 00350 . 0 00085 . 0 01653 . 0 00165 . 0 C/W 00350 . 0 ) m 8 . 16 ( C) . W/m 17 ( 1 1 C/W 00085 . 0 ) m 8 . 16 ( C) W/m. 4 . 1 ( m 02 . 0 C/W 01653 . 0 ) m 8 . 16 ( C) W/m. 72 . 0 ( m 20 . 0 C/W 00165 . 0 ) m 8 . 16 ( C) W/m. 36 . 0 ( m 01 . 0 conv,2 3 2 1 ins no total, 2 2 2 conv,2 o 2 3 3 covering 3 2 2 2 brick 2 2 1 1 plaster 1 ° = + + + = + + + = ° = ° = = = ° = ° = = = ° = ° = = = ° = ° = = = R R R R R A h R R A k L R R A k L R R A k L R R The rate of heat loss without the insulation is
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Unformatted text preview: W 666 C/W 02253 . C ) 8 23 ( ins no total, 2 1 = ° ° − = − = ∞ R T T Q & ( a ) The rate of heat transfer after insulation is W 9 . 99 666 15 . 15 . ins no ins = × = = Q Q & & The total thermal resistance with the foam insulation is C) W.m/ 42 . ( C/W 02253 . ) m C)(16.8 W/m. 025 . ( C/W 02253 . 4 2 4 conv,2 foam 3 2 1 total ° + ° = ° + ° = + + + + = L L R R R R R R T 1 T ∞ 2 R 2 R 3 R 1 R ins R o The thickness of insulation is determined from cm 5.4 m 0.054 = = ⎯→ ⎯ ° + ° ° − = ⎯→ ⎯ − = ∞ 4 4 total 2 1 ins C) W.m/ 42 . ( C/W 02253 . C ) 8 23 ( W 9 . 99 L L R T T Q & The outer surface temperature of the wall is determined from C 8.3 ° = ⎯→ ⎯ ° ° − = ⎯→ ⎯ − = ∞ 2 2 conv 2 2 ins C/W 00350 . C ) 8 ( W 9 . 99 T T R T T Q & 3-123...
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